The {@code BigDecimal} class provides operations for + * arithmetic, scale manipulation, rounding, comparison, hashing, and + * format conversion. The {@link #toString} method provides a + * canonical representation of a {@code BigDecimal}. + * + *
The {@code BigDecimal} class gives its user complete control + * over rounding behavior. If no rounding mode is specified and the + * exact result cannot be represented, an exception is thrown; + * otherwise, calculations can be carried out to a chosen precision + * and rounding mode by supplying an appropriate {@link MathContext} + * object to the operation. In either case, eight rounding + * modes are provided for the control of rounding. Using the + * integer fields in this class (such as {@link #ROUND_HALF_UP}) to + * represent rounding mode is largely obsolete; the enumeration values + * of the {@code RoundingMode} {@code enum}, (such as {@link + * RoundingMode#HALF_UP}) should be used instead. + * + *
When a {@code MathContext} object is supplied with a precision + * setting of 0 (for example, {@link MathContext#UNLIMITED}), + * arithmetic operations are exact, as are the arithmetic methods + * which take no {@code MathContext} object. (This is the only + * behavior that was supported in releases prior to 5.) As a + * corollary of computing the exact result, the rounding mode setting + * of a {@code MathContext} object with a precision setting of 0 is + * not used and thus irrelevant. In the case of divide, the exact + * quotient could have an infinitely long decimal expansion; for + * example, 1 divided by 3. If the quotient has a nonterminating + * decimal expansion and the operation is specified to return an exact + * result, an {@code ArithmeticException} is thrown. Otherwise, the + * exact result of the division is returned, as done for other + * operations. + * + *
When the precision setting is not 0, the rules of + * {@code BigDecimal} arithmetic are broadly compatible with selected + * modes of operation of the arithmetic defined in ANSI X3.274-1996 + * and ANSI X3.274-1996/AM 1-2000 (section 7.4). Unlike those + * standards, {@code BigDecimal} includes many rounding modes, which + * were mandatory for division in {@code BigDecimal} releases prior + * to 5. Any conflicts between these ANSI standards and the + * {@code BigDecimal} specification are resolved in favor of + * {@code BigDecimal}. + * + *
Since the same numerical value can have different + * representations (with different scales), the rules of arithmetic + * and rounding must specify both the numerical result and the scale + * used in the result's representation. + * + * + *
In general the rounding modes and precision setting determine + * how operations return results with a limited number of digits when + * the exact result has more digits (perhaps infinitely many in the + * case of division) than the number of digits returned. + * + * First, the + * total number of digits to return is specified by the + * {@code MathContext}'s {@code precision} setting; this determines + * the result's precision. The digit count starts from the + * leftmost nonzero digit of the exact result. The rounding mode + * determines how any discarded trailing digits affect the returned + * result. + * + *
For all arithmetic operators , the operation is carried out as + * though an exact intermediate result were first calculated and then + * rounded to the number of digits specified by the precision setting + * (if necessary), using the selected rounding mode. If the exact + * result is not returned, some digit positions of the exact result + * are discarded. When rounding increases the magnitude of the + * returned result, it is possible for a new digit position to be + * created by a carry propagating to a leading {@literal "9"} digit. + * For example, rounding the value 999.9 to three digits rounding up + * would be numerically equal to one thousand, represented as + * 100×101. In such cases, the new {@literal "1"} is + * the leading digit position of the returned result. + * + *
Besides a logical exact result, each arithmetic operation has a + * preferred scale for representing a result. The preferred + * scale for each operation is listed in the table below. + * + *
| Operation | Preferred Scale of Result |
|---|---|
| Add | max(addend.scale(), augend.scale()) | + *
| Subtract | max(minuend.scale(), subtrahend.scale()) | + *
| Multiply | multiplier.scale() + multiplicand.scale() | + *
| Divide | dividend.scale() - divisor.scale() | + *
Before rounding, the scale of the logical exact intermediate
+ * result is the preferred scale for that operation. If the exact
+ * numerical result cannot be represented in {@code precision}
+ * digits, rounding selects the set of digits to return and the scale
+ * of the result is reduced from the scale of the intermediate result
+ * to the least scale which can represent the {@code precision}
+ * digits actually returned. If the exact result can be represented
+ * with at most {@code precision} digits, the representation
+ * of the result with the scale closest to the preferred scale is
+ * returned. In particular, an exactly representable quotient may be
+ * represented in fewer than {@code precision} digits by removing
+ * trailing zeros and decreasing the scale. For example, rounding to
+ * three digits using the {@linkplain RoundingMode#FLOOR floor}
+ * rounding mode,
+ *
+ * {@code 19/100 = 0.19 // integer=19, scale=2}
+ *
+ * but
+ *
+ * {@code 21/110 = 0.190 // integer=190, scale=3}
+ *
+ *
Note that for add, subtract, and multiply, the reduction in + * scale will equal the number of digit positions of the exact result + * which are discarded. If the rounding causes a carry propagation to + * create a new high-order digit position, an additional digit of the + * result is discarded than when no new digit position is created. + * + *
Other methods may have slightly different rounding semantics. + * For example, the result of the {@code pow} method using the + * {@linkplain #pow(int, MathContext) specified algorithm} can + * occasionally differ from the rounded mathematical result by more + * than one unit in the last place, one {@linkplain #ulp() ulp}. + * + *
Two types of operations are provided for manipulating the scale + * of a {@code BigDecimal}: scaling/rounding operations and decimal + * point motion operations. Scaling/rounding operations ({@link + * #setScale setScale} and {@link #round round}) return a + * {@code BigDecimal} whose value is approximately (or exactly) equal + * to that of the operand, but whose scale or precision is the + * specified value; that is, they increase or decrease the precision + * of the stored number with minimal effect on its value. Decimal + * point motion operations ({@link #movePointLeft movePointLeft} and + * {@link #movePointRight movePointRight}) return a + * {@code BigDecimal} created from the operand by moving the decimal + * point a specified distance in the specified direction. + * + *
For the sake of brevity and clarity, pseudo-code is used + * throughout the descriptions of {@code BigDecimal} methods. The + * pseudo-code expression {@code (i + j)} is shorthand for "a + * {@code BigDecimal} whose value is that of the {@code BigDecimal} + * {@code i} added to that of the {@code BigDecimal} + * {@code j}." The pseudo-code expression {@code (i == j)} is + * shorthand for "{@code true} if and only if the + * {@code BigDecimal} {@code i} represents the same value as the + * {@code BigDecimal} {@code j}." Other pseudo-code expressions + * are interpreted similarly. Square brackets are used to represent + * the particular {@code BigInteger} and scale pair defining a + * {@code BigDecimal} value; for example [19, 2] is the + * {@code BigDecimal} numerically equal to 0.19 having a scale of 2. + * + *
Note: care should be exercised if {@code BigDecimal} objects + * are used as keys in a {@link java.util.SortedMap SortedMap} or + * elements in a {@link java.util.SortedSet SortedSet} since + * {@code BigDecimal}'s natural ordering is inconsistent + * with equals. See {@link Comparable}, {@link + * java.util.SortedMap} or {@link java.util.SortedSet} for more + * information. + * + *
All methods and constructors for this class throw
+ * {@code NullPointerException} when passed a {@code null} object
+ * reference for any input parameter.
+ *
+ * @see BigInteger
+ * @see MathContext
+ * @see RoundingMode
+ * @see java.util.SortedMap
+ * @see java.util.SortedSet
+ * @author Josh Bloch
+ * @author Mike Cowlishaw
+ * @author Joseph D. Darcy
+ */
+public class BigDecimal extends Number implements Comparable Note that if the sequence of characters is already available
+ * within a character array, using this constructor is faster than
+ * converting the {@code char} array to string and using the
+ * {@code BigDecimal(String)} constructor .
+ *
+ * @param in {@code char} array that is the source of characters.
+ * @param offset first character in the array to inspect.
+ * @param len number of characters to consider.
+ * @throws NumberFormatException if {@code in} is not a valid
+ * representation of a {@code BigDecimal} or the defined subarray
+ * is not wholly within {@code in}.
+ * @since 1.5
+ */
+ public BigDecimal(char[] in, int offset, int len) {
+ // protect against huge length.
+ if (offset+len > in.length || offset < 0)
+ throw new NumberFormatException();
+ // This is the primary string to BigDecimal constructor; all
+ // incoming strings end up here; it uses explicit (inline)
+ // parsing for speed and generates at most one intermediate
+ // (temporary) object (a char[] array) for non-compact case.
+
+ // Use locals for all fields values until completion
+ int prec = 0; // record precision value
+ int scl = 0; // record scale value
+ long rs = 0; // the compact value in long
+ BigInteger rb = null; // the inflated value in BigInteger
+
+ // use array bounds checking to handle too-long, len == 0,
+ // bad offset, etc.
+ try {
+ // handle the sign
+ boolean isneg = false; // assume positive
+ if (in[offset] == '-') {
+ isneg = true; // leading minus means negative
+ offset++;
+ len--;
+ } else if (in[offset] == '+') { // leading + allowed
+ offset++;
+ len--;
+ }
+
+ // should now be at numeric part of the significand
+ boolean dot = false; // true when there is a '.'
+ int cfirst = offset; // record start of integer
+ long exp = 0; // exponent
+ char c; // current character
+
+ boolean isCompact = (len <= MAX_COMPACT_DIGITS);
+ // integer significand array & idx is the index to it. The array
+ // is ONLY used when we can't use a compact representation.
+ char coeff[] = isCompact ? null : new char[len];
+ int idx = 0;
+
+ for (; len > 0; offset++, len--) {
+ c = in[offset];
+ // have digit
+ if ((c >= '0' && c <= '9') || Character.isDigit(c)) {
+ // First compact case, we need not to preserve the character
+ // and we can just compute the value in place.
+ if (isCompact) {
+ int digit = Character.digit(c, 10);
+ if (digit == 0) {
+ if (prec == 0)
+ prec = 1;
+ else if (rs != 0) {
+ rs *= 10;
+ ++prec;
+ } // else digit is a redundant leading zero
+ } else {
+ if (prec != 1 || rs != 0)
+ ++prec; // prec unchanged if preceded by 0s
+ rs = rs * 10 + digit;
+ }
+ } else { // the unscaled value is likely a BigInteger object.
+ if (c == '0' || Character.digit(c, 10) == 0) {
+ if (prec == 0) {
+ coeff[idx] = c;
+ prec = 1;
+ } else if (idx != 0) {
+ coeff[idx++] = c;
+ ++prec;
+ } // else c must be a redundant leading zero
+ } else {
+ if (prec != 1 || idx != 0)
+ ++prec; // prec unchanged if preceded by 0s
+ coeff[idx++] = c;
+ }
+ }
+ if (dot)
+ ++scl;
+ continue;
+ }
+ // have dot
+ if (c == '.') {
+ // have dot
+ if (dot) // two dots
+ throw new NumberFormatException();
+ dot = true;
+ continue;
+ }
+ // exponent expected
+ if ((c != 'e') && (c != 'E'))
+ throw new NumberFormatException();
+ offset++;
+ c = in[offset];
+ len--;
+ boolean negexp = (c == '-');
+ // optional sign
+ if (negexp || c == '+') {
+ offset++;
+ c = in[offset];
+ len--;
+ }
+ if (len <= 0) // no exponent digits
+ throw new NumberFormatException();
+ // skip leading zeros in the exponent
+ while (len > 10 && Character.digit(c, 10) == 0) {
+ offset++;
+ c = in[offset];
+ len--;
+ }
+ if (len > 10) // too many nonzero exponent digits
+ throw new NumberFormatException();
+ // c now holds first digit of exponent
+ for (;; len--) {
+ int v;
+ if (c >= '0' && c <= '9') {
+ v = c - '0';
+ } else {
+ v = Character.digit(c, 10);
+ if (v < 0) // not a digit
+ throw new NumberFormatException();
+ }
+ exp = exp * 10 + v;
+ if (len == 1)
+ break; // that was final character
+ offset++;
+ c = in[offset];
+ }
+ if (negexp) // apply sign
+ exp = -exp;
+ // Next test is required for backwards compatibility
+ if ((int)exp != exp) // overflow
+ throw new NumberFormatException();
+ break; // [saves a test]
+ }
+ // here when no characters left
+ if (prec == 0) // no digits found
+ throw new NumberFormatException();
+
+ // Adjust scale if exp is not zero.
+ if (exp != 0) { // had significant exponent
+ // Can't call checkScale which relies on proper fields value
+ long adjustedScale = scl - exp;
+ if (adjustedScale > Integer.MAX_VALUE ||
+ adjustedScale < Integer.MIN_VALUE)
+ throw new NumberFormatException("Scale out of range.");
+ scl = (int)adjustedScale;
+ }
+
+ // Remove leading zeros from precision (digits count)
+ if (isCompact) {
+ rs = isneg ? -rs : rs;
+ } else {
+ char quick[];
+ if (!isneg) {
+ quick = (coeff.length != prec) ?
+ Arrays.copyOf(coeff, prec) : coeff;
+ } else {
+ quick = new char[prec + 1];
+ quick[0] = '-';
+ System.arraycopy(coeff, 0, quick, 1, prec);
+ }
+ rb = new BigInteger(quick);
+ rs = compactValFor(rb);
+ }
+ } catch (ArrayIndexOutOfBoundsException e) {
+ throw new NumberFormatException();
+ } catch (NegativeArraySizeException e) {
+ throw new NumberFormatException();
+ }
+ this.scale = scl;
+ this.precision = prec;
+ this.intCompact = rs;
+ this.intVal = (rs != INFLATED) ? null : rb;
+ }
+
+ /**
+ * Translates a character array representation of a
+ * {@code BigDecimal} into a {@code BigDecimal}, accepting the
+ * same sequence of characters as the {@link #BigDecimal(String)}
+ * constructor, while allowing a sub-array to be specified and
+ * with rounding according to the context settings.
+ *
+ * Note that if the sequence of characters is already available
+ * within a character array, using this constructor is faster than
+ * converting the {@code char} array to string and using the
+ * {@code BigDecimal(String)} constructor .
+ *
+ * @param in {@code char} array that is the source of characters.
+ * @param offset first character in the array to inspect.
+ * @param len number of characters to consider..
+ * @param mc the context to use.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @throws NumberFormatException if {@code in} is not a valid
+ * representation of a {@code BigDecimal} or the defined subarray
+ * is not wholly within {@code in}.
+ * @since 1.5
+ */
+ public BigDecimal(char[] in, int offset, int len, MathContext mc) {
+ this(in, offset, len);
+ if (mc.precision > 0)
+ roundThis(mc);
+ }
+
+ /**
+ * Translates a character array representation of a
+ * {@code BigDecimal} into a {@code BigDecimal}, accepting the
+ * same sequence of characters as the {@link #BigDecimal(String)}
+ * constructor.
+ *
+ * Note that if the sequence of characters is already available
+ * as a character array, using this constructor is faster than
+ * converting the {@code char} array to string and using the
+ * {@code BigDecimal(String)} constructor .
+ *
+ * @param in {@code char} array that is the source of characters.
+ * @throws NumberFormatException if {@code in} is not a valid
+ * representation of a {@code BigDecimal}.
+ * @since 1.5
+ */
+ public BigDecimal(char[] in) {
+ this(in, 0, in.length);
+ }
+
+ /**
+ * Translates a character array representation of a
+ * {@code BigDecimal} into a {@code BigDecimal}, accepting the
+ * same sequence of characters as the {@link #BigDecimal(String)}
+ * constructor and with rounding according to the context
+ * settings.
+ *
+ * Note that if the sequence of characters is already available
+ * as a character array, using this constructor is faster than
+ * converting the {@code char} array to string and using the
+ * {@code BigDecimal(String)} constructor .
+ *
+ * @param in {@code char} array that is the source of characters.
+ * @param mc the context to use.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @throws NumberFormatException if {@code in} is not a valid
+ * representation of a {@code BigDecimal}.
+ * @since 1.5
+ */
+ public BigDecimal(char[] in, MathContext mc) {
+ this(in, 0, in.length, mc);
+ }
+
+ /**
+ * Translates the string representation of a {@code BigDecimal}
+ * into a {@code BigDecimal}. The string representation consists
+ * of an optional sign, {@code '+'} ( '\u002B') or
+ * {@code '-'} ('\u002D'), followed by a sequence of
+ * zero or more decimal digits ("the integer"), optionally
+ * followed by a fraction, optionally followed by an exponent.
+ *
+ * The fraction consists of a decimal point followed by zero
+ * or more decimal digits. The string must contain at least one
+ * digit in either the integer or the fraction. The number formed
+ * by the sign, the integer and the fraction is referred to as the
+ * significand.
+ *
+ * The exponent consists of the character {@code 'e'}
+ * ('\u0065') or {@code 'E'} ('\u0045')
+ * followed by one or more decimal digits. The value of the
+ * exponent must lie between -{@link Integer#MAX_VALUE} ({@link
+ * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive.
+ *
+ * More formally, the strings this constructor accepts are
+ * described by the following grammar:
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ * The scale of the returned {@code BigDecimal} will be the
+ * number of digits in the fraction, or zero if the string
+ * contains no decimal point, subject to adjustment for any
+ * exponent; if the string contains an exponent, the exponent is
+ * subtracted from the scale. The value of the resulting scale
+ * must lie between {@code Integer.MIN_VALUE} and
+ * {@code Integer.MAX_VALUE}, inclusive.
+ *
+ * The character-to-digit mapping is provided by {@link
+ * java.lang.Character#digit} set to convert to radix 10. The
+ * String may not contain any extraneous characters (whitespace,
+ * for example).
+ *
+ * Examples: Note: For values other than {@code float} and
+ * {@code double} NaN and ±Infinity, this constructor is
+ * compatible with the values returned by {@link Float#toString}
+ * and {@link Double#toString}. This is generally the preferred
+ * way to convert a {@code float} or {@code double} into a
+ * BigDecimal, as it doesn't suffer from the unpredictability of
+ * the {@link #BigDecimal(double)} constructor.
+ *
+ * @param val String representation of {@code BigDecimal}.
+ *
+ * @throws NumberFormatException if {@code val} is not a valid
+ * representation of a {@code BigDecimal}.
+ */
+ public BigDecimal(String val) {
+ this(val.toCharArray(), 0, val.length());
+ }
+
+ /**
+ * Translates the string representation of a {@code BigDecimal}
+ * into a {@code BigDecimal}, accepting the same strings as the
+ * {@link #BigDecimal(String)} constructor, with rounding
+ * according to the context settings.
+ *
+ * @param val string representation of a {@code BigDecimal}.
+ * @param mc the context to use.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @throws NumberFormatException if {@code val} is not a valid
+ * representation of a BigDecimal.
+ * @since 1.5
+ */
+ public BigDecimal(String val, MathContext mc) {
+ this(val.toCharArray(), 0, val.length());
+ if (mc.precision > 0)
+ roundThis(mc);
+ }
+
+ /**
+ * Translates a {@code double} into a {@code BigDecimal} which
+ * is the exact decimal representation of the {@code double}'s
+ * binary floating-point value. The scale of the returned
+ * {@code BigDecimal} is the smallest value such that
+ * (10scale × val) is an integer.
+ *
+ * Notes:
+ * The results of this constructor can be somewhat unpredictable
+ * and its use is generally not recommended; see the notes under
+ * the {@link #BigDecimal(double)} constructor.
+ *
+ * @param val {@code double} value to be converted to
+ * {@code BigDecimal}.
+ * @param mc the context to use.
+ * @throws ArithmeticException if the result is inexact but the
+ * RoundingMode is UNNECESSARY.
+ * @throws NumberFormatException if {@code val} is infinite or NaN.
+ * @since 1.5
+ */
+ public BigDecimal(double val, MathContext mc) {
+ this(val);
+ if (mc.precision > 0)
+ roundThis(mc);
+ }
+
+ /**
+ * Translates a {@code BigInteger} into a {@code BigDecimal}.
+ * The scale of the {@code BigDecimal} is zero.
+ *
+ * @param val {@code BigInteger} value to be converted to
+ * {@code BigDecimal}.
+ */
+ public BigDecimal(BigInteger val) {
+ intCompact = compactValFor(val);
+ intVal = (intCompact != INFLATED) ? null : val;
+ }
+
+ /**
+ * Translates a {@code BigInteger} into a {@code BigDecimal}
+ * rounding according to the context settings. The scale of the
+ * {@code BigDecimal} is zero.
+ *
+ * @param val {@code BigInteger} value to be converted to
+ * {@code BigDecimal}.
+ * @param mc the context to use.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @since 1.5
+ */
+ public BigDecimal(BigInteger val, MathContext mc) {
+ this(val);
+ if (mc.precision > 0)
+ roundThis(mc);
+ }
+
+ /**
+ * Translates a {@code BigInteger} unscaled value and an
+ * {@code int} scale into a {@code BigDecimal}. The value of
+ * the {@code BigDecimal} is
+ * (unscaledVal × 10-scale).
+ *
+ * @param unscaledVal unscaled value of the {@code BigDecimal}.
+ * @param scale scale of the {@code BigDecimal}.
+ */
+ public BigDecimal(BigInteger unscaledVal, int scale) {
+ // Negative scales are now allowed
+ this(unscaledVal);
+ this.scale = scale;
+ }
+
+ /**
+ * Translates a {@code BigInteger} unscaled value and an
+ * {@code int} scale into a {@code BigDecimal}, with rounding
+ * according to the context settings. The value of the
+ * {@code BigDecimal} is (unscaledVal ×
+ * 10-scale), rounded according to the
+ * {@code precision} and rounding mode settings.
+ *
+ * @param unscaledVal unscaled value of the {@code BigDecimal}.
+ * @param scale scale of the {@code BigDecimal}.
+ * @param mc the context to use.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @since 1.5
+ */
+ public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) {
+ this(unscaledVal);
+ this.scale = scale;
+ if (mc.precision > 0)
+ roundThis(mc);
+ }
+
+ /**
+ * Translates an {@code int} into a {@code BigDecimal}. The
+ * scale of the {@code BigDecimal} is zero.
+ *
+ * @param val {@code int} value to be converted to
+ * {@code BigDecimal}.
+ * @since 1.5
+ */
+ public BigDecimal(int val) {
+ intCompact = val;
+ }
+
+ /**
+ * Translates an {@code int} into a {@code BigDecimal}, with
+ * rounding according to the context settings. The scale of the
+ * {@code BigDecimal}, before any rounding, is zero.
+ *
+ * @param val {@code int} value to be converted to {@code BigDecimal}.
+ * @param mc the context to use.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @since 1.5
+ */
+ public BigDecimal(int val, MathContext mc) {
+ intCompact = val;
+ if (mc.precision > 0)
+ roundThis(mc);
+ }
+
+ /**
+ * Translates a {@code long} into a {@code BigDecimal}. The
+ * scale of the {@code BigDecimal} is zero.
+ *
+ * @param val {@code long} value to be converted to {@code BigDecimal}.
+ * @since 1.5
+ */
+ public BigDecimal(long val) {
+ this.intCompact = val;
+ this.intVal = (val == INFLATED) ? BigInteger.valueOf(val) : null;
+ }
+
+ /**
+ * Translates a {@code long} into a {@code BigDecimal}, with
+ * rounding according to the context settings. The scale of the
+ * {@code BigDecimal}, before any rounding, is zero.
+ *
+ * @param val {@code long} value to be converted to {@code BigDecimal}.
+ * @param mc the context to use.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @since 1.5
+ */
+ public BigDecimal(long val, MathContext mc) {
+ this(val);
+ if (mc.precision > 0)
+ roundThis(mc);
+ }
+
+ // Static Factory Methods
+
+ /**
+ * Translates a {@code long} unscaled value and an
+ * {@code int} scale into a {@code BigDecimal}. This
+ * {@literal "static factory method"} is provided in preference to
+ * a ({@code long}, {@code int}) constructor because it
+ * allows for reuse of frequently used {@code BigDecimal} values..
+ *
+ * @param unscaledVal unscaled value of the {@code BigDecimal}.
+ * @param scale scale of the {@code BigDecimal}.
+ * @return a {@code BigDecimal} whose value is
+ * (unscaledVal × 10-scale).
+ */
+ public static BigDecimal valueOf(long unscaledVal, int scale) {
+ if (scale == 0)
+ return valueOf(unscaledVal);
+ else if (unscaledVal == 0) {
+ if (scale > 0 && scale < ZERO_SCALED_BY.length)
+ return ZERO_SCALED_BY[scale];
+ else
+ return new BigDecimal(BigInteger.ZERO, 0, scale, 1);
+ }
+ return new BigDecimal(unscaledVal == INFLATED ?
+ BigInteger.valueOf(unscaledVal) : null,
+ unscaledVal, scale, 0);
+ }
+
+ /**
+ * Translates a {@code long} value into a {@code BigDecimal}
+ * with a scale of zero. This {@literal "static factory method"}
+ * is provided in preference to a ({@code long}) constructor
+ * because it allows for reuse of frequently used
+ * {@code BigDecimal} values.
+ *
+ * @param val value of the {@code BigDecimal}.
+ * @return a {@code BigDecimal} whose value is {@code val}.
+ */
+ public static BigDecimal valueOf(long val) {
+ if (val >= 0 && val < zeroThroughTen.length)
+ return zeroThroughTen[(int)val];
+ else if (val != INFLATED)
+ return new BigDecimal(null, val, 0, 0);
+ return new BigDecimal(BigInteger.valueOf(val), val, 0, 0);
+ }
+
+ /**
+ * Translates a {@code double} into a {@code BigDecimal}, using
+ * the {@code double}'s canonical string representation provided
+ * by the {@link Double#toString(double)} method.
+ *
+ * Note: This is generally the preferred way to convert
+ * a {@code double} (or {@code float}) into a
+ * {@code BigDecimal}, as the value returned is equal to that
+ * resulting from constructing a {@code BigDecimal} from the
+ * result of using {@link Double#toString(double)}.
+ *
+ * @param val {@code double} to convert to a {@code BigDecimal}.
+ * @return a {@code BigDecimal} whose value is equal to or approximately
+ * equal to the value of {@code val}.
+ * @throws NumberFormatException if {@code val} is infinite or NaN.
+ * @since 1.5
+ */
+ public static BigDecimal valueOf(double val) {
+ // Reminder: a zero double returns '0.0', so we cannot fastpath
+ // to use the constant ZERO. This might be important enough to
+ // justify a factory approach, a cache, or a few private
+ // constants, later.
+ return new BigDecimal(Double.toString(val));
+ }
+
+ // Arithmetic Operations
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this +
+ * augend)}, and whose scale is {@code max(this.scale(),
+ * augend.scale())}.
+ *
+ * @param augend value to be added to this {@code BigDecimal}.
+ * @return {@code this + augend}
+ */
+ public BigDecimal add(BigDecimal augend) {
+ long xs = this.intCompact;
+ long ys = augend.intCompact;
+ BigInteger fst = (xs != INFLATED) ? null : this.intVal;
+ BigInteger snd = (ys != INFLATED) ? null : augend.intVal;
+ int rscale = this.scale;
+
+ long sdiff = (long)rscale - augend.scale;
+ if (sdiff != 0) {
+ if (sdiff < 0) {
+ int raise = checkScale(-sdiff);
+ rscale = augend.scale;
+ if (xs == INFLATED ||
+ (xs = longMultiplyPowerTen(xs, raise)) == INFLATED)
+ fst = bigMultiplyPowerTen(raise);
+ } else {
+ int raise = augend.checkScale(sdiff);
+ if (ys == INFLATED ||
+ (ys = longMultiplyPowerTen(ys, raise)) == INFLATED)
+ snd = augend.bigMultiplyPowerTen(raise);
+ }
+ }
+ if (xs != INFLATED && ys != INFLATED) {
+ long sum = xs + ys;
+ // See "Hacker's Delight" section 2-12 for explanation of
+ // the overflow test.
+ if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) // not overflowed
+ return BigDecimal.valueOf(sum, rscale);
+ }
+ if (fst == null)
+ fst = BigInteger.valueOf(xs);
+ if (snd == null)
+ snd = BigInteger.valueOf(ys);
+ BigInteger sum = fst.add(snd);
+ return (fst.signum == snd.signum) ?
+ new BigDecimal(sum, INFLATED, rscale, 0) :
+ new BigDecimal(sum, rscale);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this + augend)},
+ * with rounding according to the context settings.
+ *
+ * If either number is zero and the precision setting is nonzero then
+ * the other number, rounded if necessary, is used as the result.
+ *
+ * @param augend value to be added to this {@code BigDecimal}.
+ * @param mc the context to use.
+ * @return {@code this + augend}, rounded as necessary.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @since 1.5
+ */
+ public BigDecimal add(BigDecimal augend, MathContext mc) {
+ if (mc.precision == 0)
+ return add(augend);
+ BigDecimal lhs = this;
+
+ // Could optimize if values are compact
+ this.inflate();
+ augend.inflate();
+
+ // If either number is zero then the other number, rounded and
+ // scaled if necessary, is used as the result.
+ {
+ boolean lhsIsZero = lhs.signum() == 0;
+ boolean augendIsZero = augend.signum() == 0;
+
+ if (lhsIsZero || augendIsZero) {
+ int preferredScale = Math.max(lhs.scale(), augend.scale());
+ BigDecimal result;
+
+ // Could use a factory for zero instead of a new object
+ if (lhsIsZero && augendIsZero)
+ return new BigDecimal(BigInteger.ZERO, 0, preferredScale, 0);
+
+ result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc);
+
+ if (result.scale() == preferredScale)
+ return result;
+ else if (result.scale() > preferredScale) {
+ BigDecimal scaledResult =
+ new BigDecimal(result.intVal, result.intCompact,
+ result.scale, 0);
+ scaledResult.stripZerosToMatchScale(preferredScale);
+ return scaledResult;
+ } else { // result.scale < preferredScale
+ int precisionDiff = mc.precision - result.precision();
+ int scaleDiff = preferredScale - result.scale();
+
+ if (precisionDiff >= scaleDiff)
+ return result.setScale(preferredScale); // can achieve target scale
+ else
+ return result.setScale(result.scale() + precisionDiff);
+ }
+ }
+ }
+
+ long padding = (long)lhs.scale - augend.scale;
+ if (padding != 0) { // scales differ; alignment needed
+ BigDecimal arg[] = preAlign(lhs, augend, padding, mc);
+ matchScale(arg);
+ lhs = arg[0];
+ augend = arg[1];
+ }
+
+ BigDecimal d = new BigDecimal(lhs.inflate().add(augend.inflate()),
+ lhs.scale);
+ return doRound(d, mc);
+ }
+
+ /**
+ * Returns an array of length two, the sum of whose entries is
+ * equal to the rounded sum of the {@code BigDecimal} arguments.
+ *
+ * If the digit positions of the arguments have a sufficient
+ * gap between them, the value smaller in magnitude can be
+ * condensed into a {@literal "sticky bit"} and the end result will
+ * round the same way if the precision of the final
+ * result does not include the high order digit of the small
+ * magnitude operand.
+ *
+ * Note that while strictly speaking this is an optimization,
+ * it makes a much wider range of additions practical.
+ *
+ * This corresponds to a pre-shift operation in a fixed
+ * precision floating-point adder; this method is complicated by
+ * variable precision of the result as determined by the
+ * MathContext. A more nuanced operation could implement a
+ * {@literal "right shift"} on the smaller magnitude operand so
+ * that the number of digits of the smaller operand could be
+ * reduced even though the significands partially overlapped.
+ */
+ private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend,
+ long padding, MathContext mc) {
+ assert padding != 0;
+ BigDecimal big;
+ BigDecimal small;
+
+ if (padding < 0) { // lhs is big; augend is small
+ big = lhs;
+ small = augend;
+ } else { // lhs is small; augend is big
+ big = augend;
+ small = lhs;
+ }
+
+ /*
+ * This is the estimated scale of an ulp of the result; it
+ * assumes that the result doesn't have a carry-out on a true
+ * add (e.g. 999 + 1 => 1000) or any subtractive cancellation
+ * on borrowing (e.g. 100 - 1.2 => 98.8)
+ */
+ long estResultUlpScale = (long)big.scale - big.precision() + mc.precision;
+
+ /*
+ * The low-order digit position of big is big.scale(). This
+ * is true regardless of whether big has a positive or
+ * negative scale. The high-order digit position of small is
+ * small.scale - (small.precision() - 1). To do the full
+ * condensation, the digit positions of big and small must be
+ * disjoint *and* the digit positions of small should not be
+ * directly visible in the result.
+ */
+ long smallHighDigitPos = (long)small.scale - small.precision() + 1;
+ if (smallHighDigitPos > big.scale + 2 && // big and small disjoint
+ smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible
+ small = BigDecimal.valueOf(small.signum(),
+ this.checkScale(Math.max(big.scale, estResultUlpScale) + 3));
+ }
+
+ // Since addition is symmetric, preserving input order in
+ // returned operands doesn't matter
+ BigDecimal[] result = {big, small};
+ return result;
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this -
+ * subtrahend)}, and whose scale is {@code max(this.scale(),
+ * subtrahend.scale())}.
+ *
+ * @param subtrahend value to be subtracted from this {@code BigDecimal}.
+ * @return {@code this - subtrahend}
+ */
+ public BigDecimal subtract(BigDecimal subtrahend) {
+ return add(subtrahend.negate());
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)},
+ * with rounding according to the context settings.
+ *
+ * If {@code subtrahend} is zero then this, rounded if necessary, is used as the
+ * result. If this is zero then the result is {@code subtrahend.negate(mc)}.
+ *
+ * @param subtrahend value to be subtracted from this {@code BigDecimal}.
+ * @param mc the context to use.
+ * @return {@code this - subtrahend}, rounded as necessary.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @since 1.5
+ */
+ public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) {
+ BigDecimal nsubtrahend = subtrahend.negate();
+ if (mc.precision == 0)
+ return add(nsubtrahend);
+ // share the special rounding code in add()
+ return add(nsubtrahend, mc);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is (this ×
+ * multiplicand), and whose scale is {@code (this.scale() +
+ * multiplicand.scale())}.
+ *
+ * @param multiplicand value to be multiplied by this {@code BigDecimal}.
+ * @return {@code this * multiplicand}
+ */
+ public BigDecimal multiply(BigDecimal multiplicand) {
+ long x = this.intCompact;
+ long y = multiplicand.intCompact;
+ int productScale = checkScale((long)scale + multiplicand.scale);
+
+ // Might be able to do a more clever check incorporating the
+ // inflated check into the overflow computation.
+ if (x != INFLATED && y != INFLATED) {
+ /*
+ * If the product is not an overflowed value, continue
+ * to use the compact representation. if either of x or y
+ * is INFLATED, the product should also be regarded as
+ * an overflow. Before using the overflow test suggested in
+ * "Hacker's Delight" section 2-12, we perform quick checks
+ * using the precision information to see whether the overflow
+ * would occur since division is expensive on most CPUs.
+ */
+ long product = x * y;
+ long prec = this.precision() + multiplicand.precision();
+ if (prec < 19 || (prec < 21 && (y == 0 || product / y == x)))
+ return BigDecimal.valueOf(product, productScale);
+ return new BigDecimal(BigInteger.valueOf(x).multiply(y), INFLATED,
+ productScale, 0);
+ }
+ BigInteger rb;
+ if (x == INFLATED && y == INFLATED)
+ rb = this.intVal.multiply(multiplicand.intVal);
+ else if (x != INFLATED)
+ rb = multiplicand.intVal.multiply(x);
+ else
+ rb = this.intVal.multiply(y);
+ return new BigDecimal(rb, INFLATED, productScale, 0);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is (this ×
+ * multiplicand), with rounding according to the context settings.
+ *
+ * @param multiplicand value to be multiplied by this {@code BigDecimal}.
+ * @param mc the context to use.
+ * @return {@code this * multiplicand}, rounded as necessary.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @since 1.5
+ */
+ public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) {
+ if (mc.precision == 0)
+ return multiply(multiplicand);
+ return doRound(this.multiply(multiplicand), mc);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this /
+ * divisor)}, and whose scale is as specified. If rounding must
+ * be performed to generate a result with the specified scale, the
+ * specified rounding mode is applied.
+ *
+ * The new {@link #divide(BigDecimal, int, RoundingMode)} method
+ * should be used in preference to this legacy method.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @param scale scale of the {@code BigDecimal} quotient to be returned.
+ * @param roundingMode rounding mode to apply.
+ * @return {@code this / divisor}
+ * @throws ArithmeticException if {@code divisor} is zero,
+ * {@code roundingMode==ROUND_UNNECESSARY} and
+ * the specified scale is insufficient to represent the result
+ * of the division exactly.
+ * @throws IllegalArgumentException if {@code roundingMode} does not
+ * represent a valid rounding mode.
+ * @see #ROUND_UP
+ * @see #ROUND_DOWN
+ * @see #ROUND_CEILING
+ * @see #ROUND_FLOOR
+ * @see #ROUND_HALF_UP
+ * @see #ROUND_HALF_DOWN
+ * @see #ROUND_HALF_EVEN
+ * @see #ROUND_UNNECESSARY
+ */
+ public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) {
+ /*
+ * IMPLEMENTATION NOTE: This method *must* return a new object
+ * since divideAndRound uses divide to generate a value whose
+ * scale is then modified.
+ */
+ if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
+ throw new IllegalArgumentException("Invalid rounding mode");
+ /*
+ * Rescale dividend or divisor (whichever can be "upscaled" to
+ * produce correctly scaled quotient).
+ * Take care to detect out-of-range scales
+ */
+ BigDecimal dividend = this;
+ if (checkScale((long)scale + divisor.scale) > this.scale)
+ dividend = this.setScale(scale + divisor.scale, ROUND_UNNECESSARY);
+ else
+ divisor = divisor.setScale(checkScale((long)this.scale - scale),
+ ROUND_UNNECESSARY);
+ return divideAndRound(dividend.intCompact, dividend.intVal,
+ divisor.intCompact, divisor.intVal,
+ scale, roundingMode, scale);
+ }
+
+ /**
+ * Internally used for division operation. The dividend and divisor are
+ * passed both in {@code long} format and {@code BigInteger} format. The
+ * returned {@code BigDecimal} object is the quotient whose scale is set to
+ * the passed in scale. If the remainder is not zero, it will be rounded
+ * based on the passed in roundingMode. Also, if the remainder is zero and
+ * the last parameter, i.e. preferredScale is NOT equal to scale, the
+ * trailing zeros of the result is stripped to match the preferredScale.
+ */
+ private static BigDecimal divideAndRound(long ldividend, BigInteger bdividend,
+ long ldivisor, BigInteger bdivisor,
+ int scale, int roundingMode,
+ int preferredScale) {
+ boolean isRemainderZero; // record remainder is zero or not
+ int qsign; // quotient sign
+ long q = 0, r = 0; // store quotient & remainder in long
+ MutableBigInteger mq = null; // store quotient
+ MutableBigInteger mr = null; // store remainder
+ MutableBigInteger mdivisor = null;
+ boolean isLongDivision = (ldividend != INFLATED && ldivisor != INFLATED);
+ if (isLongDivision) {
+ q = ldividend / ldivisor;
+ if (roundingMode == ROUND_DOWN && scale == preferredScale)
+ return new BigDecimal(null, q, scale, 0);
+ r = ldividend % ldivisor;
+ isRemainderZero = (r == 0);
+ qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1;
+ } else {
+ if (bdividend == null)
+ bdividend = BigInteger.valueOf(ldividend);
+ // Descend into mutables for faster remainder checks
+ MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag);
+ mq = new MutableBigInteger();
+ if (ldivisor != INFLATED) {
+ r = mdividend.divide(ldivisor, mq);
+ isRemainderZero = (r == 0);
+ qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum;
+ } else {
+ mdivisor = new MutableBigInteger(bdivisor.mag);
+ mr = mdividend.divide(mdivisor, mq);
+ isRemainderZero = mr.isZero();
+ qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1;
+ }
+ }
+ boolean increment = false;
+ if (!isRemainderZero) {
+ int cmpFracHalf;
+ /* Round as appropriate */
+ if (roundingMode == ROUND_UNNECESSARY) { // Rounding prohibited
+ throw new ArithmeticException("Rounding necessary");
+ } else if (roundingMode == ROUND_UP) { // Away from zero
+ increment = true;
+ } else if (roundingMode == ROUND_DOWN) { // Towards zero
+ increment = false;
+ } else if (roundingMode == ROUND_CEILING) { // Towards +infinity
+ increment = (qsign > 0);
+ } else if (roundingMode == ROUND_FLOOR) { // Towards -infinity
+ increment = (qsign < 0);
+ } else {
+ if (isLongDivision || ldivisor != INFLATED) {
+ if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) {
+ cmpFracHalf = 1; // 2 * r can't fit into long
+ } else {
+ cmpFracHalf = longCompareMagnitude(2 * r, ldivisor);
+ }
+ } else {
+ cmpFracHalf = mr.compareHalf(mdivisor);
+ }
+ if (cmpFracHalf < 0)
+ increment = false; // We're closer to higher digit
+ else if (cmpFracHalf > 0) // We're closer to lower digit
+ increment = true;
+ else if (roundingMode == ROUND_HALF_UP)
+ increment = true;
+ else if (roundingMode == ROUND_HALF_DOWN)
+ increment = false;
+ else // roundingMode == ROUND_HALF_EVEN, true iff quotient is odd
+ increment = isLongDivision ? (q & 1L) != 0L : mq.isOdd();
+ }
+ }
+ BigDecimal res;
+ if (isLongDivision)
+ res = new BigDecimal(null, (increment ? q + qsign : q), scale, 0);
+ else {
+ if (increment)
+ mq.add(MutableBigInteger.ONE);
+ res = mq.toBigDecimal(qsign, scale);
+ }
+ if (isRemainderZero && preferredScale != scale)
+ res.stripZerosToMatchScale(preferredScale);
+ return res;
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this /
+ * divisor)}, and whose scale is as specified. If rounding must
+ * be performed to generate a result with the specified scale, the
+ * specified rounding mode is applied.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @param scale scale of the {@code BigDecimal} quotient to be returned.
+ * @param roundingMode rounding mode to apply.
+ * @return {@code this / divisor}
+ * @throws ArithmeticException if {@code divisor} is zero,
+ * {@code roundingMode==RoundingMode.UNNECESSARY} and
+ * the specified scale is insufficient to represent the result
+ * of the division exactly.
+ * @since 1.5
+ */
+ public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) {
+ return divide(divisor, scale, roundingMode.oldMode);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this /
+ * divisor)}, and whose scale is {@code this.scale()}. If
+ * rounding must be performed to generate a result with the given
+ * scale, the specified rounding mode is applied.
+ *
+ * The new {@link #divide(BigDecimal, RoundingMode)} method
+ * should be used in preference to this legacy method.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @param roundingMode rounding mode to apply.
+ * @return {@code this / divisor}
+ * @throws ArithmeticException if {@code divisor==0}, or
+ * {@code roundingMode==ROUND_UNNECESSARY} and
+ * {@code this.scale()} is insufficient to represent the result
+ * of the division exactly.
+ * @throws IllegalArgumentException if {@code roundingMode} does not
+ * represent a valid rounding mode.
+ * @see #ROUND_UP
+ * @see #ROUND_DOWN
+ * @see #ROUND_CEILING
+ * @see #ROUND_FLOOR
+ * @see #ROUND_HALF_UP
+ * @see #ROUND_HALF_DOWN
+ * @see #ROUND_HALF_EVEN
+ * @see #ROUND_UNNECESSARY
+ */
+ public BigDecimal divide(BigDecimal divisor, int roundingMode) {
+ return this.divide(divisor, scale, roundingMode);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this /
+ * divisor)}, and whose scale is {@code this.scale()}. If
+ * rounding must be performed to generate a result with the given
+ * scale, the specified rounding mode is applied.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @param roundingMode rounding mode to apply.
+ * @return {@code this / divisor}
+ * @throws ArithmeticException if {@code divisor==0}, or
+ * {@code roundingMode==RoundingMode.UNNECESSARY} and
+ * {@code this.scale()} is insufficient to represent the result
+ * of the division exactly.
+ * @since 1.5
+ */
+ public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) {
+ return this.divide(divisor, scale, roundingMode.oldMode);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this /
+ * divisor)}, and whose preferred scale is {@code (this.scale() -
+ * divisor.scale())}; if the exact quotient cannot be
+ * represented (because it has a non-terminating decimal
+ * expansion) an {@code ArithmeticException} is thrown.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @throws ArithmeticException if the exact quotient does not have a
+ * terminating decimal expansion
+ * @return {@code this / divisor}
+ * @since 1.5
+ * @author Joseph D. Darcy
+ */
+ public BigDecimal divide(BigDecimal divisor) {
+ /*
+ * Handle zero cases first.
+ */
+ if (divisor.signum() == 0) { // x/0
+ if (this.signum() == 0) // 0/0
+ throw new ArithmeticException("Division undefined"); // NaN
+ throw new ArithmeticException("Division by zero");
+ }
+
+ // Calculate preferred scale
+ int preferredScale = saturateLong((long)this.scale - divisor.scale);
+ if (this.signum() == 0) // 0/y
+ return (preferredScale >= 0 &&
+ preferredScale < ZERO_SCALED_BY.length) ?
+ ZERO_SCALED_BY[preferredScale] :
+ BigDecimal.valueOf(0, preferredScale);
+ else {
+ this.inflate();
+ divisor.inflate();
+ /*
+ * If the quotient this/divisor has a terminating decimal
+ * expansion, the expansion can have no more than
+ * (a.precision() + ceil(10*b.precision)/3) digits.
+ * Therefore, create a MathContext object with this
+ * precision and do a divide with the UNNECESSARY rounding
+ * mode.
+ */
+ MathContext mc = new MathContext( (int)Math.min(this.precision() +
+ (long)Math.ceil(10.0*divisor.precision()/3.0),
+ Integer.MAX_VALUE),
+ RoundingMode.UNNECESSARY);
+ BigDecimal quotient;
+ try {
+ quotient = this.divide(divisor, mc);
+ } catch (ArithmeticException e) {
+ throw new ArithmeticException("Non-terminating decimal expansion; " +
+ "no exact representable decimal result.");
+ }
+
+ int quotientScale = quotient.scale();
+
+ // divide(BigDecimal, mc) tries to adjust the quotient to
+ // the desired one by removing trailing zeros; since the
+ // exact divide method does not have an explicit digit
+ // limit, we can add zeros too.
+
+ if (preferredScale > quotientScale)
+ return quotient.setScale(preferredScale, ROUND_UNNECESSARY);
+
+ return quotient;
+ }
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this /
+ * divisor)}, with rounding according to the context settings.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @param mc the context to use.
+ * @return {@code this / divisor}, rounded as necessary.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY} or
+ * {@code mc.precision == 0} and the quotient has a
+ * non-terminating decimal expansion.
+ * @since 1.5
+ */
+ public BigDecimal divide(BigDecimal divisor, MathContext mc) {
+ int mcp = mc.precision;
+ if (mcp == 0)
+ return divide(divisor);
+
+ BigDecimal dividend = this;
+ long preferredScale = (long)dividend.scale - divisor.scale;
+ // Now calculate the answer. We use the existing
+ // divide-and-round method, but as this rounds to scale we have
+ // to normalize the values here to achieve the desired result.
+ // For x/y we first handle y=0 and x=0, and then normalize x and
+ // y to give x' and y' with the following constraints:
+ // (a) 0.1 <= x' < 1
+ // (b) x' <= y' < 10*x'
+ // Dividing x'/y' with the required scale set to mc.precision then
+ // will give a result in the range 0.1 to 1 rounded to exactly
+ // the right number of digits (except in the case of a result of
+ // 1.000... which can arise when x=y, or when rounding overflows
+ // The 1.000... case will reduce properly to 1.
+ if (divisor.signum() == 0) { // x/0
+ if (dividend.signum() == 0) // 0/0
+ throw new ArithmeticException("Division undefined"); // NaN
+ throw new ArithmeticException("Division by zero");
+ }
+ if (dividend.signum() == 0) // 0/y
+ return new BigDecimal(BigInteger.ZERO, 0,
+ saturateLong(preferredScale), 1);
+
+ // Normalize dividend & divisor so that both fall into [0.1, 0.999...]
+ int xscale = dividend.precision();
+ int yscale = divisor.precision();
+ dividend = new BigDecimal(dividend.intVal, dividend.intCompact,
+ xscale, xscale);
+ divisor = new BigDecimal(divisor.intVal, divisor.intCompact,
+ yscale, yscale);
+ if (dividend.compareMagnitude(divisor) > 0) // satisfy constraint (b)
+ yscale = divisor.scale -= 1; // [that is, divisor *= 10]
+
+ // In order to find out whether the divide generates the exact result,
+ // we avoid calling the above divide method. 'quotient' holds the
+ // return BigDecimal object whose scale will be set to 'scl'.
+ BigDecimal quotient;
+ int scl = checkScale(preferredScale + yscale - xscale + mcp);
+ if (checkScale((long)mcp + yscale) > xscale)
+ dividend = dividend.setScale(mcp + yscale, ROUND_UNNECESSARY);
+ else
+ divisor = divisor.setScale(checkScale((long)xscale - mcp),
+ ROUND_UNNECESSARY);
+ quotient = divideAndRound(dividend.intCompact, dividend.intVal,
+ divisor.intCompact, divisor.intVal,
+ scl, mc.roundingMode.oldMode,
+ checkScale(preferredScale));
+ // doRound, here, only affects 1000000000 case.
+ quotient = doRound(quotient, mc);
+
+ return quotient;
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is the integer part
+ * of the quotient {@code (this / divisor)} rounded down. The
+ * preferred scale of the result is {@code (this.scale() -
+ * divisor.scale())}.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @return The integer part of {@code this / divisor}.
+ * @throws ArithmeticException if {@code divisor==0}
+ * @since 1.5
+ */
+ public BigDecimal divideToIntegralValue(BigDecimal divisor) {
+ // Calculate preferred scale
+ int preferredScale = saturateLong((long)this.scale - divisor.scale);
+ if (this.compareMagnitude(divisor) < 0) {
+ // much faster when this << divisor
+ return BigDecimal.valueOf(0, preferredScale);
+ }
+
+ if(this.signum() == 0 && divisor.signum() != 0)
+ return this.setScale(preferredScale, ROUND_UNNECESSARY);
+
+ // Perform a divide with enough digits to round to a correct
+ // integer value; then remove any fractional digits
+
+ int maxDigits = (int)Math.min(this.precision() +
+ (long)Math.ceil(10.0*divisor.precision()/3.0) +
+ Math.abs((long)this.scale() - divisor.scale()) + 2,
+ Integer.MAX_VALUE);
+ BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits,
+ RoundingMode.DOWN));
+ if (quotient.scale > 0) {
+ quotient = quotient.setScale(0, RoundingMode.DOWN);
+ quotient.stripZerosToMatchScale(preferredScale);
+ }
+
+ if (quotient.scale < preferredScale) {
+ // pad with zeros if necessary
+ quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY);
+ }
+ return quotient;
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is the integer part
+ * of {@code (this / divisor)}. Since the integer part of the
+ * exact quotient does not depend on the rounding mode, the
+ * rounding mode does not affect the values returned by this
+ * method. The preferred scale of the result is
+ * {@code (this.scale() - divisor.scale())}. An
+ * {@code ArithmeticException} is thrown if the integer part of
+ * the exact quotient needs more than {@code mc.precision}
+ * digits.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @param mc the context to use.
+ * @return The integer part of {@code this / divisor}.
+ * @throws ArithmeticException if {@code divisor==0}
+ * @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result
+ * requires a precision of more than {@code mc.precision} digits.
+ * @since 1.5
+ * @author Joseph D. Darcy
+ */
+ public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) {
+ if (mc.precision == 0 || // exact result
+ (this.compareMagnitude(divisor) < 0) ) // zero result
+ return divideToIntegralValue(divisor);
+
+ // Calculate preferred scale
+ int preferredScale = saturateLong((long)this.scale - divisor.scale);
+
+ /*
+ * Perform a normal divide to mc.precision digits. If the
+ * remainder has absolute value less than the divisor, the
+ * integer portion of the quotient fits into mc.precision
+ * digits. Next, remove any fractional digits from the
+ * quotient and adjust the scale to the preferred value.
+ */
+ BigDecimal result = this.
+ divide(divisor, new MathContext(mc.precision, RoundingMode.DOWN));
+
+ if (result.scale() < 0) {
+ /*
+ * Result is an integer. See if quotient represents the
+ * full integer portion of the exact quotient; if it does,
+ * the computed remainder will be less than the divisor.
+ */
+ BigDecimal product = result.multiply(divisor);
+ // If the quotient is the full integer value,
+ // |dividend-product| < |divisor|.
+ if (this.subtract(product).compareMagnitude(divisor) >= 0) {
+ throw new ArithmeticException("Division impossible");
+ }
+ } else if (result.scale() > 0) {
+ /*
+ * Integer portion of quotient will fit into precision
+ * digits; recompute quotient to scale 0 to avoid double
+ * rounding and then try to adjust, if necessary.
+ */
+ result = result.setScale(0, RoundingMode.DOWN);
+ }
+ // else result.scale() == 0;
+
+ int precisionDiff;
+ if ((preferredScale > result.scale()) &&
+ (precisionDiff = mc.precision - result.precision()) > 0) {
+ return result.setScale(result.scale() +
+ Math.min(precisionDiff, preferredScale - result.scale) );
+ } else {
+ result.stripZerosToMatchScale(preferredScale);
+ return result;
+ }
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this % divisor)}.
+ *
+ * The remainder is given by
+ * {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}.
+ * Note that this is not the modulo operation (the result can be
+ * negative).
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @return {@code this % divisor}.
+ * @throws ArithmeticException if {@code divisor==0}
+ * @since 1.5
+ */
+ public BigDecimal remainder(BigDecimal divisor) {
+ BigDecimal divrem[] = this.divideAndRemainder(divisor);
+ return divrem[1];
+ }
+
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (this %
+ * divisor)}, with rounding according to the context settings.
+ * The {@code MathContext} settings affect the implicit divide
+ * used to compute the remainder. The remainder computation
+ * itself is by definition exact. Therefore, the remainder may
+ * contain more than {@code mc.getPrecision()} digits.
+ *
+ * The remainder is given by
+ * {@code this.subtract(this.divideToIntegralValue(divisor,
+ * mc).multiply(divisor))}. Note that this is not the modulo
+ * operation (the result can be negative).
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided.
+ * @param mc the context to use.
+ * @return {@code this % divisor}, rounded as necessary.
+ * @throws ArithmeticException if {@code divisor==0}
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
+ * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
+ * require a precision of more than {@code mc.precision} digits.
+ * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
+ * @since 1.5
+ */
+ public BigDecimal remainder(BigDecimal divisor, MathContext mc) {
+ BigDecimal divrem[] = this.divideAndRemainder(divisor, mc);
+ return divrem[1];
+ }
+
+ /**
+ * Returns a two-element {@code BigDecimal} array containing the
+ * result of {@code divideToIntegralValue} followed by the result of
+ * {@code remainder} on the two operands.
+ *
+ * Note that if both the integer quotient and remainder are
+ * needed, this method is faster than using the
+ * {@code divideToIntegralValue} and {@code remainder} methods
+ * separately because the division need only be carried out once.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided,
+ * and the remainder computed.
+ * @return a two element {@code BigDecimal} array: the quotient
+ * (the result of {@code divideToIntegralValue}) is the initial element
+ * and the remainder is the final element.
+ * @throws ArithmeticException if {@code divisor==0}
+ * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
+ * @see #remainder(java.math.BigDecimal, java.math.MathContext)
+ * @since 1.5
+ */
+ public BigDecimal[] divideAndRemainder(BigDecimal divisor) {
+ // we use the identity x = i * y + r to determine r
+ BigDecimal[] result = new BigDecimal[2];
+
+ result[0] = this.divideToIntegralValue(divisor);
+ result[1] = this.subtract(result[0].multiply(divisor));
+ return result;
+ }
+
+ /**
+ * Returns a two-element {@code BigDecimal} array containing the
+ * result of {@code divideToIntegralValue} followed by the result of
+ * {@code remainder} on the two operands calculated with rounding
+ * according to the context settings.
+ *
+ * Note that if both the integer quotient and remainder are
+ * needed, this method is faster than using the
+ * {@code divideToIntegralValue} and {@code remainder} methods
+ * separately because the division need only be carried out once.
+ *
+ * @param divisor value by which this {@code BigDecimal} is to be divided,
+ * and the remainder computed.
+ * @param mc the context to use.
+ * @return a two element {@code BigDecimal} array: the quotient
+ * (the result of {@code divideToIntegralValue}) is the
+ * initial element and the remainder is the final element.
+ * @throws ArithmeticException if {@code divisor==0}
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}, or {@code mc.precision}
+ * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would
+ * require a precision of more than {@code mc.precision} digits.
+ * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext)
+ * @see #remainder(java.math.BigDecimal, java.math.MathContext)
+ * @since 1.5
+ */
+ public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) {
+ if (mc.precision == 0)
+ return divideAndRemainder(divisor);
+
+ BigDecimal[] result = new BigDecimal[2];
+ BigDecimal lhs = this;
+
+ result[0] = lhs.divideToIntegralValue(divisor, mc);
+ result[1] = lhs.subtract(result[0].multiply(divisor));
+ return result;
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is
+ * (thisn), The power is computed exactly, to
+ * unlimited precision.
+ *
+ * The parameter {@code n} must be in the range 0 through
+ * 999999999, inclusive. {@code ZERO.pow(0)} returns {@link
+ * #ONE}.
+ *
+ * Note that future releases may expand the allowable exponent
+ * range of this method.
+ *
+ * @param n power to raise this {@code BigDecimal} to.
+ * @return thisn
+ * @throws ArithmeticException if {@code n} is out of range.
+ * @since 1.5
+ */
+ public BigDecimal pow(int n) {
+ if (n < 0 || n > 999999999)
+ throw new ArithmeticException("Invalid operation");
+ // No need to calculate pow(n) if result will over/underflow.
+ // Don't attempt to support "supernormal" numbers.
+ int newScale = checkScale((long)scale * n);
+ this.inflate();
+ return new BigDecimal(intVal.pow(n), newScale);
+ }
+
+
+ /**
+ * Returns a {@code BigDecimal} whose value is
+ * (thisn). The current implementation uses
+ * the core algorithm defined in ANSI standard X3.274-1996 with
+ * rounding according to the context settings. In general, the
+ * returned numerical value is within two ulps of the exact
+ * numerical value for the chosen precision. Note that future
+ * releases may use a different algorithm with a decreased
+ * allowable error bound and increased allowable exponent range.
+ *
+ * The X3.274-1996 algorithm is:
+ *
+ * This method, which simply returns this {@code BigDecimal}
+ * is included for symmetry with the unary minus method {@link
+ * #negate()}.
+ *
+ * @return {@code this}.
+ * @see #negate()
+ * @since 1.5
+ */
+ public BigDecimal plus() {
+ return this;
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (+this)},
+ * with rounding according to the context settings.
+ *
+ * The effect of this method is identical to that of the {@link
+ * #round(MathContext)} method.
+ *
+ * @param mc the context to use.
+ * @return {@code this}, rounded as necessary. A zero result will
+ * have a scale of 0.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @see #round(MathContext)
+ * @since 1.5
+ */
+ public BigDecimal plus(MathContext mc) {
+ if (mc.precision == 0) // no rounding please
+ return this;
+ return doRound(this, mc);
+ }
+
+ /**
+ * Returns the signum function of this {@code BigDecimal}.
+ *
+ * @return -1, 0, or 1 as the value of this {@code BigDecimal}
+ * is negative, zero, or positive.
+ */
+ public int signum() {
+ return (intCompact != INFLATED)?
+ Long.signum(intCompact):
+ intVal.signum();
+ }
+
+ /**
+ * Returns the scale of this {@code BigDecimal}. If zero
+ * or positive, the scale is the number of digits to the right of
+ * the decimal point. If negative, the unscaled value of the
+ * number is multiplied by ten to the power of the negation of the
+ * scale. For example, a scale of {@code -3} means the unscaled
+ * value is multiplied by 1000.
+ *
+ * @return the scale of this {@code BigDecimal}.
+ */
+ public int scale() {
+ return scale;
+ }
+
+ /**
+ * Returns the precision of this {@code BigDecimal}. (The
+ * precision is the number of digits in the unscaled value.)
+ *
+ * The precision of a zero value is 1.
+ *
+ * @return the precision of this {@code BigDecimal}.
+ * @since 1.5
+ */
+ public int precision() {
+ int result = precision;
+ if (result == 0) {
+ long s = intCompact;
+ if (s != INFLATED)
+ result = longDigitLength(s);
+ else
+ result = bigDigitLength(inflate());
+ precision = result;
+ }
+ return result;
+ }
+
+
+ /**
+ * Returns a {@code BigInteger} whose value is the unscaled
+ * value of this {@code BigDecimal}. (Computes (this *
+ * 10this.scale()).)
+ *
+ * @return the unscaled value of this {@code BigDecimal}.
+ * @since 1.2
+ */
+ public BigInteger unscaledValue() {
+ return this.inflate();
+ }
+
+ // Rounding Modes
+
+ /**
+ * Rounding mode to round away from zero. Always increments the
+ * digit prior to a nonzero discarded fraction. Note that this rounding
+ * mode never decreases the magnitude of the calculated value.
+ */
+ public final static int ROUND_UP = 0;
+
+ /**
+ * Rounding mode to round towards zero. Never increments the digit
+ * prior to a discarded fraction (i.e., truncates). Note that this
+ * rounding mode never increases the magnitude of the calculated value.
+ */
+ public final static int ROUND_DOWN = 1;
+
+ /**
+ * Rounding mode to round towards positive infinity. If the
+ * {@code BigDecimal} is positive, behaves as for
+ * {@code ROUND_UP}; if negative, behaves as for
+ * {@code ROUND_DOWN}. Note that this rounding mode never
+ * decreases the calculated value.
+ */
+ public final static int ROUND_CEILING = 2;
+
+ /**
+ * Rounding mode to round towards negative infinity. If the
+ * {@code BigDecimal} is positive, behave as for
+ * {@code ROUND_DOWN}; if negative, behave as for
+ * {@code ROUND_UP}. Note that this rounding mode never
+ * increases the calculated value.
+ */
+ public final static int ROUND_FLOOR = 3;
+
+ /**
+ * Rounding mode to round towards {@literal "nearest neighbor"}
+ * unless both neighbors are equidistant, in which case round up.
+ * Behaves as for {@code ROUND_UP} if the discarded fraction is
+ * ≥ 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note
+ * that this is the rounding mode that most of us were taught in
+ * grade school.
+ */
+ public final static int ROUND_HALF_UP = 4;
+
+ /**
+ * Rounding mode to round towards {@literal "nearest neighbor"}
+ * unless both neighbors are equidistant, in which case round
+ * down. Behaves as for {@code ROUND_UP} if the discarded
+ * fraction is {@literal >} 0.5; otherwise, behaves as for
+ * {@code ROUND_DOWN}.
+ */
+ public final static int ROUND_HALF_DOWN = 5;
+
+ /**
+ * Rounding mode to round towards the {@literal "nearest neighbor"}
+ * unless both neighbors are equidistant, in which case, round
+ * towards the even neighbor. Behaves as for
+ * {@code ROUND_HALF_UP} if the digit to the left of the
+ * discarded fraction is odd; behaves as for
+ * {@code ROUND_HALF_DOWN} if it's even. Note that this is the
+ * rounding mode that minimizes cumulative error when applied
+ * repeatedly over a sequence of calculations.
+ */
+ public final static int ROUND_HALF_EVEN = 6;
+
+ /**
+ * Rounding mode to assert that the requested operation has an exact
+ * result, hence no rounding is necessary. If this rounding mode is
+ * specified on an operation that yields an inexact result, an
+ * {@code ArithmeticException} is thrown.
+ */
+ public final static int ROUND_UNNECESSARY = 7;
+
+
+ // Scaling/Rounding Operations
+
+ /**
+ * Returns a {@code BigDecimal} rounded according to the
+ * {@code MathContext} settings. If the precision setting is 0 then
+ * no rounding takes place.
+ *
+ * The effect of this method is identical to that of the
+ * {@link #plus(MathContext)} method.
+ *
+ * @param mc the context to use.
+ * @return a {@code BigDecimal} rounded according to the
+ * {@code MathContext} settings.
+ * @throws ArithmeticException if the rounding mode is
+ * {@code UNNECESSARY} and the
+ * {@code BigDecimal} operation would require rounding.
+ * @see #plus(MathContext)
+ * @since 1.5
+ */
+ public BigDecimal round(MathContext mc) {
+ return plus(mc);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose scale is the specified
+ * value, and whose unscaled value is determined by multiplying or
+ * dividing this {@code BigDecimal}'s unscaled value by the
+ * appropriate power of ten to maintain its overall value. If the
+ * scale is reduced by the operation, the unscaled value must be
+ * divided (rather than multiplied), and the value may be changed;
+ * in this case, the specified rounding mode is applied to the
+ * division.
+ *
+ * Note that since BigDecimal objects are immutable, calls of
+ * this method do not result in the original object being
+ * modified, contrary to the usual convention of having methods
+ * named setX mutate field {@code X}.
+ * Instead, {@code setScale} returns an object with the proper
+ * scale; the returned object may or may not be newly allocated.
+ *
+ * @param newScale scale of the {@code BigDecimal} value to be returned.
+ * @param roundingMode The rounding mode to apply.
+ * @return a {@code BigDecimal} whose scale is the specified value,
+ * and whose unscaled value is determined by multiplying or
+ * dividing this {@code BigDecimal}'s unscaled value by the
+ * appropriate power of ten to maintain its overall value.
+ * @throws ArithmeticException if {@code roundingMode==UNNECESSARY}
+ * and the specified scaling operation would require
+ * rounding.
+ * @see RoundingMode
+ * @since 1.5
+ */
+ public BigDecimal setScale(int newScale, RoundingMode roundingMode) {
+ return setScale(newScale, roundingMode.oldMode);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose scale is the specified
+ * value, and whose unscaled value is determined by multiplying or
+ * dividing this {@code BigDecimal}'s unscaled value by the
+ * appropriate power of ten to maintain its overall value. If the
+ * scale is reduced by the operation, the unscaled value must be
+ * divided (rather than multiplied), and the value may be changed;
+ * in this case, the specified rounding mode is applied to the
+ * division.
+ *
+ * Note that since BigDecimal objects are immutable, calls of
+ * this method do not result in the original object being
+ * modified, contrary to the usual convention of having methods
+ * named setX mutate field {@code X}.
+ * Instead, {@code setScale} returns an object with the proper
+ * scale; the returned object may or may not be newly allocated.
+ *
+ * The new {@link #setScale(int, RoundingMode)} method should
+ * be used in preference to this legacy method.
+ *
+ * @param newScale scale of the {@code BigDecimal} value to be returned.
+ * @param roundingMode The rounding mode to apply.
+ * @return a {@code BigDecimal} whose scale is the specified value,
+ * and whose unscaled value is determined by multiplying or
+ * dividing this {@code BigDecimal}'s unscaled value by the
+ * appropriate power of ten to maintain its overall value.
+ * @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY}
+ * and the specified scaling operation would require
+ * rounding.
+ * @throws IllegalArgumentException if {@code roundingMode} does not
+ * represent a valid rounding mode.
+ * @see #ROUND_UP
+ * @see #ROUND_DOWN
+ * @see #ROUND_CEILING
+ * @see #ROUND_FLOOR
+ * @see #ROUND_HALF_UP
+ * @see #ROUND_HALF_DOWN
+ * @see #ROUND_HALF_EVEN
+ * @see #ROUND_UNNECESSARY
+ */
+ public BigDecimal setScale(int newScale, int roundingMode) {
+ if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY)
+ throw new IllegalArgumentException("Invalid rounding mode");
+
+ int oldScale = this.scale;
+ if (newScale == oldScale) // easy case
+ return this;
+ if (this.signum() == 0) // zero can have any scale
+ return BigDecimal.valueOf(0, newScale);
+
+ long rs = this.intCompact;
+ if (newScale > oldScale) {
+ int raise = checkScale((long)newScale - oldScale);
+ BigInteger rb = null;
+ if (rs == INFLATED ||
+ (rs = longMultiplyPowerTen(rs, raise)) == INFLATED)
+ rb = bigMultiplyPowerTen(raise);
+ return new BigDecimal(rb, rs, newScale,
+ (precision > 0) ? precision + raise : 0);
+ } else {
+ // newScale < oldScale -- drop some digits
+ // Can't predict the precision due to the effect of rounding.
+ int drop = checkScale((long)oldScale - newScale);
+ if (drop < LONG_TEN_POWERS_TABLE.length)
+ return divideAndRound(rs, this.intVal,
+ LONG_TEN_POWERS_TABLE[drop], null,
+ newScale, roundingMode, newScale);
+ else
+ return divideAndRound(rs, this.intVal,
+ INFLATED, bigTenToThe(drop),
+ newScale, roundingMode, newScale);
+ }
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose scale is the specified
+ * value, and whose value is numerically equal to this
+ * {@code BigDecimal}'s. Throws an {@code ArithmeticException}
+ * if this is not possible.
+ *
+ * This call is typically used to increase the scale, in which
+ * case it is guaranteed that there exists a {@code BigDecimal}
+ * of the specified scale and the correct value. The call can
+ * also be used to reduce the scale if the caller knows that the
+ * {@code BigDecimal} has sufficiently many zeros at the end of
+ * its fractional part (i.e., factors of ten in its integer value)
+ * to allow for the rescaling without changing its value.
+ *
+ * This method returns the same result as the two-argument
+ * versions of {@code setScale}, but saves the caller the trouble
+ * of specifying a rounding mode in cases where it is irrelevant.
+ *
+ * Note that since {@code BigDecimal} objects are immutable,
+ * calls of this method do not result in the original
+ * object being modified, contrary to the usual convention of
+ * having methods named setX mutate field
+ * {@code X}. Instead, {@code setScale} returns an
+ * object with the proper scale; the returned object may or may
+ * not be newly allocated.
+ *
+ * @param newScale scale of the {@code BigDecimal} value to be returned.
+ * @return a {@code BigDecimal} whose scale is the specified value, and
+ * whose unscaled value is determined by multiplying or dividing
+ * this {@code BigDecimal}'s unscaled value by the appropriate
+ * power of ten to maintain its overall value.
+ * @throws ArithmeticException if the specified scaling operation would
+ * require rounding.
+ * @see #setScale(int, int)
+ * @see #setScale(int, RoundingMode)
+ */
+ public BigDecimal setScale(int newScale) {
+ return setScale(newScale, ROUND_UNNECESSARY);
+ }
+
+ // Decimal Point Motion Operations
+
+ /**
+ * Returns a {@code BigDecimal} which is equivalent to this one
+ * with the decimal point moved {@code n} places to the left. If
+ * {@code n} is non-negative, the call merely adds {@code n} to
+ * the scale. If {@code n} is negative, the call is equivalent
+ * to {@code movePointRight(-n)}. The {@code BigDecimal}
+ * returned by this call has value (this ×
+ * 10-n) and scale {@code max(this.scale()+n,
+ * 0)}.
+ *
+ * @param n number of places to move the decimal point to the left.
+ * @return a {@code BigDecimal} which is equivalent to this one with the
+ * decimal point moved {@code n} places to the left.
+ * @throws ArithmeticException if scale overflows.
+ */
+ public BigDecimal movePointLeft(int n) {
+ // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE
+ int newScale = checkScale((long)scale + n);
+ BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
+ return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
+ }
+
+ /**
+ * Returns a {@code BigDecimal} which is equivalent to this one
+ * with the decimal point moved {@code n} places to the right.
+ * If {@code n} is non-negative, the call merely subtracts
+ * {@code n} from the scale. If {@code n} is negative, the call
+ * is equivalent to {@code movePointLeft(-n)}. The
+ * {@code BigDecimal} returned by this call has value (this
+ * × 10n) and scale {@code max(this.scale()-n,
+ * 0)}.
+ *
+ * @param n number of places to move the decimal point to the right.
+ * @return a {@code BigDecimal} which is equivalent to this one
+ * with the decimal point moved {@code n} places to the right.
+ * @throws ArithmeticException if scale overflows.
+ */
+ public BigDecimal movePointRight(int n) {
+ // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE
+ int newScale = checkScale((long)scale - n);
+ BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0);
+ return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num;
+ }
+
+ /**
+ * Returns a BigDecimal whose numerical value is equal to
+ * ({@code this} * 10n). The scale of
+ * the result is {@code (this.scale() - n)}.
+ *
+ * @throws ArithmeticException if the scale would be
+ * outside the range of a 32-bit integer.
+ *
+ * @since 1.5
+ */
+ public BigDecimal scaleByPowerOfTen(int n) {
+ return new BigDecimal(intVal, intCompact,
+ checkScale((long)scale - n), precision);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} which is numerically equal to
+ * this one but with any trailing zeros removed from the
+ * representation. For example, stripping the trailing zeros from
+ * the {@code BigDecimal} value {@code 600.0}, which has
+ * [{@code BigInteger}, {@code scale}] components equals to
+ * [6000, 1], yields {@code 6E2} with [{@code BigInteger},
+ * {@code scale}] components equals to [6, -2]
+ *
+ * @return a numerically equal {@code BigDecimal} with any
+ * trailing zeros removed.
+ * @since 1.5
+ */
+ public BigDecimal stripTrailingZeros() {
+ this.inflate();
+ BigDecimal result = new BigDecimal(intVal, scale);
+ result.stripZerosToMatchScale(Long.MIN_VALUE);
+ return result;
+ }
+
+ // Comparison Operations
+
+ /**
+ * Compares this {@code BigDecimal} with the specified
+ * {@code BigDecimal}. Two {@code BigDecimal} objects that are
+ * equal in value but have a different scale (like 2.0 and 2.00)
+ * are considered equal by this method. This method is provided
+ * in preference to individual methods for each of the six boolean
+ * comparison operators ({@literal <}, ==,
+ * {@literal >}, {@literal >=}, !=, {@literal <=}). The
+ * suggested idiom for performing these comparisons is:
+ * {@code (x.compareTo(y)} <op> {@code 0)}, where
+ * <op> is one of the six comparison operators.
+ *
+ * @param val {@code BigDecimal} to which this {@code BigDecimal} is
+ * to be compared.
+ * @return -1, 0, or 1 as this {@code BigDecimal} is numerically
+ * less than, equal to, or greater than {@code val}.
+ */
+ public int compareTo(BigDecimal val) {
+ // Quick path for equal scale and non-inflated case.
+ if (scale == val.scale) {
+ long xs = intCompact;
+ long ys = val.intCompact;
+ if (xs != INFLATED && ys != INFLATED)
+ return xs != ys ? ((xs > ys) ? 1 : -1) : 0;
+ }
+ int xsign = this.signum();
+ int ysign = val.signum();
+ if (xsign != ysign)
+ return (xsign > ysign) ? 1 : -1;
+ if (xsign == 0)
+ return 0;
+ int cmp = compareMagnitude(val);
+ return (xsign > 0) ? cmp : -cmp;
+ }
+
+ /**
+ * Version of compareTo that ignores sign.
+ */
+ private int compareMagnitude(BigDecimal val) {
+ // Match scales, avoid unnecessary inflation
+ long ys = val.intCompact;
+ long xs = this.intCompact;
+ if (xs == 0)
+ return (ys == 0) ? 0 : -1;
+ if (ys == 0)
+ return 1;
+
+ int sdiff = this.scale - val.scale;
+ if (sdiff != 0) {
+ // Avoid matching scales if the (adjusted) exponents differ
+ int xae = this.precision() - this.scale; // [-1]
+ int yae = val.precision() - val.scale; // [-1]
+ if (xae < yae)
+ return -1;
+ if (xae > yae)
+ return 1;
+ BigInteger rb = null;
+ if (sdiff < 0) {
+ if ( (xs == INFLATED ||
+ (xs = longMultiplyPowerTen(xs, -sdiff)) == INFLATED) &&
+ ys == INFLATED) {
+ rb = bigMultiplyPowerTen(-sdiff);
+ return rb.compareMagnitude(val.intVal);
+ }
+ } else { // sdiff > 0
+ if ( (ys == INFLATED ||
+ (ys = longMultiplyPowerTen(ys, sdiff)) == INFLATED) &&
+ xs == INFLATED) {
+ rb = val.bigMultiplyPowerTen(sdiff);
+ return this.intVal.compareMagnitude(rb);
+ }
+ }
+ }
+ if (xs != INFLATED)
+ return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1;
+ else if (ys != INFLATED)
+ return 1;
+ else
+ return this.intVal.compareMagnitude(val.intVal);
+ }
+
+ /**
+ * Compares this {@code BigDecimal} with the specified
+ * {@code Object} for equality. Unlike {@link
+ * #compareTo(BigDecimal) compareTo}, this method considers two
+ * {@code BigDecimal} objects equal only if they are equal in
+ * value and scale (thus 2.0 is not equal to 2.00 when compared by
+ * this method).
+ *
+ * @param x {@code Object} to which this {@code BigDecimal} is
+ * to be compared.
+ * @return {@code true} if and only if the specified {@code Object} is a
+ * {@code BigDecimal} whose value and scale are equal to this
+ * {@code BigDecimal}'s.
+ * @see #compareTo(java.math.BigDecimal)
+ * @see #hashCode
+ */
+ @Override
+ public boolean equals(Object x) {
+ if (!(x instanceof BigDecimal))
+ return false;
+ BigDecimal xDec = (BigDecimal) x;
+ if (x == this)
+ return true;
+ if (scale != xDec.scale)
+ return false;
+ long s = this.intCompact;
+ long xs = xDec.intCompact;
+ if (s != INFLATED) {
+ if (xs == INFLATED)
+ xs = compactValFor(xDec.intVal);
+ return xs == s;
+ } else if (xs != INFLATED)
+ return xs == compactValFor(this.intVal);
+
+ return this.inflate().equals(xDec.inflate());
+ }
+
+ /**
+ * Returns the minimum of this {@code BigDecimal} and
+ * {@code val}.
+ *
+ * @param val value with which the minimum is to be computed.
+ * @return the {@code BigDecimal} whose value is the lesser of this
+ * {@code BigDecimal} and {@code val}. If they are equal,
+ * as defined by the {@link #compareTo(BigDecimal) compareTo}
+ * method, {@code this} is returned.
+ * @see #compareTo(java.math.BigDecimal)
+ */
+ public BigDecimal min(BigDecimal val) {
+ return (compareTo(val) <= 0 ? this : val);
+ }
+
+ /**
+ * Returns the maximum of this {@code BigDecimal} and {@code val}.
+ *
+ * @param val value with which the maximum is to be computed.
+ * @return the {@code BigDecimal} whose value is the greater of this
+ * {@code BigDecimal} and {@code val}. If they are equal,
+ * as defined by the {@link #compareTo(BigDecimal) compareTo}
+ * method, {@code this} is returned.
+ * @see #compareTo(java.math.BigDecimal)
+ */
+ public BigDecimal max(BigDecimal val) {
+ return (compareTo(val) >= 0 ? this : val);
+ }
+
+ // Hash Function
+
+ /**
+ * Returns the hash code for this {@code BigDecimal}. Note that
+ * two {@code BigDecimal} objects that are numerically equal but
+ * differ in scale (like 2.0 and 2.00) will generally not
+ * have the same hash code.
+ *
+ * @return hash code for this {@code BigDecimal}.
+ * @see #equals(Object)
+ */
+ @Override
+ public int hashCode() {
+ if (intCompact != INFLATED) {
+ long val2 = (intCompact < 0)? -intCompact : intCompact;
+ int temp = (int)( ((int)(val2 >>> 32)) * 31 +
+ (val2 & LONG_MASK));
+ return 31*((intCompact < 0) ?-temp:temp) + scale;
+ } else
+ return 31*intVal.hashCode() + scale;
+ }
+
+ // Format Converters
+
+ /**
+ * Returns the string representation of this {@code BigDecimal},
+ * using scientific notation if an exponent is needed.
+ *
+ * A standard canonical string form of the {@code BigDecimal}
+ * is created as though by the following steps: first, the
+ * absolute value of the unscaled value of the {@code BigDecimal}
+ * is converted to a string in base ten using the characters
+ * {@code '0'} through {@code '9'} with no leading zeros (except
+ * if its value is zero, in which case a single {@code '0'}
+ * character is used).
+ *
+ * Next, an adjusted exponent is calculated; this is the
+ * negated scale, plus the number of characters in the converted
+ * unscaled value, less one. That is,
+ * {@code -scale+(ulength-1)}, where {@code ulength} is the
+ * length of the absolute value of the unscaled value in decimal
+ * digits (its precision).
+ *
+ * If the scale is greater than or equal to zero and the
+ * adjusted exponent is greater than or equal to {@code -6}, the
+ * number will be converted to a character form without using
+ * exponential notation. In this case, if the scale is zero then
+ * no decimal point is added and if the scale is positive a
+ * decimal point will be inserted with the scale specifying the
+ * number of characters to the right of the decimal point.
+ * {@code '0'} characters are added to the left of the converted
+ * unscaled value as necessary. If no character precedes the
+ * decimal point after this insertion then a conventional
+ * {@code '0'} character is prefixed.
+ *
+ * Otherwise (that is, if the scale is negative, or the
+ * adjusted exponent is less than {@code -6}), the number will be
+ * converted to a character form using exponential notation. In
+ * this case, if the converted {@code BigInteger} has more than
+ * one digit a decimal point is inserted after the first digit.
+ * An exponent in character form is then suffixed to the converted
+ * unscaled value (perhaps with inserted decimal point); this
+ * comprises the letter {@code 'E'} followed immediately by the
+ * adjusted exponent converted to a character form. The latter is
+ * in base ten, using the characters {@code '0'} through
+ * {@code '9'} with no leading zeros, and is always prefixed by a
+ * sign character {@code '-'} ('\u002D') if the
+ * adjusted exponent is negative, {@code '+'}
+ * ('\u002B') otherwise).
+ *
+ * Finally, the entire string is prefixed by a minus sign
+ * character {@code '-'} ('\u002D') if the unscaled
+ * value is less than zero. No sign character is prefixed if the
+ * unscaled value is zero or positive.
+ *
+ * Examples:
+ * For each representation [unscaled value, scale]
+ * on the left, the resulting string is shown on the right.
+ * Returns a string that represents the {@code BigDecimal} as
+ * described in the {@link #toString()} method, except that if
+ * exponential notation is used, the power of ten is adjusted to
+ * be a multiple of three (engineering notation) such that the
+ * integer part of nonzero values will be in the range 1 through
+ * 999. If exponential notation is used for zero values, a
+ * decimal point and one or two fractional zero digits are used so
+ * that the scale of the zero value is preserved. Note that
+ * unlike the output of {@link #toString()}, the output of this
+ * method is not guaranteed to recover the same [integer,
+ * scale] pair of this {@code BigDecimal} if the output string is
+ * converting back to a {@code BigDecimal} using the {@linkplain
+ * #BigDecimal(String) string constructor}. The result of this method meets
+ * the weaker constraint of always producing a numerically equal
+ * result from applying the string constructor to the method's output.
+ *
+ * @return string representation of this {@code BigDecimal}, using
+ * engineering notation if an exponent is needed.
+ * @since 1.5
+ */
+ public String toEngineeringString() {
+ return layoutChars(false);
+ }
+
+ /**
+ * Returns a string representation of this {@code BigDecimal}
+ * without an exponent field. For values with a positive scale,
+ * the number of digits to the right of the decimal point is used
+ * to indicate scale. For values with a zero or negative scale,
+ * the resulting string is generated as if the value were
+ * converted to a numerically equal value with zero scale and as
+ * if all the trailing zeros of the zero scale value were present
+ * in the result.
+ *
+ * The entire string is prefixed by a minus sign character '-'
+ * ('\u002D') if the unscaled value is less than
+ * zero. No sign character is prefixed if the unscaled value is
+ * zero or positive.
+ *
+ * Note that if the result of this method is passed to the
+ * {@linkplain #BigDecimal(String) string constructor}, only the
+ * numerical value of this {@code BigDecimal} will necessarily be
+ * recovered; the representation of the new {@code BigDecimal}
+ * may have a different scale. In particular, if this
+ * {@code BigDecimal} has a negative scale, the string resulting
+ * from this method will have a scale of zero when processed by
+ * the string constructor.
+ *
+ * (This method behaves analogously to the {@code toString}
+ * method in 1.4 and earlier releases.)
+ *
+ * @return a string representation of this {@code BigDecimal}
+ * without an exponent field.
+ * @since 1.5
+ * @see #toString()
+ * @see #toEngineeringString()
+ */
+ public String toPlainString() {
+ BigDecimal bd = this;
+ if (bd.scale < 0)
+ bd = bd.setScale(0);
+ bd.inflate();
+ if (bd.scale == 0) // No decimal point
+ return bd.intVal.toString();
+ return bd.getValueString(bd.signum(), bd.intVal.abs().toString(), bd.scale);
+ }
+
+ /* Returns a digit.digit string */
+ private String getValueString(int signum, String intString, int scale) {
+ /* Insert decimal point */
+ StringBuilder buf;
+ int insertionPoint = intString.length() - scale;
+ if (insertionPoint == 0) { /* Point goes right before intVal */
+ return (signum<0 ? "-0." : "0.") + intString;
+ } else if (insertionPoint > 0) { /* Point goes inside intVal */
+ buf = new StringBuilder(intString);
+ buf.insert(insertionPoint, '.');
+ if (signum < 0)
+ buf.insert(0, '-');
+ } else { /* We must insert zeros between point and intVal */
+ buf = new StringBuilder(3-insertionPoint + intString.length());
+ buf.append(signum<0 ? "-0." : "0.");
+ for (int i=0; i<-insertionPoint; i++)
+ buf.append('0');
+ buf.append(intString);
+ }
+ return buf.toString();
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to a {@code BigInteger}.
+ * This conversion is analogous to the
+ * narrowing primitive conversion from {@code double} to
+ * {@code long} as defined in section 5.1.3 of
+ * The Java™ Language Specification:
+ * any fractional part of this
+ * {@code BigDecimal} will be discarded. Note that this
+ * conversion can lose information about the precision of the
+ * {@code BigDecimal} value.
+ *
+ * To have an exception thrown if the conversion is inexact (in
+ * other words if a nonzero fractional part is discarded), use the
+ * {@link #toBigIntegerExact()} method.
+ *
+ * @return this {@code BigDecimal} converted to a {@code BigInteger}.
+ */
+ public BigInteger toBigInteger() {
+ // force to an integer, quietly
+ return this.setScale(0, ROUND_DOWN).inflate();
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to a {@code BigInteger},
+ * checking for lost information. An exception is thrown if this
+ * {@code BigDecimal} has a nonzero fractional part.
+ *
+ * @return this {@code BigDecimal} converted to a {@code BigInteger}.
+ * @throws ArithmeticException if {@code this} has a nonzero
+ * fractional part.
+ * @since 1.5
+ */
+ public BigInteger toBigIntegerExact() {
+ // round to an integer, with Exception if decimal part non-0
+ return this.setScale(0, ROUND_UNNECESSARY).inflate();
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to a {@code long}.
+ * This conversion is analogous to the
+ * narrowing primitive conversion from {@code double} to
+ * {@code short} as defined in section 5.1.3 of
+ * The Java™ Language Specification:
+ * any fractional part of this
+ * {@code BigDecimal} will be discarded, and if the resulting
+ * "{@code BigInteger}" is too big to fit in a
+ * {@code long}, only the low-order 64 bits are returned.
+ * Note that this conversion can lose information about the
+ * overall magnitude and precision of this {@code BigDecimal} value as well
+ * as return a result with the opposite sign.
+ *
+ * @return this {@code BigDecimal} converted to a {@code long}.
+ */
+ public long longValue(){
+ return (intCompact != INFLATED && scale == 0) ?
+ intCompact:
+ toBigInteger().longValue();
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to a {@code long}, checking
+ * for lost information. If this {@code BigDecimal} has a
+ * nonzero fractional part or is out of the possible range for a
+ * {@code long} result then an {@code ArithmeticException} is
+ * thrown.
+ *
+ * @return this {@code BigDecimal} converted to a {@code long}.
+ * @throws ArithmeticException if {@code this} has a nonzero
+ * fractional part, or will not fit in a {@code long}.
+ * @since 1.5
+ */
+ public long longValueExact() {
+ if (intCompact != INFLATED && scale == 0)
+ return intCompact;
+ // If more than 19 digits in integer part it cannot possibly fit
+ if ((precision() - scale) > 19) // [OK for negative scale too]
+ throw new java.lang.ArithmeticException("Overflow");
+ // Fastpath zero and < 1.0 numbers (the latter can be very slow
+ // to round if very small)
+ if (this.signum() == 0)
+ return 0;
+ if ((this.precision() - this.scale) <= 0)
+ throw new ArithmeticException("Rounding necessary");
+ // round to an integer, with Exception if decimal part non-0
+ BigDecimal num = this.setScale(0, ROUND_UNNECESSARY);
+ if (num.precision() >= 19) // need to check carefully
+ LongOverflow.check(num);
+ return num.inflate().longValue();
+ }
+
+ private static class LongOverflow {
+ /** BigInteger equal to Long.MIN_VALUE. */
+ private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE);
+
+ /** BigInteger equal to Long.MAX_VALUE. */
+ private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE);
+
+ public static void check(BigDecimal num) {
+ num.inflate();
+ if ((num.intVal.compareTo(LONGMIN) < 0) ||
+ (num.intVal.compareTo(LONGMAX) > 0))
+ throw new java.lang.ArithmeticException("Overflow");
+ }
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to an {@code int}.
+ * This conversion is analogous to the
+ * narrowing primitive conversion from {@code double} to
+ * {@code short} as defined in section 5.1.3 of
+ * The Java™ Language Specification:
+ * any fractional part of this
+ * {@code BigDecimal} will be discarded, and if the resulting
+ * "{@code BigInteger}" is too big to fit in an
+ * {@code int}, only the low-order 32 bits are returned.
+ * Note that this conversion can lose information about the
+ * overall magnitude and precision of this {@code BigDecimal}
+ * value as well as return a result with the opposite sign.
+ *
+ * @return this {@code BigDecimal} converted to an {@code int}.
+ */
+ public int intValue() {
+ return (intCompact != INFLATED && scale == 0) ?
+ (int)intCompact :
+ toBigInteger().intValue();
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to an {@code int}, checking
+ * for lost information. If this {@code BigDecimal} has a
+ * nonzero fractional part or is out of the possible range for an
+ * {@code int} result then an {@code ArithmeticException} is
+ * thrown.
+ *
+ * @return this {@code BigDecimal} converted to an {@code int}.
+ * @throws ArithmeticException if {@code this} has a nonzero
+ * fractional part, or will not fit in an {@code int}.
+ * @since 1.5
+ */
+ public int intValueExact() {
+ long num;
+ num = this.longValueExact(); // will check decimal part
+ if ((int)num != num)
+ throw new java.lang.ArithmeticException("Overflow");
+ return (int)num;
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to a {@code short}, checking
+ * for lost information. If this {@code BigDecimal} has a
+ * nonzero fractional part or is out of the possible range for a
+ * {@code short} result then an {@code ArithmeticException} is
+ * thrown.
+ *
+ * @return this {@code BigDecimal} converted to a {@code short}.
+ * @throws ArithmeticException if {@code this} has a nonzero
+ * fractional part, or will not fit in a {@code short}.
+ * @since 1.5
+ */
+ public short shortValueExact() {
+ long num;
+ num = this.longValueExact(); // will check decimal part
+ if ((short)num != num)
+ throw new java.lang.ArithmeticException("Overflow");
+ return (short)num;
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to a {@code byte}, checking
+ * for lost information. If this {@code BigDecimal} has a
+ * nonzero fractional part or is out of the possible range for a
+ * {@code byte} result then an {@code ArithmeticException} is
+ * thrown.
+ *
+ * @return this {@code BigDecimal} converted to a {@code byte}.
+ * @throws ArithmeticException if {@code this} has a nonzero
+ * fractional part, or will not fit in a {@code byte}.
+ * @since 1.5
+ */
+ public byte byteValueExact() {
+ long num;
+ num = this.longValueExact(); // will check decimal part
+ if ((byte)num != num)
+ throw new java.lang.ArithmeticException("Overflow");
+ return (byte)num;
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to a {@code float}.
+ * This conversion is similar to the
+ * narrowing primitive conversion from {@code double} to
+ * {@code float} as defined in section 5.1.3 of
+ * The Java™ Language Specification:
+ * if this {@code BigDecimal} has too great a
+ * magnitude to represent as a {@code float}, it will be
+ * converted to {@link Float#NEGATIVE_INFINITY} or {@link
+ * Float#POSITIVE_INFINITY} as appropriate. Note that even when
+ * the return value is finite, this conversion can lose
+ * information about the precision of the {@code BigDecimal}
+ * value.
+ *
+ * @return this {@code BigDecimal} converted to a {@code float}.
+ */
+ public float floatValue(){
+ if (scale == 0 && intCompact != INFLATED)
+ return (float)intCompact;
+ // Somewhat inefficient, but guaranteed to work.
+ return Float.parseFloat(this.toString());
+ }
+
+ /**
+ * Converts this {@code BigDecimal} to a {@code double}.
+ * This conversion is similar to the
+ * narrowing primitive conversion from {@code double} to
+ * {@code float} as defined in section 5.1.3 of
+ * The Java™ Language Specification:
+ * if this {@code BigDecimal} has too great a
+ * magnitude represent as a {@code double}, it will be
+ * converted to {@link Double#NEGATIVE_INFINITY} or {@link
+ * Double#POSITIVE_INFINITY} as appropriate. Note that even when
+ * the return value is finite, this conversion can lose
+ * information about the precision of the {@code BigDecimal}
+ * value.
+ *
+ * @return this {@code BigDecimal} converted to a {@code double}.
+ */
+ public double doubleValue(){
+ if (scale == 0 && intCompact != INFLATED)
+ return (double)intCompact;
+ // Somewhat inefficient, but guaranteed to work.
+ return Double.parseDouble(this.toString());
+ }
+
+ /**
+ * Returns the size of an ulp, a unit in the last place, of this
+ * {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal}
+ * value is the positive distance between this value and the
+ * {@code BigDecimal} value next larger in magnitude with the
+ * same number of digits. An ulp of a zero value is numerically
+ * equal to 1 with the scale of {@code this}. The result is
+ * stored with the same scale as {@code this} so the result
+ * for zero and nonzero values is equal to {@code [1,
+ * this.scale()]}.
+ *
+ * @return the size of an ulp of {@code this}
+ * @since 1.5
+ */
+ public BigDecimal ulp() {
+ return BigDecimal.valueOf(1, this.scale());
+ }
+
+
+ // Private class to build a string representation for BigDecimal object.
+ // "StringBuilderHelper" is constructed as a thread local variable so it is
+ // thread safe. The StringBuilder field acts as a buffer to hold the temporary
+ // representation of BigDecimal. The cmpCharArray holds all the characters for
+ // the compact representation of BigDecimal (except for '-' sign' if it is
+ // negative) if its intCompact field is not INFLATED. It is shared by all
+ // calls to toString() and its variants in that particular thread.
+ static class StringBuilderHelper {
+ final StringBuilder sb; // Placeholder for BigDecimal string
+ final char[] cmpCharArray; // character array to place the intCompact
+
+ StringBuilderHelper() {
+ sb = new StringBuilder();
+ // All non negative longs can be made to fit into 19 character array.
+ cmpCharArray = new char[19];
+ }
+
+ // Accessors.
+ StringBuilder getStringBuilder() {
+ sb.setLength(0);
+ return sb;
+ }
+
+ char[] getCompactCharArray() {
+ return cmpCharArray;
+ }
+
+ /**
+ * Places characters representing the intCompact in {@code long} into
+ * cmpCharArray and returns the offset to the array where the
+ * representation starts.
+ *
+ * @param intCompact the number to put into the cmpCharArray.
+ * @return offset to the array where the representation starts.
+ * Note: intCompact must be greater or equal to zero.
+ */
+ int putIntCompact(long intCompact) {
+ assert intCompact >= 0;
+
+ long q;
+ int r;
+ // since we start from the least significant digit, charPos points to
+ // the last character in cmpCharArray.
+ int charPos = cmpCharArray.length;
+
+ // Get 2 digits/iteration using longs until quotient fits into an int
+ while (intCompact > Integer.MAX_VALUE) {
+ q = intCompact / 100;
+ r = (int)(intCompact - q * 100);
+ intCompact = q;
+ cmpCharArray[--charPos] = DIGIT_ONES[r];
+ cmpCharArray[--charPos] = DIGIT_TENS[r];
+ }
+
+ // Get 2 digits/iteration using ints when i2 >= 100
+ int q2;
+ int i2 = (int)intCompact;
+ while (i2 >= 100) {
+ q2 = i2 / 100;
+ r = i2 - q2 * 100;
+ i2 = q2;
+ cmpCharArray[--charPos] = DIGIT_ONES[r];
+ cmpCharArray[--charPos] = DIGIT_TENS[r];
+ }
+
+ cmpCharArray[--charPos] = DIGIT_ONES[i2];
+ if (i2 >= 10)
+ cmpCharArray[--charPos] = DIGIT_TENS[i2];
+
+ return charPos;
+ }
+
+ final static char[] DIGIT_TENS = {
+ '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
+ '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
+ '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
+ '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
+ '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
+ '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
+ '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
+ '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
+ '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
+ '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
+ };
+
+ final static char[] DIGIT_ONES = {
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ };
+ }
+
+ /**
+ * Lay out this {@code BigDecimal} into a {@code char[]} array.
+ * The Java 1.2 equivalent to this was called {@code getValueString}.
+ *
+ * @param sci {@code true} for Scientific exponential notation;
+ * {@code false} for Engineering
+ * @return string with canonical string representation of this
+ * {@code BigDecimal}
+ */
+ private String layoutChars(boolean sci) {
+ if (scale == 0) // zero scale is trivial
+ return (intCompact != INFLATED) ?
+ Long.toString(intCompact):
+ intVal.toString();
+
+ StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get();
+ char[] coeff;
+ int offset; // offset is the starting index for coeff array
+ // Get the significand as an absolute value
+ if (intCompact != INFLATED) {
+ offset = sbHelper.putIntCompact(Math.abs(intCompact));
+ coeff = sbHelper.getCompactCharArray();
+ } else {
+ offset = 0;
+ coeff = intVal.abs().toString().toCharArray();
+ }
+
+ // Construct a buffer, with sufficient capacity for all cases.
+ // If E-notation is needed, length will be: +1 if negative, +1
+ // if '.' needed, +2 for "E+", + up to 10 for adjusted exponent.
+ // Otherwise it could have +1 if negative, plus leading "0.00000"
+ StringBuilder buf = sbHelper.getStringBuilder();
+ if (signum() < 0) // prefix '-' if negative
+ buf.append('-');
+ int coeffLen = coeff.length - offset;
+ long adjusted = -(long)scale + (coeffLen -1);
+ if ((scale >= 0) && (adjusted >= -6)) { // plain number
+ int pad = scale - coeffLen; // count of padding zeros
+ if (pad >= 0) { // 0.xxx form
+ buf.append('0');
+ buf.append('.');
+ for (; pad>0; pad--) {
+ buf.append('0');
+ }
+ buf.append(coeff, offset, coeffLen);
+ } else { // xx.xx form
+ buf.append(coeff, offset, -pad);
+ buf.append('.');
+ buf.append(coeff, -pad + offset, scale);
+ }
+ } else { // E-notation is needed
+ if (sci) { // Scientific notation
+ buf.append(coeff[offset]); // first character
+ if (coeffLen > 1) { // more to come
+ buf.append('.');
+ buf.append(coeff, offset + 1, coeffLen - 1);
+ }
+ } else { // Engineering notation
+ int sig = (int)(adjusted % 3);
+ if (sig < 0)
+ sig += 3; // [adjusted was negative]
+ adjusted -= sig; // now a multiple of 3
+ sig++;
+ if (signum() == 0) {
+ switch (sig) {
+ case 1:
+ buf.append('0'); // exponent is a multiple of three
+ break;
+ case 2:
+ buf.append("0.00");
+ adjusted += 3;
+ break;
+ case 3:
+ buf.append("0.0");
+ adjusted += 3;
+ break;
+ default:
+ throw new AssertionError("Unexpected sig value " + sig);
+ }
+ } else if (sig >= coeffLen) { // significand all in integer
+ buf.append(coeff, offset, coeffLen);
+ // may need some zeros, too
+ for (int i = sig - coeffLen; i > 0; i--)
+ buf.append('0');
+ } else { // xx.xxE form
+ buf.append(coeff, offset, sig);
+ buf.append('.');
+ buf.append(coeff, offset + sig, coeffLen - sig);
+ }
+ }
+ if (adjusted != 0) { // [!sci could have made 0]
+ buf.append('E');
+ if (adjusted > 0) // force sign for positive
+ buf.append('+');
+ buf.append(adjusted);
+ }
+ }
+ return buf.toString();
+ }
+
+ /**
+ * Return 10 to the power n, as a {@code BigInteger}.
+ *
+ * @param n the power of ten to be returned (>=0)
+ * @return a {@code BigInteger} with the value (10n)
+ */
+ private static BigInteger bigTenToThe(int n) {
+ if (n < 0)
+ return BigInteger.ZERO;
+
+ if (n < BIG_TEN_POWERS_TABLE_MAX) {
+ BigInteger[] pows = BIG_TEN_POWERS_TABLE;
+ if (n < pows.length)
+ return pows[n];
+ else
+ return expandBigIntegerTenPowers(n);
+ }
+ // BigInteger.pow is slow, so make 10**n by constructing a
+ // BigInteger from a character string (still not very fast)
+ char tenpow[] = new char[n + 1];
+ tenpow[0] = '1';
+ for (int i = 1; i <= n; i++)
+ tenpow[i] = '0';
+ return new BigInteger(tenpow);
+ }
+
+ /**
+ * Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n.
+ *
+ * @param n the power of ten to be returned (>=0)
+ * @return a {@code BigDecimal} with the value (10n) and
+ * in the meantime, the BIG_TEN_POWERS_TABLE array gets
+ * expanded to the size greater than n.
+ */
+ private static BigInteger expandBigIntegerTenPowers(int n) {
+ synchronized(BigDecimal.class) {
+ BigInteger[] pows = BIG_TEN_POWERS_TABLE;
+ int curLen = pows.length;
+ // The following comparison and the above synchronized statement is
+ // to prevent multiple threads from expanding the same array.
+ if (curLen <= n) {
+ int newLen = curLen << 1;
+ while (newLen <= n)
+ newLen <<= 1;
+ pows = Arrays.copyOf(pows, newLen);
+ for (int i = curLen; i < newLen; i++)
+ pows[i] = pows[i - 1].multiply(BigInteger.TEN);
+ // Based on the following facts:
+ // 1. pows is a private local varible;
+ // 2. the following store is a volatile store.
+ // the newly created array elements can be safely published.
+ BIG_TEN_POWERS_TABLE = pows;
+ }
+ return pows[n];
+ }
+ }
+
+ private static final long[] LONG_TEN_POWERS_TABLE = {
+ 1, // 0 / 10^0
+ 10, // 1 / 10^1
+ 100, // 2 / 10^2
+ 1000, // 3 / 10^3
+ 10000, // 4 / 10^4
+ 100000, // 5 / 10^5
+ 1000000, // 6 / 10^6
+ 10000000, // 7 / 10^7
+ 100000000, // 8 / 10^8
+ 1000000000, // 9 / 10^9
+ 10000000000L, // 10 / 10^10
+ 100000000000L, // 11 / 10^11
+ 1000000000000L, // 12 / 10^12
+ 10000000000000L, // 13 / 10^13
+ 100000000000000L, // 14 / 10^14
+ 1000000000000000L, // 15 / 10^15
+ 10000000000000000L, // 16 / 10^16
+ 100000000000000000L, // 17 / 10^17
+ 1000000000000000000L // 18 / 10^18
+ };
+
+ private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = {BigInteger.ONE,
+ BigInteger.valueOf(10), BigInteger.valueOf(100),
+ BigInteger.valueOf(1000), BigInteger.valueOf(10000),
+ BigInteger.valueOf(100000), BigInteger.valueOf(1000000),
+ BigInteger.valueOf(10000000), BigInteger.valueOf(100000000),
+ BigInteger.valueOf(1000000000),
+ BigInteger.valueOf(10000000000L),
+ BigInteger.valueOf(100000000000L),
+ BigInteger.valueOf(1000000000000L),
+ BigInteger.valueOf(10000000000000L),
+ BigInteger.valueOf(100000000000000L),
+ BigInteger.valueOf(1000000000000000L),
+ BigInteger.valueOf(10000000000000000L),
+ BigInteger.valueOf(100000000000000000L),
+ BigInteger.valueOf(1000000000000000000L)
+ };
+
+ private static final int BIG_TEN_POWERS_TABLE_INITLEN =
+ BIG_TEN_POWERS_TABLE.length;
+ private static final int BIG_TEN_POWERS_TABLE_MAX =
+ 16 * BIG_TEN_POWERS_TABLE_INITLEN;
+
+ private static final long THRESHOLDS_TABLE[] = {
+ Long.MAX_VALUE, // 0
+ Long.MAX_VALUE/10L, // 1
+ Long.MAX_VALUE/100L, // 2
+ Long.MAX_VALUE/1000L, // 3
+ Long.MAX_VALUE/10000L, // 4
+ Long.MAX_VALUE/100000L, // 5
+ Long.MAX_VALUE/1000000L, // 6
+ Long.MAX_VALUE/10000000L, // 7
+ Long.MAX_VALUE/100000000L, // 8
+ Long.MAX_VALUE/1000000000L, // 9
+ Long.MAX_VALUE/10000000000L, // 10
+ Long.MAX_VALUE/100000000000L, // 11
+ Long.MAX_VALUE/1000000000000L, // 12
+ Long.MAX_VALUE/10000000000000L, // 13
+ Long.MAX_VALUE/100000000000000L, // 14
+ Long.MAX_VALUE/1000000000000000L, // 15
+ Long.MAX_VALUE/10000000000000000L, // 16
+ Long.MAX_VALUE/100000000000000000L, // 17
+ Long.MAX_VALUE/1000000000000000000L // 18
+ };
+
+ /**
+ * Compute val * 10 ^ n; return this product if it is
+ * representable as a long, INFLATED otherwise.
+ */
+ private static long longMultiplyPowerTen(long val, int n) {
+ if (val == 0 || n <= 0)
+ return val;
+ long[] tab = LONG_TEN_POWERS_TABLE;
+ long[] bounds = THRESHOLDS_TABLE;
+ if (n < tab.length && n < bounds.length) {
+ long tenpower = tab[n];
+ if (val == 1)
+ return tenpower;
+ if (Math.abs(val) <= bounds[n])
+ return val * tenpower;
+ }
+ return INFLATED;
+ }
+
+ /**
+ * Compute this * 10 ^ n.
+ * Needed mainly to allow special casing to trap zero value
+ */
+ private BigInteger bigMultiplyPowerTen(int n) {
+ if (n <= 0)
+ return this.inflate();
+
+ if (intCompact != INFLATED)
+ return bigTenToThe(n).multiply(intCompact);
+ else
+ return intVal.multiply(bigTenToThe(n));
+ }
+
+ /**
+ * Assign appropriate BigInteger to intVal field if intVal is
+ * null, i.e. the compact representation is in use.
+ */
+ private BigInteger inflate() {
+ if (intVal == null)
+ intVal = BigInteger.valueOf(intCompact);
+ return intVal;
+ }
+
+ /**
+ * Match the scales of two {@code BigDecimal}s to align their
+ * least significant digits.
+ *
+ * If the scales of val[0] and val[1] differ, rescale
+ * (non-destructively) the lower-scaled {@code BigDecimal} so
+ * they match. That is, the lower-scaled reference will be
+ * replaced by a reference to a new object with the same scale as
+ * the other {@code BigDecimal}.
+ *
+ * @param val array of two elements referring to the two
+ * {@code BigDecimal}s to be aligned.
+ */
+ private static void matchScale(BigDecimal[] val) {
+ if (val[0].scale == val[1].scale) {
+ return;
+ } else if (val[0].scale < val[1].scale) {
+ val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY);
+ } else if (val[1].scale < val[0].scale) {
+ val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY);
+ }
+ }
+
+ /**
+ * Reconstitute the {@code BigDecimal} instance from a stream (that is,
+ * deserialize it).
+ *
+ * @param s the stream being read.
+ */
+ private void readObject(java.io.ObjectInputStream s)
+ throws java.io.IOException, ClassNotFoundException {
+ // Read in all fields
+ s.defaultReadObject();
+ // validate possibly bad fields
+ if (intVal == null) {
+ String message = "BigDecimal: null intVal in stream";
+ throw new java.io.StreamCorruptedException(message);
+ // [all values of scale are now allowed]
+ }
+ intCompact = compactValFor(intVal);
+ }
+
+ /**
+ * Serialize this {@code BigDecimal} to the stream in question
+ *
+ * @param s the stream to serialize to.
+ */
+ private void writeObject(java.io.ObjectOutputStream s)
+ throws java.io.IOException {
+ // Must inflate to maintain compatible serial form.
+ this.inflate();
+
+ // Write proper fields
+ s.defaultWriteObject();
+ }
+
+
+ /**
+ * Returns the length of the absolute value of a {@code long}, in decimal
+ * digits.
+ *
+ * @param x the {@code long}
+ * @return the length of the unscaled value, in deciaml digits.
+ */
+ private static int longDigitLength(long x) {
+ /*
+ * As described in "Bit Twiddling Hacks" by Sean Anderson,
+ * (http://graphics.stanford.edu/~seander/bithacks.html)
+ * integer log 10 of x is within 1 of
+ * (1233/4096)* (1 + integer log 2 of x).
+ * The fraction 1233/4096 approximates log10(2). So we first
+ * do a version of log2 (a variant of Long class with
+ * pre-checks and opposite directionality) and then scale and
+ * check against powers table. This is a little simpler in
+ * present context than the version in Hacker's Delight sec
+ * 11-4. Adding one to bit length allows comparing downward
+ * from the LONG_TEN_POWERS_TABLE that we need anyway.
+ */
+ assert x != INFLATED;
+ if (x < 0)
+ x = -x;
+ if (x < 10) // must screen for 0, might as well 10
+ return 1;
+ int n = 64; // not 63, to avoid needing to add 1 later
+ int y = (int)(x >>> 32);
+ if (y == 0) { n -= 32; y = (int)x; }
+ if (y >>> 16 == 0) { n -= 16; y <<= 16; }
+ if (y >>> 24 == 0) { n -= 8; y <<= 8; }
+ if (y >>> 28 == 0) { n -= 4; y <<= 4; }
+ if (y >>> 30 == 0) { n -= 2; y <<= 2; }
+ int r = (((y >>> 31) + n) * 1233) >>> 12;
+ long[] tab = LONG_TEN_POWERS_TABLE;
+ // if r >= length, must have max possible digits for long
+ return (r >= tab.length || x < tab[r])? r : r+1;
+ }
+
+ /**
+ * Returns the length of the absolute value of a BigInteger, in
+ * decimal digits.
+ *
+ * @param b the BigInteger
+ * @return the length of the unscaled value, in decimal digits
+ */
+ private static int bigDigitLength(BigInteger b) {
+ /*
+ * Same idea as the long version, but we need a better
+ * approximation of log10(2). Using 646456993/2^31
+ * is accurate up to max possible reported bitLength.
+ */
+ if (b.signum == 0)
+ return 1;
+ int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31);
+ return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1;
+ }
+
+
+ /**
+ * Remove insignificant trailing zeros from this
+ * {@code BigDecimal} until the preferred scale is reached or no
+ * more zeros can be removed. If the preferred scale is less than
+ * Integer.MIN_VALUE, all the trailing zeros will be removed.
+ *
+ * {@code BigInteger} assistance could help, here?
+ *
+ * WARNING: This method should only be called on new objects as
+ * it mutates the value fields.
+ *
+ * @return this {@code BigDecimal} with a scale possibly reduced
+ * to be closed to the preferred scale.
+ */
+ private BigDecimal stripZerosToMatchScale(long preferredScale) {
+ this.inflate();
+ BigInteger qr[]; // quotient-remainder pair
+ while ( intVal.compareMagnitude(BigInteger.TEN) >= 0 &&
+ scale > preferredScale) {
+ if (intVal.testBit(0))
+ break; // odd number cannot end in 0
+ qr = intVal.divideAndRemainder(BigInteger.TEN);
+ if (qr[1].signum() != 0)
+ break; // non-0 remainder
+ intVal=qr[0];
+ scale = checkScale((long)scale-1); // could Overflow
+ if (precision > 0) // adjust precision if known
+ precision--;
+ }
+ if (intVal != null)
+ intCompact = compactValFor(intVal);
+ return this;
+ }
+
+ /**
+ * Check a scale for Underflow or Overflow. If this BigDecimal is
+ * nonzero, throw an exception if the scale is outof range. If this
+ * is zero, saturate the scale to the extreme value of the right
+ * sign if the scale is out of range.
+ *
+ * @param val The new scale.
+ * @throws ArithmeticException (overflow or underflow) if the new
+ * scale is out of range.
+ * @return validated scale as an int.
+ */
+ private int checkScale(long val) {
+ int asInt = (int)val;
+ if (asInt != val) {
+ asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE;
+ BigInteger b;
+ if (intCompact != 0 &&
+ ((b = intVal) == null || b.signum() != 0))
+ throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow");
+ }
+ return asInt;
+ }
+
+ /**
+ * Round an operand; used only if digits > 0. Does not change
+ * {@code this}; if rounding is needed a new {@code BigDecimal}
+ * is created and returned.
+ *
+ * @param mc the context to use.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ */
+ private BigDecimal roundOp(MathContext mc) {
+ BigDecimal rounded = doRound(this, mc);
+ return rounded;
+ }
+
+ /** Round this BigDecimal according to the MathContext settings;
+ * used only if precision {@literal >} 0.
+ *
+ * WARNING: This method should only be called on new objects as
+ * it mutates the value fields.
+ *
+ * @param mc the context to use.
+ * @throws ArithmeticException if the rounding mode is
+ * {@code RoundingMode.UNNECESSARY} and the
+ * {@code BigDecimal} operation would require rounding.
+ */
+ private void roundThis(MathContext mc) {
+ BigDecimal rounded = doRound(this, mc);
+ if (rounded == this) // wasn't rounded
+ return;
+ this.intVal = rounded.intVal;
+ this.intCompact = rounded.intCompact;
+ this.scale = rounded.scale;
+ this.precision = rounded.precision;
+ }
+
+ /**
+ * Returns a {@code BigDecimal} rounded according to the
+ * MathContext settings; used only if {@code mc.precision > 0}.
+ * Does not change {@code this}; if rounding is needed a new
+ * {@code BigDecimal} is created and returned.
+ *
+ * @param mc the context to use.
+ * @return a {@code BigDecimal} rounded according to the MathContext
+ * settings. May return this, if no rounding needed.
+ * @throws ArithmeticException if the rounding mode is
+ * {@code RoundingMode.UNNECESSARY} and the
+ * result is inexact.
+ */
+ private static BigDecimal doRound(BigDecimal d, MathContext mc) {
+ int mcp = mc.precision;
+ int drop;
+ // This might (rarely) iterate to cover the 999=>1000 case
+ while ((drop = d.precision() - mcp) > 0) {
+ int newScale = d.checkScale((long)d.scale - drop);
+ int mode = mc.roundingMode.oldMode;
+ if (drop < LONG_TEN_POWERS_TABLE.length)
+ d = divideAndRound(d.intCompact, d.intVal,
+ LONG_TEN_POWERS_TABLE[drop], null,
+ newScale, mode, newScale);
+ else
+ d = divideAndRound(d.intCompact, d.intVal,
+ INFLATED, bigTenToThe(drop),
+ newScale, mode, newScale);
+ }
+ return d;
+ }
+
+ /**
+ * Returns the compact value for given {@code BigInteger}, or
+ * INFLATED if too big. Relies on internal representation of
+ * {@code BigInteger}.
+ */
+ private static long compactValFor(BigInteger b) {
+ int[] m = b.mag;
+ int len = m.length;
+ if (len == 0)
+ return 0;
+ int d = m[0];
+ if (len > 2 || (len == 2 && d < 0))
+ return INFLATED;
+
+ long u = (len == 2)?
+ (((long) m[1] & LONG_MASK) + (((long)d) << 32)) :
+ (((long)d) & LONG_MASK);
+ return (b.signum < 0)? -u : u;
+ }
+
+ private static int longCompareMagnitude(long x, long y) {
+ if (x < 0)
+ x = -x;
+ if (y < 0)
+ y = -y;
+ return (x < y) ? -1 : ((x == y) ? 0 : 1);
+ }
+
+ private static int saturateLong(long s) {
+ int i = (int)s;
+ return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE);
+ }
+
+ /*
+ * Internal printing routine
+ */
+ private static void print(String name, BigDecimal bd) {
+ System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n",
+ name,
+ bd.intCompact,
+ bd.intVal,
+ bd.scale,
+ bd.precision);
+ }
+
+ /**
+ * Check internal invariants of this BigDecimal. These invariants
+ * include:
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ * The value of the returned {@code BigDecimal} is equal to
+ * significand × 10 exponent.
+ * For each string on the left, the resulting representation
+ * [{@code BigInteger}, {@code scale}] is shown on the right.
+ *
+ * "0" [0,0]
+ * "0.00" [0,2]
+ * "123" [123,0]
+ * "-123" [-123,0]
+ * "1.23E3" [123,-1]
+ * "1.23E+3" [123,-1]
+ * "12.3E+7" [123,-6]
+ * "12.0" [120,1]
+ * "12.3" [123,1]
+ * "0.00123" [123,5]
+ * "-1.23E-12" [-123,14]
+ * "1234.5E-4" [12345,5]
+ * "0E+7" [0,-7]
+ * "-0" [0,0]
+ *
+ *
+ *
+ *
+ *
+ * @param val {@code double} value to be converted to
+ * {@code BigDecimal}.
+ * @throws NumberFormatException if {@code val} is infinite or NaN.
+ */
+ public BigDecimal(double val) {
+ if (Double.isInfinite(val) || Double.isNaN(val))
+ throw new NumberFormatException("Infinite or NaN");
+
+ // Translate the double into sign, exponent and significand, according
+ // to the formulae in JLS, Section 20.10.22.
+ long valBits = Double.doubleToLongBits(val);
+ int sign = ((valBits >> 63)==0 ? 1 : -1);
+ int exponent = (int) ((valBits >> 52) & 0x7ffL);
+ long significand = (exponent==0 ? (valBits & ((1L<<52) - 1)) << 1
+ : (valBits & ((1L<<52) - 1)) | (1L<<52));
+ exponent -= 1075;
+ // At this point, val == sign * significand * 2**exponent.
+
+ /*
+ * Special case zero to supress nonterminating normalization
+ * and bogus scale calculation.
+ */
+ if (significand == 0) {
+ intVal = BigInteger.ZERO;
+ intCompact = 0;
+ precision = 1;
+ return;
+ }
+
+ // Normalize
+ while((significand & 1) == 0) { // i.e., significand is even
+ significand >>= 1;
+ exponent++;
+ }
+
+ // Calculate intVal and scale
+ long s = sign * significand;
+ BigInteger b;
+ if (exponent < 0) {
+ b = BigInteger.valueOf(5).pow(-exponent).multiply(s);
+ scale = -exponent;
+ } else if (exponent > 0) {
+ b = BigInteger.valueOf(2).pow(exponent).multiply(s);
+ } else {
+ b = BigInteger.valueOf(s);
+ }
+ intCompact = compactValFor(b);
+ intVal = (intCompact != INFLATED) ? null : b;
+ }
+
+ /**
+ * Translates a {@code double} into a {@code BigDecimal}, with
+ * rounding according to the context settings. The scale of the
+ * {@code BigDecimal} is the smallest value such that
+ * (10scale × val) is an integer.
+ *
+ *
+ *
+ *
+ * @param n power to raise this {@code BigDecimal} to.
+ * @param mc the context to use.
+ * @return thisn using the ANSI standard X3.274-1996
+ * algorithm
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}, or {@code n} is out
+ * of range.
+ * @since 1.5
+ */
+ public BigDecimal pow(int n, MathContext mc) {
+ if (mc.precision == 0)
+ return pow(n);
+ if (n < -999999999 || n > 999999999)
+ throw new ArithmeticException("Invalid operation");
+ if (n == 0)
+ return ONE; // x**0 == 1 in X3.274
+ this.inflate();
+ BigDecimal lhs = this;
+ MathContext workmc = mc; // working settings
+ int mag = Math.abs(n); // magnitude of n
+ if (mc.precision > 0) {
+
+ int elength = longDigitLength(mag); // length of n in digits
+ if (elength > mc.precision) // X3.274 rule
+ throw new ArithmeticException("Invalid operation");
+ workmc = new MathContext(mc.precision + elength + 1,
+ mc.roundingMode);
+ }
+ // ready to carry out power calculation...
+ BigDecimal acc = ONE; // accumulator
+ boolean seenbit = false; // set once we've seen a 1-bit
+ for (int i=1;;i++) { // for each bit [top bit ignored]
+ mag += mag; // shift left 1 bit
+ if (mag < 0) { // top bit is set
+ seenbit = true; // OK, we're off
+ acc = acc.multiply(lhs, workmc); // acc=acc*x
+ }
+ if (i == 31)
+ break; // that was the last bit
+ if (seenbit)
+ acc=acc.multiply(acc, workmc); // acc=acc*acc [square]
+ // else (!seenbit) no point in squaring ONE
+ }
+ // if negative n, calculate the reciprocal using working precision
+ if (n<0) // [hence mc.precision>0]
+ acc=ONE.divide(acc, workmc);
+ // round to final precision and strip zeros
+ return doRound(acc, mc);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is the absolute value
+ * of this {@code BigDecimal}, and whose scale is
+ * {@code this.scale()}.
+ *
+ * @return {@code abs(this)}
+ */
+ public BigDecimal abs() {
+ return (signum() < 0 ? negate() : this);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is the absolute value
+ * of this {@code BigDecimal}, with rounding according to the
+ * context settings.
+ *
+ * @param mc the context to use.
+ * @return {@code abs(this)}, rounded as necessary.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @since 1.5
+ */
+ public BigDecimal abs(MathContext mc) {
+ return (signum() < 0 ? negate(mc) : plus(mc));
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (-this)},
+ * and whose scale is {@code this.scale()}.
+ *
+ * @return {@code -this}.
+ */
+ public BigDecimal negate() {
+ BigDecimal result;
+ if (intCompact != INFLATED)
+ result = BigDecimal.valueOf(-intCompact, scale);
+ else {
+ result = new BigDecimal(intVal.negate(), scale);
+ result.precision = precision;
+ }
+ return result;
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (-this)},
+ * with rounding according to the context settings.
+ *
+ * @param mc the context to use.
+ * @return {@code -this}, rounded as necessary.
+ * @throws ArithmeticException if the result is inexact but the
+ * rounding mode is {@code UNNECESSARY}.
+ * @since 1.5
+ */
+ public BigDecimal negate(MathContext mc) {
+ return negate().plus(mc);
+ }
+
+ /**
+ * Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose
+ * scale is {@code this.scale()}.
+ *
+ *
+ *
+ *
+ *
+ *
+ *
+ * [123,0] "123"
+ * [-123,0] "-123"
+ * [123,-1] "1.23E+3"
+ * [123,-3] "1.23E+5"
+ * [123,1] "12.3"
+ * [123,5] "0.00123"
+ * [123,10] "1.23E-8"
+ * [-123,12] "-1.23E-10"
+ *
+ *
+ * Notes:
+ *
+ *
+ *
+ *
+ * @return string representation of this {@code BigDecimal}.
+ * @see Character#forDigit
+ * @see #BigDecimal(java.lang.String)
+ */
+ @Override
+ public String toString() {
+ String sc = stringCache;
+ if (sc == null)
+ stringCache = sc = layoutChars(true);
+ return sc;
+ }
+
+ /**
+ * Returns a string representation of this {@code BigDecimal},
+ * using engineering notation if an exponent is needed.
+ *
+ *
+ *
+ *
+ *
+ * Note: Since this is an audit method, we are not supposed to change the
+ * state of this BigDecimal object.
+ */
+ private BigDecimal audit() {
+ if (intCompact == INFLATED) {
+ if (intVal == null) {
+ print("audit", this);
+ throw new AssertionError("null intVal");
+ }
+ // Check precision
+ if (precision > 0 && precision != bigDigitLength(intVal)) {
+ print("audit", this);
+ throw new AssertionError("precision mismatch");
+ }
+ } else {
+ if (intVal != null) {
+ long val = intVal.longValue();
+ if (val != intCompact) {
+ print("audit", this);
+ throw new AssertionError("Inconsistent state, intCompact=" +
+ intCompact + "\t intVal=" + val);
+ }
+ }
+ // Check precision
+ if (precision > 0 && precision != longDigitLength(intCompact)) {
+ print("audit", this);
+ throw new AssertionError("precision mismatch");
+ }
+ }
+ return this;
+ }
+}