/*
* Copyright (c) 1996, 2019, Oracle and/or its affiliates. All rights reserved.
* ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
/*
* Portions Copyright IBM Corporation, 2001. All Rights Reserved.
*/
package java.math;
import static java.math.
BigInteger.
LONG_MASK;
import java.util.
Arrays;
/**
* Immutable, arbitrary-precision signed decimal numbers. A
* {@code BigDecimal} consists of an arbitrary precision integer
* <i>unscaled value</i> and a 32-bit integer <i>scale</i>. 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. The
* value of the number represented by the {@code BigDecimal} is
* therefore <tt>(unscaledValue × 10<sup>-scale</sup>)</tt>.
*
* <p>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}.
*
* <p>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 <em>rounding
* modes</em> 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.
*
* <p>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.
*
* <p>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}.
*
* <p>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.
*
*
* <p>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 <i>precision</i>. 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.
*
* <p>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
* 100×10<sup>1</sup>. In such cases, the new {@literal "1"} is
* the leading digit position of the returned result.
*
* <p>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.
*
* <table border>
* <caption><b>Preferred Scales for Results of Arithmetic Operations
* </b></caption>
* <tr><th>Operation</th><th>Preferred Scale of Result</th></tr>
* <tr><td>Add</td><td>max(addend.scale(), augend.scale())</td>
* <tr><td>Subtract</td><td>max(minuend.scale(), subtrahend.scale())</td>
* <tr><td>Multiply</td><td>multiplier.scale() + multiplicand.scale()</td>
* <tr><td>Divide</td><td>dividend.scale() - divisor.scale()</td>
* </table>
*
* These scales are the ones used by the methods which return exact
* arithmetic results; except that an exact divide may have to use a
* larger scale since the exact result may have more digits. For
* example, {@code 1/32} is {@code 0.03125}.
*
* <p>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, <br>
*
* {@code 19/100 = 0.19 // integer=19, scale=2} <br>
*
* but<br>
*
* {@code 21/110 = 0.190 // integer=190, scale=3} <br>
*
* <p>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.
*
* <p>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 <i>{@linkplain #ulp() ulp}</i>.
*
* <p>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.
*
* <p>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.
*
* <p>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 <i>natural ordering</i> is <i>inconsistent
* with equals</i>. See {@link Comparable}, {@link
* java.util.SortedMap} or {@link java.util.SortedSet} for more
* information.
*
* <p>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
* @author Sergey V. Kuksenko
*/
public class
BigDecimal extends
Number implements
Comparable<
BigDecimal> {
/**
* The unscaled value of this BigDecimal, as returned by {@link
* #unscaledValue}.
*
* @serial
* @see #unscaledValue
*/
private final
BigInteger intVal;
/**
* The scale of this BigDecimal, as returned by {@link #scale}.
*
* @serial
* @see #scale
*/
private final int
scale; // Note: this may have any value, so
// calculations must be done in longs
/**
* The number of decimal digits in this BigDecimal, or 0 if the
* number of digits are not known (lookaside information). If
* nonzero, the value is guaranteed correct. Use the precision()
* method to obtain and set the value if it might be 0. This
* field is mutable until set nonzero.
*
* @since 1.5
*/
private transient int
precision;
/**
* Used to store the canonical string representation, if computed.
*/
private transient
String stringCache;
/**
* Sentinel value for {@link #intCompact} indicating the
* significand information is only available from {@code intVal}.
*/
static final long
INFLATED =
Long.
MIN_VALUE;
private static final
BigInteger INFLATED_BIGINT =
BigInteger.
valueOf(
INFLATED);
/**
* If the absolute value of the significand of this BigDecimal is
* less than or equal to {@code Long.MAX_VALUE}, the value can be
* compactly stored in this field and used in computations.
*/
private final transient long
intCompact;
// All 18-digit base ten strings fit into a long; not all 19-digit
// strings will
private static final int
MAX_COMPACT_DIGITS = 18;
/* Appease the serialization gods */
private static final long
serialVersionUID = 6108874887143696463L;
private static final
ThreadLocal<
StringBuilderHelper>
threadLocalStringBuilderHelper = new
ThreadLocal<
StringBuilderHelper>() {
@
Override
protected
StringBuilderHelper initialValue() {
return new
StringBuilderHelper();
}
};
// Cache of common small BigDecimal values.
private static final
BigDecimal zeroThroughTen[] = {
new
BigDecimal(
BigInteger.
ZERO, 0, 0, 1),
new
BigDecimal(
BigInteger.
ONE, 1, 0, 1),
new
BigDecimal(
BigInteger.
valueOf(2), 2, 0, 1),
new
BigDecimal(
BigInteger.
valueOf(3), 3, 0, 1),
new
BigDecimal(
BigInteger.
valueOf(4), 4, 0, 1),
new
BigDecimal(
BigInteger.
valueOf(5), 5, 0, 1),
new
BigDecimal(
BigInteger.
valueOf(6), 6, 0, 1),
new
BigDecimal(
BigInteger.
valueOf(7), 7, 0, 1),
new
BigDecimal(
BigInteger.
valueOf(8), 8, 0, 1),
new
BigDecimal(
BigInteger.
valueOf(9), 9, 0, 1),
new
BigDecimal(
BigInteger.
TEN, 10, 0, 2),
};
// Cache of zero scaled by 0 - 15
private static final
BigDecimal[]
ZERO_SCALED_BY = {
zeroThroughTen[0],
new
BigDecimal(
BigInteger.
ZERO, 0, 1, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 2, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 3, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 4, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 5, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 6, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 7, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 8, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 9, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 10, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 11, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 12, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 13, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 14, 1),
new
BigDecimal(
BigInteger.
ZERO, 0, 15, 1),
};
// Half of Long.MIN_VALUE & Long.MAX_VALUE.
private static final long
HALF_LONG_MAX_VALUE =
Long.
MAX_VALUE / 2;
private static final long
HALF_LONG_MIN_VALUE =
Long.
MIN_VALUE / 2;
// Constants
/**
* The value 0, with a scale of 0.
*
* @since 1.5
*/
public static final
BigDecimal ZERO =
zeroThroughTen[0];
/**
* The value 1, with a scale of 0.
*
* @since 1.5
*/
public static final
BigDecimal ONE =
zeroThroughTen[1];
/**
* The value 10, with a scale of 0.
*
* @since 1.5
*/
public static final
BigDecimal TEN =
zeroThroughTen[10];
// Constructors
/**
* Trusted package private constructor.
* Trusted simply means if val is INFLATED, intVal could not be null and
* if intVal is null, val could not be INFLATED.
*/
BigDecimal(
BigInteger intVal, long
val, int
scale, int
prec) {
this.
scale =
scale;
this.
precision =
prec;
this.
intCompact =
val;
this.
intVal =
intVal;
}
/**
* 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.
*
* <p>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) {
this(
in,
offset,
len,
MathContext.
UNLIMITED);
}
/**
* 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.
*
* <p>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) {
// protect against huge length, negative values, and integer overflow
if ((
in.length |
len |
offset) < 0 ||
len >
in.length -
offset) {
throw new
NumberFormatException
("Bad offset or len arguments for char[] input.");
}
// 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 '.'
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.
int
idx = 0;
if (
isCompact) {
// First compact case, we need not to preserve the character
// and we can just compute the value in place.
for (;
len > 0;
offset++,
len--) {
c =
in[
offset];
if ((
c == '0')) { // have zero
if (
prec == 0)
prec = 1;
else if (
rs != 0) {
rs *= 10;
++
prec;
} // else digit is a redundant leading zero
if (
dot)
++
scl;
} else if ((
c >= '1' &&
c <= '9')) { // have digit
int
digit =
c - '0';
if (
prec != 1 ||
rs != 0)
++
prec; // prec unchanged if preceded by 0s
rs =
rs * 10 +
digit;
if (
dot)
++
scl;
} else if (
c == '.') { // have dot
// have dot
if (
dot) // two dots
throw new
NumberFormatException();
dot = true;
} else if (
Character.
isDigit(
c)) { // slow path
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;
}
if (
dot)
++
scl;
} else if ((
c == 'e') || (
c == 'E')) {
exp =
parseExp(
in,
offset,
len);
// Next test is required for backwards compatibility
if ((int)
exp !=
exp) // overflow
throw new
NumberFormatException();
break; // [saves a test]
} else {
throw new
NumberFormatException();
}
}
if (
prec == 0) // no digits found
throw new
NumberFormatException();
// Adjust scale if exp is not zero.
if (
exp != 0) { // had significant exponent
scl =
adjustScale(
scl,
exp);
}
rs =
isneg ? -
rs :
rs;
int
mcp =
mc.
precision;
int
drop =
prec -
mcp; // prec has range [1, MAX_INT], mcp has range [0, MAX_INT];
// therefore, this subtract cannot overflow
if (
mcp > 0 &&
drop > 0) { // do rounding
while (
drop > 0) {
scl =
checkScaleNonZero((long)
scl -
drop);
rs =
divideAndRound(
rs,
LONG_TEN_POWERS_TABLE[
drop],
mc.
roundingMode.
oldMode);
prec =
longDigitLength(
rs);
drop =
prec -
mcp;
}
}
} else {
char
coeff[] = new char[
len];
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 (
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();
exp =
parseExp(
in,
offset,
len);
// 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
scl =
adjustScale(
scl,
exp);
}
// Remove leading zeros from precision (digits count)
rb = new
BigInteger(
coeff,
isneg ? -1 : 1,
prec);
rs =
compactValFor(
rb);
int
mcp =
mc.
precision;
if (
mcp > 0 && (
prec >
mcp)) {
if (
rs ==
INFLATED) {
int
drop =
prec -
mcp;
while (
drop > 0) {
scl =
checkScaleNonZero((long)
scl -
drop);
rb =
divideAndRoundByTenPow(
rb,
drop,
mc.
roundingMode.
oldMode);
rs =
compactValFor(
rb);
if (
rs !=
INFLATED) {
prec =
longDigitLength(
rs);
break;
}
prec =
bigDigitLength(
rb);
drop =
prec -
mcp;
}
}
if (
rs !=
INFLATED) {
int
drop =
prec -
mcp;
while (
drop > 0) {
scl =
checkScaleNonZero((long)
scl -
drop);
rs =
divideAndRound(
rs,
LONG_TEN_POWERS_TABLE[
drop],
mc.
roundingMode.
oldMode);
prec =
longDigitLength(
rs);
drop =
prec -
mcp;
}
rb = null;
}
}
}
} catch (
ArrayIndexOutOfBoundsException e) {
throw new
NumberFormatException();
} catch (
NegativeArraySizeException e) {
throw new
NumberFormatException();
}
this.
scale =
scl;
this.
precision =
prec;
this.
intCompact =
rs;
this.
intVal =
rb;
}
private int
adjustScale(int
scl, long
exp) {
long
adjustedScale =
scl -
exp;
if (
adjustedScale >
Integer.
MAX_VALUE ||
adjustedScale <
Integer.
MIN_VALUE)
throw new
NumberFormatException("Scale out of range.");
scl = (int)
adjustedScale;
return
scl;
}
/*
* parse exponent
*/
private static long
parseExp(char[]
in, int
offset, int
len){
long
exp = 0;
offset++;
char
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 && (
c=='0' || (
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;
return
exp;
}
/**
* 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.
*
* <p>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.
*
* <p>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 '+'} (<tt> '\u002B'</tt>) or
* {@code '-'} (<tt>'\u002D'</tt>), followed by a sequence of
* zero or more decimal digits ("the integer"), optionally
* followed by a fraction, optionally followed by an exponent.
*
* <p>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
* <i>significand</i>.
*
* <p>The exponent consists of the character {@code 'e'}
* (<tt>'\u0065'</tt>) or {@code 'E'} (<tt>'\u0045'</tt>)
* 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.
*
* <p>More formally, the strings this constructor accepts are
* described by the following grammar:
* <blockquote>
* <dl>
* <dt><i>BigDecimalString:</i>
* <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i>
* <dt><i>Sign:</i>
* <dd>{@code +}
* <dd>{@code -}
* <dt><i>Significand:</i>
* <dd><i>IntegerPart</i> {@code .} <i>FractionPart<sub>opt</sub></i>
* <dd>{@code .} <i>FractionPart</i>
* <dd><i>IntegerPart</i>
* <dt><i>IntegerPart:</i>
* <dd><i>Digits</i>
* <dt><i>FractionPart:</i>
* <dd><i>Digits</i>
* <dt><i>Exponent:</i>
* <dd><i>ExponentIndicator SignedInteger</i>
* <dt><i>ExponentIndicator:</i>
* <dd>{@code e}
* <dd>{@code E}
* <dt><i>SignedInteger:</i>
* <dd><i>Sign<sub>opt</sub> Digits</i>
* <dt><i>Digits:</i>
* <dd><i>Digit</i>
* <dd><i>Digits Digit</i>
* <dt><i>Digit:</i>
* <dd>any character for which {@link Character#isDigit}
* returns {@code true}, including 0, 1, 2 ...
* </dl>
* </blockquote>
*
* <p>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.
*
* <p>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).
*
* <p><b>Examples:</b><br>
* The value of the returned {@code BigDecimal} is equal to
* <i>significand</i> × 10<sup> <i>exponent</i></sup>.
* For each string on the left, the resulting representation
* [{@code BigInteger}, {@code scale}] is shown on the right.
* <pre>
* "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]
* </pre>
*
* <p>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(),
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
* <tt>(10<sup>scale</sup> × val)</tt> is an integer.
* <p>
* <b>Notes:</b>
* <ol>
* <li>
* The results of this constructor can be somewhat unpredictable.
* One might assume that writing {@code new BigDecimal(0.1)} in
* Java creates a {@code BigDecimal} which is exactly equal to
* 0.1 (an unscaled value of 1, with a scale of 1), but it is
* actually equal to
* 0.1000000000000000055511151231257827021181583404541015625.
* This is because 0.1 cannot be represented exactly as a
* {@code double} (or, for that matter, as a binary fraction of
* any finite length). Thus, the value that is being passed
* <i>in</i> to the constructor is not exactly equal to 0.1,
* appearances notwithstanding.
*
* <li>
* The {@code String} constructor, on the other hand, is
* perfectly predictable: writing {@code new BigDecimal("0.1")}
* creates a {@code BigDecimal} which is <i>exactly</i> equal to
* 0.1, as one would expect. Therefore, it is generally
* recommended that the {@linkplain #BigDecimal(String)
* <tt>String</tt> constructor} be used in preference to this one.
*
* <li>
* When a {@code double} must be used as a source for a
* {@code BigDecimal}, note that this constructor provides an
* exact conversion; it does not give the same result as
* converting the {@code double} to a {@code String} using the
* {@link Double#toString(double)} method and then using the
* {@link #BigDecimal(String)} constructor. To get that result,
* use the {@code static} {@link #valueOf(double)} method.
* </ol>
*
* @param val {@code double} value to be converted to
* {@code BigDecimal}.
* @throws NumberFormatException if {@code val} is infinite or NaN.
*/
public
BigDecimal(double
val) {
this(
val,
MathContext.
UNLIMITED);
}
/**
* 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
* <tt>(10<sup>scale</sup> × val)</tt> is an integer.
*
* <p>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) {
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) {
this.
intVal =
BigInteger.
ZERO;
this.
scale = 0;
this.
intCompact = 0;
this.
precision = 1;
return;
}
// Normalize
while ((
significand & 1) == 0) { // i.e., significand is even
significand >>= 1;
exponent++;
}
int
scale = 0;
// Calculate intVal and scale
BigInteger intVal;
long
compactVal =
sign *
significand;
if (
exponent == 0) {
intVal = (
compactVal ==
INFLATED) ?
INFLATED_BIGINT : null;
} else {
if (
exponent < 0) {
intVal =
BigInteger.
valueOf(5).
pow(-
exponent).
multiply(
compactVal);
scale = -
exponent;
} else { // (exponent > 0)
intVal =
BigInteger.
valueOf(2).
pow(
exponent).
multiply(
compactVal);
}
compactVal =
compactValFor(
intVal);
}
int
prec = 0;
int
mcp =
mc.
precision;
if (
mcp > 0) { // do rounding
int
mode =
mc.
roundingMode.
oldMode;
int
drop;
if (
compactVal ==
INFLATED) {
prec =
bigDigitLength(
intVal);
drop =
prec -
mcp;
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
intVal =
divideAndRoundByTenPow(
intVal,
drop,
mode);
compactVal =
compactValFor(
intVal);
if (
compactVal !=
INFLATED) {
break;
}
prec =
bigDigitLength(
intVal);
drop =
prec -
mcp;
}
}
if (
compactVal !=
INFLATED) {
prec =
longDigitLength(
compactVal);
drop =
prec -
mcp;
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
compactVal =
divideAndRound(
compactVal,
LONG_TEN_POWERS_TABLE[
drop],
mc.
roundingMode.
oldMode);
prec =
longDigitLength(
compactVal);
drop =
prec -
mcp;
}
intVal = null;
}
}
this.
intVal =
intVal;
this.
intCompact =
compactVal;
this.
scale =
scale;
this.
precision =
prec;
}
/**
* 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) {
scale = 0;
intVal =
val;
intCompact =
compactValFor(
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,0,
mc);
}
/**
* Translates a {@code BigInteger} unscaled value and an
* {@code int} scale into a {@code BigDecimal}. The value of
* the {@code BigDecimal} is
* <tt>(unscaledVal × 10<sup>-scale</sup>)</tt>.
*
* @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.
intVal =
unscaledVal;
this.
intCompact =
compactValFor(
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 <tt>(unscaledVal ×
* 10<sup>-scale</sup>)</tt>, 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) {
long
compactVal =
compactValFor(
unscaledVal);
int
mcp =
mc.
precision;
int
prec = 0;
if (
mcp > 0) { // do rounding
int
mode =
mc.
roundingMode.
oldMode;
if (
compactVal ==
INFLATED) {
prec =
bigDigitLength(
unscaledVal);
int
drop =
prec -
mcp;
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
unscaledVal =
divideAndRoundByTenPow(
unscaledVal,
drop,
mode);
compactVal =
compactValFor(
unscaledVal);
if (
compactVal !=
INFLATED) {
break;
}
prec =
bigDigitLength(
unscaledVal);
drop =
prec -
mcp;
}
}
if (
compactVal !=
INFLATED) {
prec =
longDigitLength(
compactVal);
int
drop =
prec -
mcp; // drop can't be more than 18
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
compactVal =
divideAndRound(
compactVal,
LONG_TEN_POWERS_TABLE[
drop],
mode);
prec =
longDigitLength(
compactVal);
drop =
prec -
mcp;
}
unscaledVal = null;
}
}
this.
intVal =
unscaledVal;
this.
intCompact =
compactVal;
this.
scale =
scale;
this.
precision =
prec;
}
/**
* 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) {
this.
intCompact =
val;
this.
scale = 0;
this.
intVal = null;
}
/**
* 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) {
int
mcp =
mc.
precision;
long
compactVal =
val;
int
scale = 0;
int
prec = 0;
if (
mcp > 0) { // do rounding
prec =
longDigitLength(
compactVal);
int
drop =
prec -
mcp; // drop can't be more than 18
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
compactVal =
divideAndRound(
compactVal,
LONG_TEN_POWERS_TABLE[
drop],
mc.
roundingMode.
oldMode);
prec =
longDigitLength(
compactVal);
drop =
prec -
mcp;
}
}
this.
intVal = null;
this.
intCompact =
compactVal;
this.
scale =
scale;
this.
precision =
prec;
}
/**
* 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) ?
INFLATED_BIGINT : null;
this.
scale = 0;
}
/**
* 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) {
int
mcp =
mc.
precision;
int
mode =
mc.
roundingMode.
oldMode;
int
prec = 0;
int
scale = 0;
BigInteger intVal = (
val ==
INFLATED) ?
INFLATED_BIGINT : null;
if (
mcp > 0) { // do rounding
if (
val ==
INFLATED) {
prec = 19;
int
drop =
prec -
mcp;
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
intVal =
divideAndRoundByTenPow(
intVal,
drop,
mode);
val =
compactValFor(
intVal);
if (
val !=
INFLATED) {
break;
}
prec =
bigDigitLength(
intVal);
drop =
prec -
mcp;
}
}
if (
val !=
INFLATED) {
prec =
longDigitLength(
val);
int
drop =
prec -
mcp;
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
val =
divideAndRound(
val,
LONG_TEN_POWERS_TABLE[
drop],
mc.
roundingMode.
oldMode);
prec =
longDigitLength(
val);
drop =
prec -
mcp;
}
intVal = null;
}
}
this.
intVal =
intVal;
this.
intCompact =
val;
this.
scale =
scale;
this.
precision =
prec;
}
// 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
* <tt>(unscaledVal × 10<sup>-scale</sup>)</tt>.
*/
public static
BigDecimal valueOf(long
unscaledVal, int
scale) {
if (
scale == 0)
return
valueOf(
unscaledVal);
else if (
unscaledVal == 0) {
return
zeroValueOf(
scale);
}
return new
BigDecimal(
unscaledVal ==
INFLATED ?
INFLATED_BIGINT : 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(
INFLATED_BIGINT,
val, 0, 0);
}
static
BigDecimal valueOf(long
unscaledVal, int
scale, int
prec) {
if (
scale == 0 &&
unscaledVal >= 0 &&
unscaledVal <
zeroThroughTen.length) {
return
zeroThroughTen[(int)
unscaledVal];
} else if (
unscaledVal == 0) {
return
zeroValueOf(
scale);
}
return new
BigDecimal(
unscaledVal ==
INFLATED ?
INFLATED_BIGINT : null,
unscaledVal,
scale,
prec);
}
static
BigDecimal valueOf(
BigInteger intVal, int
scale, int
prec) {
long
val =
compactValFor(
intVal);
if (
val == 0) {
return
zeroValueOf(
scale);
} else if (
scale == 0 &&
val >= 0 &&
val <
zeroThroughTen.length) {
return
zeroThroughTen[(int)
val];
}
return new
BigDecimal(
intVal,
val,
scale,
prec);
}
static
BigDecimal zeroValueOf(int
scale) {
if (
scale >= 0 &&
scale <
ZERO_SCALED_BY.length)
return
ZERO_SCALED_BY[
scale];
else
return new
BigDecimal(
BigInteger.
ZERO, 0,
scale, 1);
}
/**
* Translates a {@code double} into a {@code BigDecimal}, using
* the {@code double}'s canonical string representation provided
* by the {@link Double#toString(double)} method.
*
* <p><b>Note:</b> 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) {
if (this.
intCompact !=
INFLATED) {
if ((
augend.
intCompact !=
INFLATED)) {
return
add(this.
intCompact, this.
scale,
augend.
intCompact,
augend.
scale);
} else {
return
add(this.
intCompact, this.
scale,
augend.
intVal,
augend.
scale);
}
} else {
if ((
augend.
intCompact !=
INFLATED)) {
return
add(
augend.
intCompact,
augend.
scale, this.
intVal, this.
scale);
} else {
return
add(this.
intVal, this.
scale,
augend.
intVal,
augend.
scale);
}
}
}
/**
* 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;
// 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;
if (
lhsIsZero &&
augendIsZero)
return
zeroValueOf(
preferredScale);
result =
lhsIsZero ?
doRound(
augend,
mc) :
doRound(
lhs,
mc);
if (
result.
scale() ==
preferredScale)
return
result;
else if (
result.
scale() >
preferredScale) {
return
stripZerosToMatchScale(
result.
intVal,
result.
intCompact,
result.
scale,
preferredScale);
} 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];
}
return
doRound(
lhs.
inflated().
add(
augend.
inflated()),
lhs.
scale,
mc);
}
/**
* Returns an array of length two, the sum of whose entries is
* equal to the rounded sum of the {@code BigDecimal} arguments.
*
* <p>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 <em>if</em> the precision of the final
* result does not include the high order digit of the small
* magnitude operand.
*
* <p>Note that while strictly speaking this is an optimization,
* it makes a much wider range of additions practical.
*
* <p>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) {
if (this.
intCompact !=
INFLATED) {
if ((
subtrahend.
intCompact !=
INFLATED)) {
return
add(this.
intCompact, this.
scale, -
subtrahend.
intCompact,
subtrahend.
scale);
} else {
return
add(this.
intCompact, this.
scale,
subtrahend.
intVal.
negate(),
subtrahend.
scale);
}
} else {
if ((
subtrahend.
intCompact !=
INFLATED)) {
// Pair of subtrahend values given before pair of
// values from this BigDecimal to avoid need for
// method overloading on the specialized add method
return
add(-
subtrahend.
intCompact,
subtrahend.
scale, this.
intVal, this.
scale);
} else {
return
add(this.
intVal, this.
scale,
subtrahend.
intVal.
negate(),
subtrahend.
scale);
}
}
}
/**
* 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) {
if (
mc.
precision == 0)
return
subtract(
subtrahend);
// share the special rounding code in add()
return
add(
subtrahend.
negate(),
mc);
}
/**
* Returns a {@code BigDecimal} whose value is <tt>(this ×
* multiplicand)</tt>, 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) {
int
productScale =
checkScale((long)
scale +
multiplicand.
scale);
if (this.
intCompact !=
INFLATED) {
if ((
multiplicand.
intCompact !=
INFLATED)) {
return
multiply(this.
intCompact,
multiplicand.
intCompact,
productScale);
} else {
return
multiply(this.
intCompact,
multiplicand.
intVal,
productScale);
}
} else {
if ((
multiplicand.
intCompact !=
INFLATED)) {
return
multiply(
multiplicand.
intCompact, this.
intVal,
productScale);
} else {
return
multiply(this.
intVal,
multiplicand.
intVal,
productScale);
}
}
}
/**
* Returns a {@code BigDecimal} whose value is <tt>(this ×
* multiplicand)</tt>, 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);
int
productScale =
checkScale((long)
scale +
multiplicand.
scale);
if (this.
intCompact !=
INFLATED) {
if ((
multiplicand.
intCompact !=
INFLATED)) {
return
multiplyAndRound(this.
intCompact,
multiplicand.
intCompact,
productScale,
mc);
} else {
return
multiplyAndRound(this.
intCompact,
multiplicand.
intVal,
productScale,
mc);
}
} else {
if ((
multiplicand.
intCompact !=
INFLATED)) {
return
multiplyAndRound(
multiplicand.
intCompact, this.
intVal,
productScale,
mc);
} else {
return
multiplyAndRound(this.
intVal,
multiplicand.
intVal,
productScale,
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.
*
* <p>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) {
if (
roundingMode <
ROUND_UP ||
roundingMode >
ROUND_UNNECESSARY)
throw new
IllegalArgumentException("Invalid rounding mode");
if (this.
intCompact !=
INFLATED) {
if ((
divisor.
intCompact !=
INFLATED)) {
return
divide(this.
intCompact, this.
scale,
divisor.
intCompact,
divisor.
scale,
scale,
roundingMode);
} else {
return
divide(this.
intCompact, this.
scale,
divisor.
intVal,
divisor.
scale,
scale,
roundingMode);
}
} else {
if ((
divisor.
intCompact !=
INFLATED)) {
return
divide(this.
intVal, this.
scale,
divisor.
intCompact,
divisor.
scale,
scale,
roundingMode);
} else {
return
divide(this.
intVal, this.
scale,
divisor.
intVal,
divisor.
scale,
scale,
roundingMode);
}
}
}
/**
* 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.
*
* <p>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
zeroValueOf(
preferredScale);
else {
/*
* 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
zeroValueOf(
saturateLong(
preferredScale));
int
xscale =
dividend.
precision();
int
yscale =
divisor.
precision();
if(
dividend.
intCompact!=
INFLATED) {
if(
divisor.
intCompact!=
INFLATED) {
return
divide(
dividend.
intCompact,
xscale,
divisor.
intCompact,
yscale,
preferredScale,
mc);
} else {
return
divide(
dividend.
intCompact,
xscale,
divisor.
intVal,
yscale,
preferredScale,
mc);
}
} else {
if(
divisor.
intCompact!=
INFLATED) {
return
divide(
dividend.
intVal,
xscale,
divisor.
intCompact,
yscale,
preferredScale,
mc);
} else {
return
divide(
dividend.
intVal,
xscale,
divisor.
intVal,
yscale,
preferredScale,
mc);
}
}
}
/**
* 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
zeroValueOf(
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(
quotient.
intVal,
quotient.
intCompact,
quotient.
scale,
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 {
return
stripZerosToMatchScale(
result.
intVal,
result.
intCompact,
result.
scale,
preferredScale);
}
}
/**
* Returns a {@code BigDecimal} whose value is {@code (this % divisor)}.
*
* <p>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.
*
* <p>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.
*
* <p>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.
*
* <p>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
* <tt>(this<sup>n</sup>)</tt>, The power is computed exactly, to
* unlimited precision.
*
* <p>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 <tt>this<sup>n</sup></tt>
* @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);
return new
BigDecimal(this.
inflated().
pow(
n),
newScale);
}
/**
* Returns a {@code BigDecimal} whose value is
* <tt>(this<sup>n</sup>)</tt>. 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.
*
* <p>The X3.274-1996 algorithm is:
*
* <ul>
* <li> An {@code ArithmeticException} exception is thrown if
* <ul>
* <li>{@code abs(n) > 999999999}
* <li>{@code mc.precision == 0} and {@code n < 0}
* <li>{@code mc.precision > 0} and {@code n} has more than
* {@code mc.precision} decimal digits
* </ul>
*
* <li> if {@code n} is zero, {@link #ONE} is returned even if
* {@code this} is zero, otherwise
* <ul>
* <li> if {@code n} is positive, the result is calculated via
* the repeated squaring technique into a single accumulator.
* The individual multiplications with the accumulator use the
* same math context settings as in {@code mc} except for a
* precision increased to {@code mc.precision + elength + 1}
* where {@code elength} is the number of decimal digits in
* {@code n}.
*
* <li> if {@code n} is negative, the result is calculated as if
* {@code n} were positive; this value is then divided into one
* using the working precision specified above.
*
* <li> The final value from either the positive or negative case
* is then rounded to the destination precision.
* </ul>
* </ul>
*
* @param n power to raise this {@code BigDecimal} to.
* @param mc the context to use.
* @return <tt>this<sup>n</sup></tt> 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
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() {
if (
intCompact ==
INFLATED) {
return new
BigDecimal(
intVal.
negate(),
INFLATED,
scale,
precision);
} else {
return
valueOf(-
intCompact,
scale,
precision);
}
}
/**
* 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()}.
*
* <p>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.
*
* <p>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 <i>scale</i> 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 <i>precision</i> of this {@code BigDecimal}. (The
* precision is the number of digits in the unscaled value.)
*
* <p>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(
intVal);
precision =
result;
}
return
result;
}
/**
* Returns a {@code BigInteger} whose value is the <i>unscaled
* value</i> of this {@code BigDecimal}. (Computes <tt>(this *
* 10<sup>this.scale()</sup>)</tt>.)
*
* @return the unscaled value of this {@code BigDecimal}.
* @since 1.2
*/
public
BigInteger unscaledValue() {
return this.
inflated();
}
// 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.
*
* <p>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.
*
* <p>Note that since BigDecimal objects are immutable, calls of
* this method do <i>not</i> result in the original object being
* modified, contrary to the usual convention of having methods
* named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
* 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.
*
* <p>Note that since BigDecimal objects are immutable, calls of
* this method do <i>not</i> result in the original object being
* modified, contrary to the usual convention of having methods
* named <tt>set<i>X</i></tt> mutate field <i>{@code X}</i>.
* Instead, {@code setScale} returns an object with the proper
* scale; the returned object may or may not be newly allocated.
*
* <p>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
zeroValueOf(
newScale);
if(this.
intCompact!=
INFLATED) {
long
rs = this.
intCompact;
if (
newScale >
oldScale) {
int
raise =
checkScale((long)
newScale -
oldScale);
if ((
rs =
longMultiplyPowerTen(
rs,
raise)) !=
INFLATED) {
return
valueOf(
rs,
newScale);
}
BigInteger rb =
bigMultiplyPowerTen(
raise);
return new
BigDecimal(
rb,
INFLATED,
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,
LONG_TEN_POWERS_TABLE[
drop],
newScale,
roundingMode,
newScale);
} else {
return
divideAndRound(this.
inflated(),
bigTenToThe(
drop),
newScale,
roundingMode,
newScale);
}
}
} else {
if (
newScale >
oldScale) {
int
raise =
checkScale((long)
newScale -
oldScale);
BigInteger rb =
bigMultiplyPowerTen(this.
intVal,
raise);
return new
BigDecimal(
rb,
INFLATED,
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(this.
intVal,
LONG_TEN_POWERS_TABLE[
drop],
newScale,
roundingMode,
newScale);
else
return
divideAndRound(this.
intVal,
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.
*
* <p>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.
*
* <p>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.
*
* <p>Note that since {@code BigDecimal} objects are immutable,
* calls of this method do <i>not</i> result in the original
* object being modified, contrary to the usual convention of
* having methods named <tt>set<i>X</i></tt> mutate field
* <i>{@code X}</i>. 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 <tt>(this ×
* 10<sup>-n</sup>)</tt> 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 <tt>(this
* × 10<sup>n</sup>)</tt> 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} * 10<sup>n</sup>). The scale of
* the result is {@code (this.scale() - n)}.
*
* @param n the exponent power of ten to scale by
* @return a BigDecimal whose numerical value is equal to
* ({@code this} * 10<sup>n</sup>)
* @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]. If
* this BigDecimal is numerically equal to zero, then
* {@code BigDecimal.ZERO} is returned.
*
* @return a numerically equal {@code BigDecimal} with any
* trailing zeros removed.
* @since 1.5
*/
public
BigDecimal stripTrailingZeros() {
if (
intCompact == 0 || (
intVal != null &&
intVal.
signum() == 0)) {
return
BigDecimal.
ZERO;
} else if (
intCompact !=
INFLATED) {
return
createAndStripZerosToMatchScale(
intCompact,
scale,
Long.
MIN_VALUE);
} else {
return
createAndStripZerosToMatchScale(
intVal,
scale,
Long.
MIN_VALUE);
}
}
// 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)} <<i>op</i>> {@code 0)}, where
* <<i>op</i>> 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;
long
sdiff = (long)this.
scale -
val.
scale;
if (
sdiff != 0) {
// Avoid matching scales if the (adjusted) exponents differ
long
xae = (long)this.
precision() - this.
scale; // [-1]
long
yae = (long)
val.
precision() -
val.
scale; // [-1]
if (
xae <
yae)
return -1;
if (
xae >
yae)
return 1;
BigInteger rb = null;
if (
sdiff < 0) {
// The cases sdiff <= Integer.MIN_VALUE intentionally fall through.
if (
sdiff >
Integer.
MIN_VALUE &&
(
xs ==
INFLATED ||
(
xs =
longMultiplyPowerTen(
xs, (int)-
sdiff)) ==
INFLATED) &&
ys ==
INFLATED) {
rb =
bigMultiplyPowerTen((int)-
sdiff);
return
rb.
compareMagnitude(
val.
intVal);
}
} else { // sdiff > 0
// The cases sdiff > Integer.MAX_VALUE intentionally fall through.
if (
sdiff <=
Integer.
MAX_VALUE &&
(
ys ==
INFLATED ||
(
ys =
longMultiplyPowerTen(
ys, (int)
sdiff)) ==
INFLATED) &&
xs ==
INFLATED) {
rb =
val.
bigMultiplyPowerTen((int)
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.
inflated().
equals(
xDec.
inflated());
}
/**
* 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 <i>not</i>
* 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.
*
* <p>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).
*
* <p>Next, an <i>adjusted exponent</i> 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 <i>precision</i>).
*
* <p>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.
*
* <p>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 '-'} (<tt>'\u002D'</tt>) if the
* adjusted exponent is negative, {@code '+'}
* (<tt>'\u002B'</tt>) otherwise).
*
* <p>Finally, the entire string is prefixed by a minus sign
* character {@code '-'} (<tt>'\u002D'</tt>) if the unscaled
* value is less than zero. No sign character is prefixed if the
* unscaled value is zero or positive.
*
* <p><b>Examples:</b>
* <p>For each representation [<i>unscaled value</i>, <i>scale</i>]
* on the left, the resulting string is shown on the right.
* <pre>
* [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"
* </pre>
*
* <b>Notes:</b>
* <ol>
*
* <li>There is a one-to-one mapping between the distinguishable
* {@code BigDecimal} values and the result of this conversion.
* That is, every distinguishable {@code BigDecimal} value
* (unscaled value and scale) has a unique string representation
* as a result of using {@code toString}. If that string
* representation is converted back to a {@code BigDecimal} using
* the {@link #BigDecimal(String)} constructor, then the original
* value will be recovered.
*
* <li>The string produced for a given number is always the same;
* it is not affected by locale. This means that it can be used
* as a canonical string representation for exchanging decimal
* data, or as a key for a Hashtable, etc. Locale-sensitive
* number formatting and parsing is handled by the {@link
* java.text.NumberFormat} class and its subclasses.
*
* <li>The {@link #toEngineeringString} method may be used for
* presenting numbers with exponents in engineering notation, and the
* {@link #setScale(int,RoundingMode) setScale} method may be used for
* rounding a {@code BigDecimal} so it has a known number of digits after
* the decimal point.
*
* <li>The digit-to-character mapping provided by
* {@code Character.forDigit} is used.
*
* </ol>
*
* @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.
*
* <p>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 <em>not</em> 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 '-'
* (<tt>'\u002D'</tt>) 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() {
if(
scale==0) {
if(
intCompact!=
INFLATED) {
return
Long.
toString(
intCompact);
} else {
return
intVal.
toString();
}
}
if(this.
scale<0) { // No decimal point
if(
signum()==0) {
return "0";
}
int
tailingZeros =
checkScaleNonZero((-(long)
scale));
StringBuilder buf;
if(
intCompact!=
INFLATED) {
buf = new
StringBuilder(20+
tailingZeros);
buf.
append(
intCompact);
} else {
String str =
intVal.
toString();
buf = new
StringBuilder(
str.
length()+
tailingZeros);
buf.
append(
str);
}
for (int
i = 0;
i <
tailingZeros;
i++)
buf.
append('0');
return
buf.
toString();
}
String str ;
if(
intCompact!=
INFLATED) {
str =
Long.
toString(
Math.
abs(
intCompact));
} else {
str =
intVal.
abs().
toString();
}
return
getValueString(
signum(),
str,
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
* <i>narrowing primitive conversion</i> from {@code double} to
* {@code long} as defined in section 5.1.3 of
* <cite>The Java™ Language Specification</cite>:
* 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.
* <p>
* 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).
inflated();
}
/**
* 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).
inflated();
}
/**
* Converts this {@code BigDecimal} to a {@code long}.
* This conversion is analogous to the
* <i>narrowing primitive conversion</i> from {@code double} to
* {@code short} as defined in section 5.1.3 of
* <cite>The Java™ Language Specification</cite>:
* 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(){
if (
intCompact !=
INFLATED &&
scale == 0) {
return
intCompact;
} else {
// Fastpath zero and small values
if (this.
signum() == 0 ||
fractionOnly() ||
// Fastpath very large-scale values that will result
// in a truncated value of zero. If the scale is -64
// or less, there are at least 64 powers of 10 in the
// value of the numerical result. Since 10 = 2*5, in
// that case there would also be 64 powers of 2 in the
// result, meaning all 64 bits of a long will be zero.
scale <= -64) {
return 0;
} else {
return
toBigInteger().
longValue();
}
}
}
/**
* Return true if a nonzero BigDecimal has an absolute value less
* than one; i.e. only has fraction digits.
*/
private boolean
fractionOnly() {
assert this.
signum() != 0;
return (this.
precision() - this.
scale) <= 0;
}
/**
* 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;
// Fastpath zero
if (this.
signum() == 0)
return 0;
// Fastpath numbers less than 1.0 (the latter can be very slow
// to round if very small)
if (
fractionOnly())
throw new
ArithmeticException("Rounding necessary");
// 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");
// 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.
inflated().
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) {
BigInteger intVal =
num.
inflated();
if (
intVal.
compareTo(
LONGMIN) < 0 ||
intVal.
compareTo(
LONGMAX) > 0)
throw new java.lang.
ArithmeticException("Overflow");
}
}
/**
* Converts this {@code BigDecimal} to an {@code int}.
* This conversion is analogous to the
* <i>narrowing primitive conversion</i> from {@code double} to
* {@code short} as defined in section 5.1.3 of
* <cite>The Java™ Language Specification</cite>:
* 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 :
(int)
longValue();
}
/**
* 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
* <i>narrowing primitive conversion</i> from {@code double} to
* {@code float} as defined in section 5.1.3 of
* <cite>The Java™ Language Specification</cite>:
* 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(
intCompact !=
INFLATED) {
if (
scale == 0) {
return (float)
intCompact;
} else {
/*
* If both intCompact and the scale can be exactly
* represented as float values, perform a single float
* multiply or divide to compute the (properly
* rounded) result.
*/
if (
Math.
abs(
intCompact) < 1L<<22 ) {
// Don't have too guard against
// Math.abs(MIN_VALUE) because of outer check
// against INFLATED.
if (
scale > 0 &&
scale <
float10pow.length) {
return (float)
intCompact /
float10pow[
scale];
} else if (
scale < 0 &&
scale > -
float10pow.length) {
return (float)
intCompact *
float10pow[-
scale];
}
}
}
}
// 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
* <i>narrowing primitive conversion</i> from {@code double} to
* {@code float} as defined in section 5.1.3 of
* <cite>The Java™ Language Specification</cite>:
* 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(
intCompact !=
INFLATED) {
if (
scale == 0) {
return (double)
intCompact;
} else {
/*
* If both intCompact and the scale can be exactly
* represented as double values, perform a single
* double multiply or divide to compute the (properly
* rounded) result.
*/
if (
Math.
abs(
intCompact) < 1L<<52 ) {
// Don't have too guard against
// Math.abs(MIN_VALUE) because of outer check
// against INFLATED.
if (
scale > 0 &&
scale <
double10pow.length) {
return (double)
intCompact /
double10pow[
scale];
} else if (
scale < 0 &&
scale > -
double10pow.length) {
return (double)
intCompact *
double10pow[-
scale];
}
}
}
}
// Somewhat inefficient, but guaranteed to work.
return
Double.
parseDouble(this.
toString());
}
/**
* Powers of 10 which can be represented exactly in {@code
* double}.
*/
private static final double
double10pow[] = {
1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5,
1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, 1.0e11,
1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17,
1.0e18, 1.0e19, 1.0e20, 1.0e21, 1.0e22
};
/**
* Powers of 10 which can be represented exactly in {@code
* float}.
*/
private static final float
float10pow[] = {
1.0e0f, 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f,
1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f
};
/**
* 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(), 1);
}
// 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();
if (
scale == 2 &&
intCompact >= 0 &&
intCompact <
Integer.
MAX_VALUE) {
// currency fast path
int
lowInt = (int)
intCompact % 100;
int
highInt = (int)
intCompact / 100;
return (
Integer.
toString(
highInt) + '.' +
StringBuilderHelper.
DIGIT_TENS[
lowInt] +
StringBuilderHelper.
DIGIT_ONES[
lowInt]) ;
}
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 (10<sup>n</sup>)
*/
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);
}
return
BigInteger.
TEN.
pow(
n);
}
/**
* 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 (10<sup>n</sup>) 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.
inflated();
if (
intCompact !=
INFLATED)
return
bigTenToThe(
n).
multiply(
intCompact);
else
return
intVal.
multiply(
bigTenToThe(
n));
}
/**
* Returns appropriate BigInteger from intVal field if intVal is
* null, i.e. the compact representation is in use.
*/
private
BigInteger inflated() {
if (
intVal == null) {
return
BigInteger.
valueOf(
intCompact);
}
return
intVal;
}
/**
* Match the scales of two {@code BigDecimal}s to align their
* least significant digits.
*
* <p>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);
}
}
private static class
UnsafeHolder {
private static final sun.misc.
Unsafe unsafe;
private static final long
intCompactOffset;
private static final long
intValOffset;
static {
try {
unsafe = sun.misc.
Unsafe.
getUnsafe();
intCompactOffset =
unsafe.
objectFieldOffset
(
BigDecimal.class.
getDeclaredField("intCompact"));
intValOffset =
unsafe.
objectFieldOffset
(
BigDecimal.class.
getDeclaredField("intVal"));
} catch (
Exception ex) {
throw new
ExceptionInInitializerError(
ex);
}
}
static void
setIntCompactVolatile(
BigDecimal bd, long
val) {
unsafe.
putLongVolatile(
bd,
intCompactOffset,
val);
}
static void
setIntValVolatile(
BigDecimal bd,
BigInteger val) {
unsafe.
putObjectVolatile(
bd,
intValOffset,
val);
}
}
/**
* 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]
}
UnsafeHolder.
setIntCompactVolatile(this,
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.
if (this.
intVal == null)
UnsafeHolder.
setIntValVolatile(this,
BigInteger.
valueOf(this.
intCompact));
// Could reset intVal back to null if it has to be set.
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.
*/
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 !=
BigDecimal.
INFLATED;
if (
x < 0)
x = -
x;
if (
x < 10) // must screen for 0, might as well 10
return 1;
int
r = ((64 -
Long.
numberOfLeadingZeros(
x) + 1) * 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;
}
/**
* 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;
}
/**
* 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:
*
* <ul>
*
* <li>The object must be initialized; either intCompact must not be
* INFLATED or intVal is non-null. Both of these conditions may
* be true.
*
* <li>If both intCompact and intVal and set, their values must be
* consistent.
*
* <li>If precision is nonzero, it must have the right value.
* </ul>
*
* 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;
}
/* the same as checkScale where value!=0 */
private static int
checkScaleNonZero(long
val) {
int
asInt = (int)
val;
if (
asInt !=
val) {
throw new
ArithmeticException(
asInt>0 ? "Underflow":"Overflow");
}
return
asInt;
}
private static int
checkScale(long
intCompact, long
val) {
int
asInt = (int)
val;
if (
asInt !=
val) {
asInt =
val>
Integer.
MAX_VALUE ?
Integer.
MAX_VALUE :
Integer.
MIN_VALUE;
if (
intCompact != 0)
throw new
ArithmeticException(
asInt>0 ? "Underflow":"Overflow");
}
return
asInt;
}
private static int
checkScale(
BigInteger intVal, long
val) {
int
asInt = (int)
val;
if (
asInt !=
val) {
asInt =
val>
Integer.
MAX_VALUE ?
Integer.
MAX_VALUE :
Integer.
MIN_VALUE;
if (
intVal.
signum() != 0)
throw new
ArithmeticException(
asInt>0 ? "Underflow":"Overflow");
}
return
asInt;
}
/**
* Returns a {@code BigDecimal} rounded according to the MathContext
* settings;
* If rounding is needed a new {@code BigDecimal} is created and returned.
*
* @param val the value to be rounded
* @param mc the context to use.
* @return a {@code BigDecimal} rounded according to the MathContext
* settings. May return {@code value}, if no rounding needed.
* @throws ArithmeticException if the rounding mode is
* {@code RoundingMode.UNNECESSARY} and the
* result is inexact.
*/
private static
BigDecimal doRound(
BigDecimal val,
MathContext mc) {
int
mcp =
mc.
precision;
boolean
wasDivided = false;
if (
mcp > 0) {
BigInteger intVal =
val.
intVal;
long
compactVal =
val.
intCompact;
int
scale =
val.
scale;
int
prec =
val.
precision();
int
mode =
mc.
roundingMode.
oldMode;
int
drop;
if (
compactVal ==
INFLATED) {
drop =
prec -
mcp;
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
intVal =
divideAndRoundByTenPow(
intVal,
drop,
mode);
wasDivided = true;
compactVal =
compactValFor(
intVal);
if (
compactVal !=
INFLATED) {
prec =
longDigitLength(
compactVal);
break;
}
prec =
bigDigitLength(
intVal);
drop =
prec -
mcp;
}
}
if (
compactVal !=
INFLATED) {
drop =
prec -
mcp; // drop can't be more than 18
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
compactVal =
divideAndRound(
compactVal,
LONG_TEN_POWERS_TABLE[
drop],
mc.
roundingMode.
oldMode);
wasDivided = true;
prec =
longDigitLength(
compactVal);
drop =
prec -
mcp;
intVal = null;
}
}
return
wasDivided ? new
BigDecimal(
intVal,
compactVal,
scale,
prec) :
val;
}
return
val;
}
/*
* Returns a {@code BigDecimal} created from {@code long} value with
* given scale rounded according to the MathContext settings
*/
private static
BigDecimal doRound(long
compactVal, int
scale,
MathContext mc) {
int
mcp =
mc.
precision;
if (
mcp > 0 &&
mcp < 19) {
int
prec =
longDigitLength(
compactVal);
int
drop =
prec -
mcp; // drop can't be more than 18
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
compactVal =
divideAndRound(
compactVal,
LONG_TEN_POWERS_TABLE[
drop],
mc.
roundingMode.
oldMode);
prec =
longDigitLength(
compactVal);
drop =
prec -
mcp;
}
return
valueOf(
compactVal,
scale,
prec);
}
return
valueOf(
compactVal,
scale);
}
/*
* Returns a {@code BigDecimal} created from {@code BigInteger} value with
* given scale rounded according to the MathContext settings
*/
private static
BigDecimal doRound(
BigInteger intVal, int
scale,
MathContext mc) {
int
mcp =
mc.
precision;
int
prec = 0;
if (
mcp > 0) {
long
compactVal =
compactValFor(
intVal);
int
mode =
mc.
roundingMode.
oldMode;
int
drop;
if (
compactVal ==
INFLATED) {
prec =
bigDigitLength(
intVal);
drop =
prec -
mcp;
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
intVal =
divideAndRoundByTenPow(
intVal,
drop,
mode);
compactVal =
compactValFor(
intVal);
if (
compactVal !=
INFLATED) {
break;
}
prec =
bigDigitLength(
intVal);
drop =
prec -
mcp;
}
}
if (
compactVal !=
INFLATED) {
prec =
longDigitLength(
compactVal);
drop =
prec -
mcp; // drop can't be more than 18
while (
drop > 0) {
scale =
checkScaleNonZero((long)
scale -
drop);
compactVal =
divideAndRound(
compactVal,
LONG_TEN_POWERS_TABLE[
drop],
mc.
roundingMode.
oldMode);
prec =
longDigitLength(
compactVal);
drop =
prec -
mcp;
}
return
valueOf(
compactVal,
scale,
prec);
}
}
return new
BigDecimal(
intVal,
INFLATED,
scale,
prec);
}
/*
* Divides {@code BigInteger} value by ten power.
*/
private static
BigInteger divideAndRoundByTenPow(
BigInteger intVal, int
tenPow, int
roundingMode) {
if (
tenPow <
LONG_TEN_POWERS_TABLE.length)
intVal =
divideAndRound(
intVal,
LONG_TEN_POWERS_TABLE[
tenPow],
roundingMode);
else
intVal =
divideAndRound(
intVal,
bigTenToThe(
tenPow),
roundingMode);
return
intVal;
}
/**
* Internally used for division operation for division {@code long} by
* {@code long}.
* 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, long
ldivisor, int
scale, int
roundingMode,
int
preferredScale) {
int
qsign; // quotient sign
long
q =
ldividend /
ldivisor; // store quotient in long
if (
roundingMode ==
ROUND_DOWN &&
scale ==
preferredScale)
return
valueOf(
q,
scale);
long
r =
ldividend %
ldivisor; // store remainder in long
qsign = ((
ldividend < 0) == (
ldivisor < 0)) ? 1 : -1;
if (
r != 0) {
boolean
increment =
needIncrement(
ldivisor,
roundingMode,
qsign,
q,
r);
return
valueOf((
increment ?
q +
qsign :
q),
scale);
} else {
if (
preferredScale !=
scale)
return
createAndStripZerosToMatchScale(
q,
scale,
preferredScale);
else
return
valueOf(
q,
scale);
}
}
/**
* Divides {@code long} by {@code long} and do rounding based on the
* passed in roundingMode.
*/
private static long
divideAndRound(long
ldividend, long
ldivisor, int
roundingMode) {
int
qsign; // quotient sign
long
q =
ldividend /
ldivisor; // store quotient in long
if (
roundingMode ==
ROUND_DOWN)
return
q;
long
r =
ldividend %
ldivisor; // store remainder in long
qsign = ((
ldividend < 0) == (
ldivisor < 0)) ? 1 : -1;
if (
r != 0) {
boolean
increment =
needIncrement(
ldivisor,
roundingMode,
qsign,
q,
r);
return
increment ?
q +
qsign :
q;
} else {
return
q;
}
}
/**
* Shared logic of need increment computation.
*/
private static boolean
commonNeedIncrement(int
roundingMode, int
qsign,
int
cmpFracHalf, boolean
oddQuot) {
switch(
roundingMode) {
case
ROUND_UNNECESSARY:
throw new
ArithmeticException("Rounding necessary");
case
ROUND_UP: // Away from zero
return true;
case
ROUND_DOWN: // Towards zero
return false;
case
ROUND_CEILING: // Towards +infinity
return
qsign > 0;
case
ROUND_FLOOR: // Towards -infinity
return
qsign < 0;
default: // Some kind of half-way rounding
assert
roundingMode >=
ROUND_HALF_UP &&
roundingMode <=
ROUND_HALF_EVEN: "Unexpected rounding mode" +
RoundingMode.
valueOf(
roundingMode);
if (
cmpFracHalf < 0 ) // We're closer to higher digit
return false;
else if (
cmpFracHalf > 0 ) // We're closer to lower digit
return true;
else { // half-way
assert
cmpFracHalf == 0;
switch(
roundingMode) {
case
ROUND_HALF_DOWN:
return false;
case
ROUND_HALF_UP:
return true;
case
ROUND_HALF_EVEN:
return
oddQuot;
default:
throw new
AssertionError("Unexpected rounding mode" +
roundingMode);
}
}
}
}
/**
* Tests if quotient has to be incremented according the roundingMode
*/
private static boolean
needIncrement(long
ldivisor, int
roundingMode,
int
qsign, long
q, long
r) {
assert
r != 0L;
int
cmpFracHalf;
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);
}
return
commonNeedIncrement(
roundingMode,
qsign,
cmpFracHalf, (
q & 1L) != 0L);
}
/**
* Divides {@code BigInteger} value by {@code long} value and
* do rounding based on the passed in roundingMode.
*/
private static
BigInteger divideAndRound(
BigInteger bdividend, long
ldivisor, int
roundingMode) {
boolean
isRemainderZero; // record remainder is zero or not
int
qsign; // quotient sign
long
r = 0; // store quotient & remainder in long
MutableBigInteger mq = null; // store quotient
// Descend into mutables for faster remainder checks
MutableBigInteger mdividend = new
MutableBigInteger(
bdividend.
mag);
mq = new
MutableBigInteger();
r =
mdividend.
divide(
ldivisor,
mq);
isRemainderZero = (
r == 0);
qsign = (
ldivisor < 0) ? -
bdividend.
signum :
bdividend.
signum;
if (!
isRemainderZero) {
if(
needIncrement(
ldivisor,
roundingMode,
qsign,
mq,
r)) {
mq.
add(
MutableBigInteger.
ONE);
}
}
return
mq.
toBigInteger(
qsign);
}
/**
* Internally used for division operation for division {@code BigInteger}
* by {@code long}.
* 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(
BigInteger bdividend,
long
ldivisor, int
scale, int
roundingMode, int
preferredScale) {
boolean
isRemainderZero; // record remainder is zero or not
int
qsign; // quotient sign
long
r = 0; // store quotient & remainder in long
MutableBigInteger mq = null; // store quotient
// Descend into mutables for faster remainder checks
MutableBigInteger mdividend = new
MutableBigInteger(
bdividend.
mag);
mq = new
MutableBigInteger();
r =
mdividend.
divide(
ldivisor,
mq);
isRemainderZero = (
r == 0);
qsign = (
ldivisor < 0) ? -
bdividend.
signum :
bdividend.
signum;
if (!
isRemainderZero) {
if(
needIncrement(
ldivisor,
roundingMode,
qsign,
mq,
r)) {
mq.
add(
MutableBigInteger.
ONE);
}
return
mq.
toBigDecimal(
qsign,
scale);
} else {
if (
preferredScale !=
scale) {
long
compactVal =
mq.
toCompactValue(
qsign);
if(
compactVal!=
INFLATED) {
return
createAndStripZerosToMatchScale(
compactVal,
scale,
preferredScale);
}
BigInteger intVal =
mq.
toBigInteger(
qsign);
return
createAndStripZerosToMatchScale(
intVal,
scale,
preferredScale);
} else {
return
mq.
toBigDecimal(
qsign,
scale);
}
}
}
/**
* Tests if quotient has to be incremented according the roundingMode
*/
private static boolean
needIncrement(long
ldivisor, int
roundingMode,
int
qsign,
MutableBigInteger mq, long
r) {
assert
r != 0L;
int
cmpFracHalf;
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);
}
return
commonNeedIncrement(
roundingMode,
qsign,
cmpFracHalf,
mq.
isOdd());
}
/**
* Divides {@code BigInteger} value by {@code BigInteger} value and
* do rounding based on the passed in roundingMode.
*/
private static
BigInteger divideAndRound(
BigInteger bdividend,
BigInteger bdivisor, int
roundingMode) {
boolean
isRemainderZero; // record remainder is zero or not
int
qsign; // quotient sign
// Descend into mutables for faster remainder checks
MutableBigInteger mdividend = new
MutableBigInteger(
bdividend.
mag);
MutableBigInteger mq = new
MutableBigInteger();
MutableBigInteger mdivisor = new
MutableBigInteger(
bdivisor.
mag);
MutableBigInteger mr =
mdividend.
divide(
mdivisor,
mq);
isRemainderZero =
mr.
isZero();
qsign = (
bdividend.
signum !=
bdivisor.
signum) ? -1 : 1;
if (!
isRemainderZero) {
if (
needIncrement(
mdivisor,
roundingMode,
qsign,
mq,
mr)) {
mq.
add(
MutableBigInteger.
ONE);
}
}
return
mq.
toBigInteger(
qsign);
}
/**
* Internally used for division operation for division {@code BigInteger}
* by {@code BigInteger}.
* 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(
BigInteger bdividend,
BigInteger bdivisor, int
scale, int
roundingMode,
int
preferredScale) {
boolean
isRemainderZero; // record remainder is zero or not
int
qsign; // quotient sign
// Descend into mutables for faster remainder checks
MutableBigInteger mdividend = new
MutableBigInteger(
bdividend.
mag);
MutableBigInteger mq = new
MutableBigInteger();
MutableBigInteger mdivisor = new
MutableBigInteger(
bdivisor.
mag);
MutableBigInteger mr =
mdividend.
divide(
mdivisor,
mq);
isRemainderZero =
mr.
isZero();
qsign = (
bdividend.
signum !=
bdivisor.
signum) ? -1 : 1;
if (!
isRemainderZero) {
if (
needIncrement(
mdivisor,
roundingMode,
qsign,
mq,
mr)) {
mq.
add(
MutableBigInteger.
ONE);
}
return
mq.
toBigDecimal(
qsign,
scale);
} else {
if (
preferredScale !=
scale) {
long
compactVal =
mq.
toCompactValue(
qsign);
if (
compactVal !=
INFLATED) {
return
createAndStripZerosToMatchScale(
compactVal,
scale,
preferredScale);
}
BigInteger intVal =
mq.
toBigInteger(
qsign);
return
createAndStripZerosToMatchScale(
intVal,
scale,
preferredScale);
} else {
return
mq.
toBigDecimal(
qsign,
scale);
}
}
}
/**
* Tests if quotient has to be incremented according the roundingMode
*/
private static boolean
needIncrement(
MutableBigInteger mdivisor, int
roundingMode,
int
qsign,
MutableBigInteger mq,
MutableBigInteger mr) {
assert !
mr.
isZero();
int
cmpFracHalf =
mr.
compareHalf(
mdivisor);
return
commonNeedIncrement(
roundingMode,
qsign,
cmpFracHalf,
mq.
isOdd());
}
/**
* Remove insignificant trailing zeros from this
* {@code BigInteger} value 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.
*
* @return new {@code BigDecimal} with a scale possibly reduced
* to be closed to the preferred scale.
*/
private static
BigDecimal createAndStripZerosToMatchScale(
BigInteger intVal, int
scale, long
preferredScale) {
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(
intVal,(long)
scale - 1); // could Overflow
}
return
valueOf(
intVal,
scale, 0);
}
/**
* Remove insignificant trailing zeros from this
* {@code long} value 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.
*
* @return new {@code BigDecimal} with a scale possibly reduced
* to be closed to the preferred scale.
*/
private static
BigDecimal createAndStripZerosToMatchScale(long
compactVal, int
scale, long
preferredScale) {
while (
Math.
abs(
compactVal) >= 10L &&
scale >
preferredScale) {
if ((
compactVal & 1L) != 0L)
break; // odd number cannot end in 0
long
r =
compactVal % 10L;
if (
r != 0L)
break; // non-0 remainder
compactVal /= 10;
scale =
checkScale(
compactVal, (long)
scale - 1); // could Overflow
}
return
valueOf(
compactVal,
scale);
}
private static
BigDecimal stripZerosToMatchScale(
BigInteger intVal, long
intCompact, int
scale, int
preferredScale) {
if(
intCompact!=
INFLATED) {
return
createAndStripZerosToMatchScale(
intCompact,
scale,
preferredScale);
} else {
return
createAndStripZerosToMatchScale(
intVal==null ?
INFLATED_BIGINT :
intVal,
scale,
preferredScale);
}
}
/*
* returns INFLATED if oveflow
*/
private static long
add(long
xs, long
ys){
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
sum;
}
return
INFLATED;
}
private static
BigDecimal add(long
xs, long
ys, int
scale){
long
sum =
add(
xs,
ys);
if (
sum!=
INFLATED)
return
BigDecimal.
valueOf(
sum,
scale);
return new
BigDecimal(
BigInteger.
valueOf(
xs).
add(
ys),
scale);
}
private static
BigDecimal add(final long
xs, int
scale1, final long
ys, int
scale2) {
long
sdiff = (long)
scale1 -
scale2;
if (
sdiff == 0) {
return
add(
xs,
ys,
scale1);
} else if (
sdiff < 0) {
int
raise =
checkScale(
xs,-
sdiff);
long
scaledX =
longMultiplyPowerTen(
xs,
raise);
if (
scaledX !=
INFLATED) {
return
add(
scaledX,
ys,
scale2);
} else {
BigInteger bigsum =
bigMultiplyPowerTen(
xs,
raise).
add(
ys);
return ((
xs^
ys)>=0) ? // same sign test
new
BigDecimal(
bigsum,
INFLATED,
scale2, 0)
:
valueOf(
bigsum,
scale2, 0);
}
} else {
int
raise =
checkScale(
ys,
sdiff);
long
scaledY =
longMultiplyPowerTen(
ys,
raise);
if (
scaledY !=
INFLATED) {
return
add(
xs,
scaledY,
scale1);
} else {
BigInteger bigsum =
bigMultiplyPowerTen(
ys,
raise).
add(
xs);
return ((
xs^
ys)>=0) ?
new
BigDecimal(
bigsum,
INFLATED,
scale1, 0)
:
valueOf(
bigsum,
scale1, 0);
}
}
}
private static
BigDecimal add(final long
xs, int
scale1,
BigInteger snd, int
scale2) {
int
rscale =
scale1;
long
sdiff = (long)
rscale -
scale2;
boolean
sameSigns = (
Long.
signum(
xs) ==
snd.
signum);
BigInteger sum;
if (
sdiff < 0) {
int
raise =
checkScale(
xs,-
sdiff);
rscale =
scale2;
long
scaledX =
longMultiplyPowerTen(
xs,
raise);
if (
scaledX ==
INFLATED) {
sum =
snd.
add(
bigMultiplyPowerTen(
xs,
raise));
} else {
sum =
snd.
add(
scaledX);
}
} else { //if (sdiff > 0) {
int
raise =
checkScale(
snd,
sdiff);
snd =
bigMultiplyPowerTen(
snd,
raise);
sum =
snd.
add(
xs);
}
return (
sameSigns) ?
new
BigDecimal(
sum,
INFLATED,
rscale, 0) :
valueOf(
sum,
rscale, 0);
}
private static
BigDecimal add(
BigInteger fst, int
scale1,
BigInteger snd, int
scale2) {
int
rscale =
scale1;
long
sdiff = (long)
rscale -
scale2;
if (
sdiff != 0) {
if (
sdiff < 0) {
int
raise =
checkScale(
fst,-
sdiff);
rscale =
scale2;
fst =
bigMultiplyPowerTen(
fst,
raise);
} else {
int
raise =
checkScale(
snd,
sdiff);
snd =
bigMultiplyPowerTen(
snd,
raise);
}
}
BigInteger sum =
fst.
add(
snd);
return (
fst.
signum ==
snd.
signum) ?
new
BigDecimal(
sum,
INFLATED,
rscale, 0) :
valueOf(
sum,
rscale, 0);
}
private static
BigInteger bigMultiplyPowerTen(long
value, int
n) {
if (
n <= 0)
return
BigInteger.
valueOf(
value);
return
bigTenToThe(
n).
multiply(
value);
}
private static
BigInteger bigMultiplyPowerTen(
BigInteger value, int
n) {
if (
n <= 0)
return
value;
if(
n<
LONG_TEN_POWERS_TABLE.length) {
return
value.
multiply(
LONG_TEN_POWERS_TABLE[
n]);
}
return
value.
multiply(
bigTenToThe(
n));
}
/**
* Returns a {@code BigDecimal} whose value is {@code (xs /
* ys)}, with rounding according to the context settings.
*
* Fast path - used only when (xscale <= yscale && yscale < 18
* && mc.presision<18) {
*/
private static
BigDecimal divideSmallFastPath(final long
xs, int
xscale,
final long
ys, int
yscale,
long
preferredScale,
MathContext mc) {
int
mcp =
mc.
precision;
int
roundingMode =
mc.
roundingMode.
oldMode;
assert (
xscale <=
yscale) && (
yscale < 18) && (
mcp < 18);
int
xraise =
yscale -
xscale; // xraise >=0
long
scaledX = (
xraise==0) ?
xs :
longMultiplyPowerTen(
xs,
xraise); // can't overflow here!
BigDecimal quotient;
int
cmp =
longCompareMagnitude(
scaledX,
ys);
if(
cmp > 0) { // satisfy constraint (b)
yscale -= 1; // [that is, divisor *= 10]
int
scl =
checkScaleNonZero(
preferredScale +
yscale -
xscale +
mcp);
if (
checkScaleNonZero((long)
mcp +
yscale -
xscale) > 0) {
// assert newScale >= xscale
int
raise =
checkScaleNonZero((long)
mcp +
yscale -
xscale);
long
scaledXs;
if ((
scaledXs =
longMultiplyPowerTen(
xs,
raise)) ==
INFLATED) {
quotient = null;
if((
mcp-1) >=0 && (
mcp-1)<
LONG_TEN_POWERS_TABLE.length) {
quotient =
multiplyDivideAndRound(
LONG_TEN_POWERS_TABLE[
mcp-1],
scaledX,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
if(
quotient==null) {
BigInteger rb =
bigMultiplyPowerTen(
scaledX,
mcp-1);
quotient =
divideAndRound(
rb,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
} else {
quotient =
divideAndRound(
scaledXs,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
} else {
int
newScale =
checkScaleNonZero((long)
xscale -
mcp);
// assert newScale >= yscale
if (
newScale ==
yscale) { // easy case
quotient =
divideAndRound(
xs,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
int
raise =
checkScaleNonZero((long)
newScale -
yscale);
long
scaledYs;
if ((
scaledYs =
longMultiplyPowerTen(
ys,
raise)) ==
INFLATED) {
BigInteger rb =
bigMultiplyPowerTen(
ys,
raise);
quotient =
divideAndRound(
BigInteger.
valueOf(
xs),
rb,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
quotient =
divideAndRound(
xs,
scaledYs,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
}
}
} else {
// abs(scaledX) <= abs(ys)
// result is "scaledX * 10^msp / ys"
int
scl =
checkScaleNonZero(
preferredScale +
yscale -
xscale +
mcp);
if(
cmp==0) {
// abs(scaleX)== abs(ys) => result will be scaled 10^mcp + correct sign
quotient =
roundedTenPower(((
scaledX < 0) == (
ys < 0)) ? 1 : -1,
mcp,
scl,
checkScaleNonZero(
preferredScale));
} else {
// abs(scaledX) < abs(ys)
long
scaledXs;
if ((
scaledXs =
longMultiplyPowerTen(
scaledX,
mcp)) ==
INFLATED) {
quotient = null;
if(
mcp<
LONG_TEN_POWERS_TABLE.length) {
quotient =
multiplyDivideAndRound(
LONG_TEN_POWERS_TABLE[
mcp],
scaledX,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
if(
quotient==null) {
BigInteger rb =
bigMultiplyPowerTen(
scaledX,
mcp);
quotient =
divideAndRound(
rb,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
} else {
quotient =
divideAndRound(
scaledXs,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
}
}
// doRound, here, only affects 1000000000 case.
return
doRound(
quotient,
mc);
}
/**
* Returns a {@code BigDecimal} whose value is {@code (xs /
* ys)}, with rounding according to the context settings.
*/
private static
BigDecimal divide(final long
xs, int
xscale, final long
ys, int
yscale, long
preferredScale,
MathContext mc) {
int
mcp =
mc.
precision;
if(
xscale <=
yscale &&
yscale < 18 &&
mcp<18) {
return
divideSmallFastPath(
xs,
xscale,
ys,
yscale,
preferredScale,
mc);
}
if (
compareMagnitudeNormalized(
xs,
xscale,
ys,
yscale) > 0) {// satisfy constraint (b)
yscale -= 1; // [that is, divisor *= 10]
}
int
roundingMode =
mc.
roundingMode.
oldMode;
// 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'.
int
scl =
checkScaleNonZero(
preferredScale +
yscale -
xscale +
mcp);
BigDecimal quotient;
if (
checkScaleNonZero((long)
mcp +
yscale -
xscale) > 0) {
int
raise =
checkScaleNonZero((long)
mcp +
yscale -
xscale);
long
scaledXs;
if ((
scaledXs =
longMultiplyPowerTen(
xs,
raise)) ==
INFLATED) {
BigInteger rb =
bigMultiplyPowerTen(
xs,
raise);
quotient =
divideAndRound(
rb,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
quotient =
divideAndRound(
scaledXs,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
} else {
int
newScale =
checkScaleNonZero((long)
xscale -
mcp);
// assert newScale >= yscale
if (
newScale ==
yscale) { // easy case
quotient =
divideAndRound(
xs,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
int
raise =
checkScaleNonZero((long)
newScale -
yscale);
long
scaledYs;
if ((
scaledYs =
longMultiplyPowerTen(
ys,
raise)) ==
INFLATED) {
BigInteger rb =
bigMultiplyPowerTen(
ys,
raise);
quotient =
divideAndRound(
BigInteger.
valueOf(
xs),
rb,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
quotient =
divideAndRound(
xs,
scaledYs,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
}
}
// doRound, here, only affects 1000000000 case.
return
doRound(
quotient,
mc);
}
/**
* Returns a {@code BigDecimal} whose value is {@code (xs /
* ys)}, with rounding according to the context settings.
*/
private static
BigDecimal divide(
BigInteger xs, int
xscale, long
ys, int
yscale, long
preferredScale,
MathContext mc) {
// Normalize dividend & divisor so that both fall into [0.1, 0.999...]
if ((-
compareMagnitudeNormalized(
ys,
yscale,
xs,
xscale)) > 0) {// satisfy constraint (b)
yscale -= 1; // [that is, divisor *= 10]
}
int
mcp =
mc.
precision;
int
roundingMode =
mc.
roundingMode.
oldMode;
// 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 =
checkScaleNonZero(
preferredScale +
yscale -
xscale +
mcp);
if (
checkScaleNonZero((long)
mcp +
yscale -
xscale) > 0) {
int
raise =
checkScaleNonZero((long)
mcp +
yscale -
xscale);
BigInteger rb =
bigMultiplyPowerTen(
xs,
raise);
quotient =
divideAndRound(
rb,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
int
newScale =
checkScaleNonZero((long)
xscale -
mcp);
// assert newScale >= yscale
if (
newScale ==
yscale) { // easy case
quotient =
divideAndRound(
xs,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
int
raise =
checkScaleNonZero((long)
newScale -
yscale);
long
scaledYs;
if ((
scaledYs =
longMultiplyPowerTen(
ys,
raise)) ==
INFLATED) {
BigInteger rb =
bigMultiplyPowerTen(
ys,
raise);
quotient =
divideAndRound(
xs,
rb,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
quotient =
divideAndRound(
xs,
scaledYs,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
}
}
// doRound, here, only affects 1000000000 case.
return
doRound(
quotient,
mc);
}
/**
* Returns a {@code BigDecimal} whose value is {@code (xs /
* ys)}, with rounding according to the context settings.
*/
private static
BigDecimal divide(long
xs, int
xscale,
BigInteger ys, int
yscale, long
preferredScale,
MathContext mc) {
// Normalize dividend & divisor so that both fall into [0.1, 0.999...]
if (
compareMagnitudeNormalized(
xs,
xscale,
ys,
yscale) > 0) {// satisfy constraint (b)
yscale -= 1; // [that is, divisor *= 10]
}
int
mcp =
mc.
precision;
int
roundingMode =
mc.
roundingMode.
oldMode;
// 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 =
checkScaleNonZero(
preferredScale +
yscale -
xscale +
mcp);
if (
checkScaleNonZero((long)
mcp +
yscale -
xscale) > 0) {
int
raise =
checkScaleNonZero((long)
mcp +
yscale -
xscale);
BigInteger rb =
bigMultiplyPowerTen(
xs,
raise);
quotient =
divideAndRound(
rb,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
int
newScale =
checkScaleNonZero((long)
xscale -
mcp);
int
raise =
checkScaleNonZero((long)
newScale -
yscale);
BigInteger rb =
bigMultiplyPowerTen(
ys,
raise);
quotient =
divideAndRound(
BigInteger.
valueOf(
xs),
rb,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
// doRound, here, only affects 1000000000 case.
return
doRound(
quotient,
mc);
}
/**
* Returns a {@code BigDecimal} whose value is {@code (xs /
* ys)}, with rounding according to the context settings.
*/
private static
BigDecimal divide(
BigInteger xs, int
xscale,
BigInteger ys, int
yscale, long
preferredScale,
MathContext mc) {
// Normalize dividend & divisor so that both fall into [0.1, 0.999...]
if (
compareMagnitudeNormalized(
xs,
xscale,
ys,
yscale) > 0) {// satisfy constraint (b)
yscale -= 1; // [that is, divisor *= 10]
}
int
mcp =
mc.
precision;
int
roundingMode =
mc.
roundingMode.
oldMode;
// 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 =
checkScaleNonZero(
preferredScale +
yscale -
xscale +
mcp);
if (
checkScaleNonZero((long)
mcp +
yscale -
xscale) > 0) {
int
raise =
checkScaleNonZero((long)
mcp +
yscale -
xscale);
BigInteger rb =
bigMultiplyPowerTen(
xs,
raise);
quotient =
divideAndRound(
rb,
ys,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
} else {
int
newScale =
checkScaleNonZero((long)
xscale -
mcp);
int
raise =
checkScaleNonZero((long)
newScale -
yscale);
BigInteger rb =
bigMultiplyPowerTen(
ys,
raise);
quotient =
divideAndRound(
xs,
rb,
scl,
roundingMode,
checkScaleNonZero(
preferredScale));
}
// doRound, here, only affects 1000000000 case.
return
doRound(
quotient,
mc);
}
/*
* performs divideAndRound for (dividend0*dividend1, divisor)
* returns null if quotient can't fit into long value;
*/
private static
BigDecimal multiplyDivideAndRound(long
dividend0, long
dividend1, long
divisor, int
scale, int
roundingMode,
int
preferredScale) {
int
qsign =
Long.
signum(
dividend0)*
Long.
signum(
dividend1)*
Long.
signum(
divisor);
dividend0 =
Math.
abs(
dividend0);
dividend1 =
Math.
abs(
dividend1);
divisor =
Math.
abs(
divisor);
// multiply dividend0 * dividend1
long
d0_hi =
dividend0 >>> 32;
long
d0_lo =
dividend0 &
LONG_MASK;
long
d1_hi =
dividend1 >>> 32;
long
d1_lo =
dividend1 &
LONG_MASK;
long
product =
d0_lo *
d1_lo;
long
d0 =
product &
LONG_MASK;
long
d1 =
product >>> 32;
product =
d0_hi *
d1_lo +
d1;
d1 =
product &
LONG_MASK;
long
d2 =
product >>> 32;
product =
d0_lo *
d1_hi +
d1;
d1 =
product &
LONG_MASK;
d2 +=
product >>> 32;
long
d3 =
d2>>>32;
d2 &=
LONG_MASK;
product =
d0_hi*
d1_hi +
d2;
d2 =
product &
LONG_MASK;
d3 = ((
product>>>32) +
d3) &
LONG_MASK;
final long
dividendHi =
make64(
d3,
d2);
final long
dividendLo =
make64(
d1,
d0);
// divide
return
divideAndRound128(
dividendHi,
dividendLo,
divisor,
qsign,
scale,
roundingMode,
preferredScale);
}
private static final long
DIV_NUM_BASE = (1L<<32); // Number base (32 bits).
/*
* divideAndRound 128-bit value by long divisor.
* returns null if quotient can't fit into long value;
* Specialized version of Knuth's division
*/
private static
BigDecimal divideAndRound128(final long
dividendHi, final long
dividendLo, long
divisor, int
sign,
int
scale, int
roundingMode, int
preferredScale) {
if (
dividendHi >=
divisor) {
return null;
}
final int
shift =
Long.
numberOfLeadingZeros(
divisor);
divisor <<=
shift;
final long
v1 =
divisor >>> 32;
final long
v0 =
divisor &
LONG_MASK;
long
tmp =
dividendLo <<
shift;
long
u1 =
tmp >>> 32;
long
u0 =
tmp &
LONG_MASK;
tmp = (
dividendHi <<
shift) | (
dividendLo >>> 64 -
shift);
long
u2 =
tmp &
LONG_MASK;
long
q1,
r_tmp;
if (
v1 == 1) {
q1 =
tmp;
r_tmp = 0;
} else if (
tmp >= 0) {
q1 =
tmp /
v1;
r_tmp =
tmp -
q1 *
v1;
} else {
long[]
rq =
divRemNegativeLong(
tmp,
v1);
q1 =
rq[1];
r_tmp =
rq[0];
}
while(
q1 >=
DIV_NUM_BASE ||
unsignedLongCompare(
q1*
v0,
make64(
r_tmp,
u1))) {
q1--;
r_tmp +=
v1;
if (
r_tmp >=
DIV_NUM_BASE)
break;
}
tmp =
mulsub(
u2,
u1,
v1,
v0,
q1);
u1 =
tmp &
LONG_MASK;
long
q0;
if (
v1 == 1) {
q0 =
tmp;
r_tmp = 0;
} else if (
tmp >= 0) {
q0 =
tmp /
v1;
r_tmp =
tmp -
q0 *
v1;
} else {
long[]
rq =
divRemNegativeLong(
tmp,
v1);
q0 =
rq[1];
r_tmp =
rq[0];
}
while(
q0 >=
DIV_NUM_BASE ||
unsignedLongCompare(
q0*
v0,
make64(
r_tmp,
u0))) {
q0--;
r_tmp +=
v1;
if (
r_tmp >=
DIV_NUM_BASE)
break;
}
if((int)
q1 < 0) {
// result (which is positive and unsigned here)
// can't fit into long due to sign bit is used for value
MutableBigInteger mq = new
MutableBigInteger(new int[]{(int)
q1, (int)
q0});
if (
roundingMode ==
ROUND_DOWN &&
scale ==
preferredScale) {
return
mq.
toBigDecimal(
sign,
scale);
}
long
r =
mulsub(
u1,
u0,
v1,
v0,
q0) >>>
shift;
if (
r != 0) {
if(
needIncrement(
divisor >>>
shift,
roundingMode,
sign,
mq,
r)){
mq.
add(
MutableBigInteger.
ONE);
}
return
mq.
toBigDecimal(
sign,
scale);
} else {
if (
preferredScale !=
scale) {
BigInteger intVal =
mq.
toBigInteger(
sign);
return
createAndStripZerosToMatchScale(
intVal,
scale,
preferredScale);
} else {
return
mq.
toBigDecimal(
sign,
scale);
}
}
}
long
q =
make64(
q1,
q0);
q*=
sign;
if (
roundingMode ==
ROUND_DOWN &&
scale ==
preferredScale)
return
valueOf(
q,
scale);
long
r =
mulsub(
u1,
u0,
v1,
v0,
q0) >>>
shift;
if (
r != 0) {
boolean
increment =
needIncrement(
divisor >>>
shift,
roundingMode,
sign,
q,
r);
return
valueOf((
increment ?
q +
sign :
q),
scale);
} else {
if (
preferredScale !=
scale) {
return
createAndStripZerosToMatchScale(
q,
scale,
preferredScale);
} else {
return
valueOf(
q,
scale);
}
}
}
/*
* calculate divideAndRound for ldividend*10^raise / divisor
* when abs(dividend)==abs(divisor);
*/
private static
BigDecimal roundedTenPower(int
qsign, int
raise, int
scale, int
preferredScale) {
if (
scale >
preferredScale) {
int
diff =
scale -
preferredScale;
if(
diff <
raise) {
return
scaledTenPow(
raise -
diff,
qsign,
preferredScale);
} else {
return
valueOf(
qsign,
scale-
raise);
}
} else {
return
scaledTenPow(
raise,
qsign,
scale);
}
}
static
BigDecimal scaledTenPow(int
n, int
sign, int
scale) {
if (
n <
LONG_TEN_POWERS_TABLE.length)
return
valueOf(
sign*
LONG_TEN_POWERS_TABLE[
n],
scale);
else {
BigInteger unscaledVal =
bigTenToThe(
n);
if(
sign==-1) {
unscaledVal =
unscaledVal.
negate();
}
return new
BigDecimal(
unscaledVal,
INFLATED,
scale,
n+1);
}
}
/**
* Calculate the quotient and remainder of dividing a negative long by
* another long.
*
* @param n the numerator; must be negative
* @param d the denominator; must not be unity
* @return a two-element {@long} array with the remainder and quotient in
* the initial and final elements, respectively
*/
private static long[]
divRemNegativeLong(long
n, long
d) {
assert
n < 0 : "Non-negative numerator " +
n;
assert
d != 1 : "Unity denominator";
// Approximate the quotient and remainder
long
q = (
n >>> 1) / (
d >>> 1);
long
r =
n -
q *
d;
// Correct the approximation
while (
r < 0) {
r +=
d;
q--;
}
while (
r >=
d) {
r -=
d;
q++;
}
// n - q*d == r && 0 <= r < d, hence we're done.
return new long[] {
r,
q};
}
private static long
make64(long
hi, long
lo) {
return
hi<<32 |
lo;
}
private static long
mulsub(long
u1, long
u0, final long
v1, final long
v0, long
q0) {
long
tmp =
u0 -
q0*
v0;
return
make64(
u1 + (
tmp>>>32) -
q0*
v1,
tmp &
LONG_MASK);
}
private static boolean
unsignedLongCompare(long
one, long
two) {
return (
one+
Long.
MIN_VALUE) > (
two+
Long.
MIN_VALUE);
}
private static boolean
unsignedLongCompareEq(long
one, long
two) {
return (
one+
Long.
MIN_VALUE) >= (
two+
Long.
MIN_VALUE);
}
// Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
private static int
compareMagnitudeNormalized(long
xs, int
xscale, long
ys, int
yscale) {
// assert xs!=0 && ys!=0
int
sdiff =
xscale -
yscale;
if (
sdiff != 0) {
if (
sdiff < 0) {
xs =
longMultiplyPowerTen(
xs, -
sdiff);
} else { // sdiff > 0
ys =
longMultiplyPowerTen(
ys,
sdiff);
}
}
if (
xs !=
INFLATED)
return (
ys !=
INFLATED) ?
longCompareMagnitude(
xs,
ys) : -1;
else
return 1;
}
// Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
private static int
compareMagnitudeNormalized(long
xs, int
xscale,
BigInteger ys, int
yscale) {
// assert "ys can't be represented as long"
if (
xs == 0)
return -1;
int
sdiff =
xscale -
yscale;
if (
sdiff < 0) {
if (
longMultiplyPowerTen(
xs, -
sdiff) ==
INFLATED ) {
return
bigMultiplyPowerTen(
xs, -
sdiff).
compareMagnitude(
ys);
}
}
return -1;
}
// Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...]
private static int
compareMagnitudeNormalized(
BigInteger xs, int
xscale,
BigInteger ys, int
yscale) {
int
sdiff =
xscale -
yscale;
if (
sdiff < 0) {
return
bigMultiplyPowerTen(
xs, -
sdiff).
compareMagnitude(
ys);
} else { // sdiff >= 0
return
xs.
compareMagnitude(
bigMultiplyPowerTen(
ys,
sdiff));
}
}
private static long
multiply(long
x, long
y){
long
product =
x *
y;
long
ax =
Math.
abs(
x);
long
ay =
Math.
abs(
y);
if (((
ax |
ay) >>> 31 == 0) || (
y == 0) || (
product /
y ==
x)){
return
product;
}
return
INFLATED;
}
private static
BigDecimal multiply(long
x, long
y, int
scale) {
long
product =
multiply(
x,
y);
if(
product!=
INFLATED) {
return
valueOf(
product,
scale);
}
return new
BigDecimal(
BigInteger.
valueOf(
x).
multiply(
y),
INFLATED,
scale,0);
}
private static
BigDecimal multiply(long
x,
BigInteger y, int
scale) {
if(
x==0) {
return
zeroValueOf(
scale);
}
return new
BigDecimal(
y.
multiply(
x),
INFLATED,
scale,0);
}
private static
BigDecimal multiply(
BigInteger x,
BigInteger y, int
scale) {
return new
BigDecimal(
x.
multiply(
y),
INFLATED,
scale,0);
}
/**
* Multiplies two long values and rounds according {@code MathContext}
*/
private static
BigDecimal multiplyAndRound(long
x, long
y, int
scale,
MathContext mc) {
long
product =
multiply(
x,
y);
if(
product!=
INFLATED) {
return
doRound(
product,
scale,
mc);
}
// attempt to do it in 128 bits
int
rsign = 1;
if(
x < 0) {
x = -
x;
rsign = -1;
}
if(
y < 0) {
y = -
y;
rsign *= -1;
}
// multiply dividend0 * dividend1
long
m0_hi =
x >>> 32;
long
m0_lo =
x &
LONG_MASK;
long
m1_hi =
y >>> 32;
long
m1_lo =
y &
LONG_MASK;
product =
m0_lo *
m1_lo;
long
m0 =
product &
LONG_MASK;
long
m1 =
product >>> 32;
product =
m0_hi *
m1_lo +
m1;
m1 =
product &
LONG_MASK;
long
m2 =
product >>> 32;
product =
m0_lo *
m1_hi +
m1;
m1 =
product &
LONG_MASK;
m2 +=
product >>> 32;
long
m3 =
m2>>>32;
m2 &=
LONG_MASK;
product =
m0_hi*
m1_hi +
m2;
m2 =
product &
LONG_MASK;
m3 = ((
product>>>32) +
m3) &
LONG_MASK;
final long
mHi =
make64(
m3,
m2);
final long
mLo =
make64(
m1,
m0);
BigDecimal res =
doRound128(
mHi,
mLo,
rsign,
scale,
mc);
if(
res!=null) {
return
res;
}
res = new
BigDecimal(
BigInteger.
valueOf(
x).
multiply(
y*
rsign),
INFLATED,
scale, 0);
return
doRound(
res,
mc);
}
private static
BigDecimal multiplyAndRound(long
x,
BigInteger y, int
scale,
MathContext mc) {
if(
x==0) {
return
zeroValueOf(
scale);
}
return
doRound(
y.
multiply(
x),
scale,
mc);
}
private static
BigDecimal multiplyAndRound(
BigInteger x,
BigInteger y, int
scale,
MathContext mc) {
return
doRound(
x.
multiply(
y),
scale,
mc);
}
/**
* rounds 128-bit value according {@code MathContext}
* returns null if result can't be repsented as compact BigDecimal.
*/
private static
BigDecimal doRound128(long
hi, long
lo, int
sign, int
scale,
MathContext mc) {
int
mcp =
mc.
precision;
int
drop;
BigDecimal res = null;
if(((
drop =
precision(
hi,
lo) -
mcp) > 0)&&(
drop<
LONG_TEN_POWERS_TABLE.length)) {
scale =
checkScaleNonZero((long)
scale -
drop);
res =
divideAndRound128(
hi,
lo,
LONG_TEN_POWERS_TABLE[
drop],
sign,
scale,
mc.
roundingMode.
oldMode,
scale);
}
if(
res!=null) {
return
doRound(
res,
mc);
}
return null;
}
private static final long[][]
LONGLONG_TEN_POWERS_TABLE = {
{ 0L, 0x8AC7230489E80000L }, //10^19
{ 0x5L, 0x6bc75e2d63100000L }, //10^20
{ 0x36L, 0x35c9adc5dea00000L }, //10^21
{ 0x21eL, 0x19e0c9bab2400000L }, //10^22
{ 0x152dL, 0x02c7e14af6800000L }, //10^23
{ 0xd3c2L, 0x1bcecceda1000000L }, //10^24
{ 0x84595L, 0x161401484a000000L }, //10^25
{ 0x52b7d2L, 0xdcc80cd2e4000000L }, //10^26
{ 0x33b2e3cL, 0x9fd0803ce8000000L }, //10^27
{ 0x204fce5eL, 0x3e25026110000000L }, //10^28
{ 0x1431e0faeL, 0x6d7217caa0000000L }, //10^29
{ 0xc9f2c9cd0L, 0x4674edea40000000L }, //10^30
{ 0x7e37be2022L, 0xc0914b2680000000L }, //10^31
{ 0x4ee2d6d415bL, 0x85acef8100000000L }, //10^32
{ 0x314dc6448d93L, 0x38c15b0a00000000L }, //10^33
{ 0x1ed09bead87c0L, 0x378d8e6400000000L }, //10^34
{ 0x13426172c74d82L, 0x2b878fe800000000L }, //10^35
{ 0xc097ce7bc90715L, 0xb34b9f1000000000L }, //10^36
{ 0x785ee10d5da46d9L, 0x00f436a000000000L }, //10^37
{ 0x4b3b4ca85a86c47aL, 0x098a224000000000L }, //10^38
};
/*
* returns precision of 128-bit value
*/
private static int
precision(long
hi, long
lo){
if(
hi==0) {
if(
lo>=0) {
return
longDigitLength(
lo);
}
return (
unsignedLongCompareEq(
lo,
LONGLONG_TEN_POWERS_TABLE[0][1])) ? 20 : 19;
// 0x8AC7230489E80000L = unsigned 2^19
}
int
r = ((128 -
Long.
numberOfLeadingZeros(
hi) + 1) * 1233) >>> 12;
int
idx =
r-19;
return (
idx >=
LONGLONG_TEN_POWERS_TABLE.length ||
longLongCompareMagnitude(
hi,
lo,
LONGLONG_TEN_POWERS_TABLE[
idx][0],
LONGLONG_TEN_POWERS_TABLE[
idx][1])) ?
r :
r + 1;
}
/*
* returns true if 128 bit number <hi0,lo0> is less then <hi1,lo1>
* hi0 & hi1 should be non-negative
*/
private static boolean
longLongCompareMagnitude(long
hi0, long
lo0, long
hi1, long
lo1) {
if(
hi0!=
hi1) {
return
hi0<
hi1;
}
return (
lo0+
Long.
MIN_VALUE) <(
lo1+
Long.
MIN_VALUE);
}
private static
BigDecimal divide(long
dividend, int
dividendScale, long
divisor, int
divisorScale, int
scale, int
roundingMode) {
if (
checkScale(
dividend,(long)
scale +
divisorScale) >
dividendScale) {
int
newScale =
scale +
divisorScale;
int
raise =
newScale -
dividendScale;
if(
raise<
LONG_TEN_POWERS_TABLE.length) {
long
xs =
dividend;
if ((
xs =
longMultiplyPowerTen(
xs,
raise)) !=
INFLATED) {
return
divideAndRound(
xs,
divisor,
scale,
roundingMode,
scale);
}
BigDecimal q =
multiplyDivideAndRound(
LONG_TEN_POWERS_TABLE[
raise],
dividend,
divisor,
scale,
roundingMode,
scale);
if(
q!=null) {
return
q;
}
}
BigInteger scaledDividend =
bigMultiplyPowerTen(
dividend,
raise);
return
divideAndRound(
scaledDividend,
divisor,
scale,
roundingMode,
scale);
} else {
int
newScale =
checkScale(
divisor,(long)
dividendScale -
scale);
int
raise =
newScale -
divisorScale;
if(
raise<
LONG_TEN_POWERS_TABLE.length) {
long
ys =
divisor;
if ((
ys =
longMultiplyPowerTen(
ys,
raise)) !=
INFLATED) {
return
divideAndRound(
dividend,
ys,
scale,
roundingMode,
scale);
}
}
BigInteger scaledDivisor =
bigMultiplyPowerTen(
divisor,
raise);
return
divideAndRound(
BigInteger.
valueOf(
dividend),
scaledDivisor,
scale,
roundingMode,
scale);
}
}
private static
BigDecimal divide(
BigInteger dividend, int
dividendScale, long
divisor, int
divisorScale, int
scale, int
roundingMode) {
if (
checkScale(
dividend,(long)
scale +
divisorScale) >
dividendScale) {
int
newScale =
scale +
divisorScale;
int
raise =
newScale -
dividendScale;
BigInteger scaledDividend =
bigMultiplyPowerTen(
dividend,
raise);
return
divideAndRound(
scaledDividend,
divisor,
scale,
roundingMode,
scale);
} else {
int
newScale =
checkScale(
divisor,(long)
dividendScale -
scale);
int
raise =
newScale -
divisorScale;
if(
raise<
LONG_TEN_POWERS_TABLE.length) {
long
ys =
divisor;
if ((
ys =
longMultiplyPowerTen(
ys,
raise)) !=
INFLATED) {
return
divideAndRound(
dividend,
ys,
scale,
roundingMode,
scale);
}
}
BigInteger scaledDivisor =
bigMultiplyPowerTen(
divisor,
raise);
return
divideAndRound(
dividend,
scaledDivisor,
scale,
roundingMode,
scale);
}
}
private static
BigDecimal divide(long
dividend, int
dividendScale,
BigInteger divisor, int
divisorScale, int
scale, int
roundingMode) {
if (
checkScale(
dividend,(long)
scale +
divisorScale) >
dividendScale) {
int
newScale =
scale +
divisorScale;
int
raise =
newScale -
dividendScale;
BigInteger scaledDividend =
bigMultiplyPowerTen(
dividend,
raise);
return
divideAndRound(
scaledDividend,
divisor,
scale,
roundingMode,
scale);
} else {
int
newScale =
checkScale(
divisor,(long)
dividendScale -
scale);
int
raise =
newScale -
divisorScale;
BigInteger scaledDivisor =
bigMultiplyPowerTen(
divisor,
raise);
return
divideAndRound(
BigInteger.
valueOf(
dividend),
scaledDivisor,
scale,
roundingMode,
scale);
}
}
private static
BigDecimal divide(
BigInteger dividend, int
dividendScale,
BigInteger divisor, int
divisorScale, int
scale, int
roundingMode) {
if (
checkScale(
dividend,(long)
scale +
divisorScale) >
dividendScale) {
int
newScale =
scale +
divisorScale;
int
raise =
newScale -
dividendScale;
BigInteger scaledDividend =
bigMultiplyPowerTen(
dividend,
raise);
return
divideAndRound(
scaledDividend,
divisor,
scale,
roundingMode,
scale);
} else {
int
newScale =
checkScale(
divisor,(long)
dividendScale -
scale);
int
raise =
newScale -
divisorScale;
BigInteger scaledDivisor =
bigMultiplyPowerTen(
divisor,
raise);
return
divideAndRound(
dividend,
scaledDivisor,
scale,
roundingMode,
scale);
}
}
}