java.lang.Object java.lang.Number java.math.BigDecimal
All Implemented Interfaces:
Comparable, Serializable
The {@code BigDecimal} class provides operations for arithmetic, scale manipulation, rounding, comparison, hashing, and format conversion. The #toString method provides a canonical representation of a {@code BigDecimal}.
The {@code BigDecimal} class gives its user complete control over rounding behavior. If no rounding mode is specified and the exact result cannot be represented, an exception is thrown; otherwise, calculations can be carried out to a chosen precision and rounding mode by supplying an appropriate MathContext object to the operation. In either case, eight rounding modes are provided for the control of rounding. Using the integer fields in this class (such as #ROUND_HALF_UP ) to represent rounding mode is largely obsolete; the enumeration values of the {@code RoundingMode} {@code enum}, (such as RoundingMode#HALF_UP ) should be used instead.
When a {@code MathContext} object is supplied with a precision setting of 0 (for example, MathContext#UNLIMITED ), arithmetic operations are exact, as are the arithmetic methods which take no {@code MathContext} object. (This is the only behavior that was supported in releases prior to 5.) As a corollary of computing the exact result, the rounding mode setting of a {@code MathContext} object with a precision setting of 0 is not used and thus irrelevant. In the case of divide, the exact quotient could have an infinitely long decimal expansion; for example, 1 divided by 3. If the quotient has a nonterminating decimal expansion and the operation is specified to return an exact result, an {@code ArithmeticException} is thrown. Otherwise, the exact result of the division is returned, as done for other operations.
When the precision setting is not 0, the rules of {@code BigDecimal} arithmetic are broadly compatible with selected modes of operation of the arithmetic defined in ANSI X3.2741996 and ANSI X3.2741996/AM 12000 (section 7.4). Unlike those standards, {@code BigDecimal} includes many rounding modes, which were mandatory for division in {@code BigDecimal} releases prior to 5. Any conflicts between these ANSI standards and the {@code BigDecimal} specification are resolved in favor of {@code BigDecimal}.
Since the same numerical value can have different representations (with different scales), the rules of arithmetic and rounding must specify both the numerical result and the scale used in the result's representation.
In general the rounding modes and precision setting determine how operations return results with a limited number of digits when the exact result has more digits (perhaps infinitely many in the case of division) than the number of digits returned. First, the total number of digits to return is specified by the {@code MathContext}'s {@code precision} setting; this determines the result's precision. The digit count starts from the leftmost nonzero digit of the exact result. The rounding mode determines how any discarded trailing digits affect the returned result.
For all arithmetic operators , the operation is carried out as though an exact intermediate result were first calculated and then rounded to the number of digits specified by the precision setting (if necessary), using the selected rounding mode. If the exact result is not returned, some digit positions of the exact result are discarded. When rounding increases the magnitude of the returned result, it is possible for a new digit position to be created by a carry propagating to a leading {@literal "9"} digit. For example, rounding the value 999.9 to three digits rounding up would be numerically equal to one thousand, represented as 100×10^{1}. In such cases, the new {@literal "1"} is the leading digit position of the returned result.
Besides a logical exact result, each arithmetic operation has a preferred scale for representing a result. The preferred scale for each operation is listed in the table below.
Operation  Preferred Scale of Result 

Add  max(addend.scale(), augend.scale()) 
Subtract  max(minuend.scale(), subtrahend.scale()) 
Multiply  multiplier.scale() + multiplicand.scale() 
Divide  dividend.scale()  divisor.scale() 
Before rounding, the scale of the logical exact intermediate
result is the preferred scale for that operation. If the exact
numerical result cannot be represented in {@code precision}
digits, rounding selects the set of digits to return and the scale
of the result is reduced from the scale of the intermediate result
to the least scale which can represent the {@code precision}
digits actually returned. If the exact result can be represented
with at most {@code precision} digits, the representation
of the result with the scale closest to the preferred scale is
returned. In particular, an exactly representable quotient may be
represented in fewer than {@code precision} digits by removing
trailing zeros and decreasing the scale. For example, rounding to
three digits using the {@linkplain RoundingMode#FLOOR floor}
rounding mode,
{@code 19/100 = 0.19 // integer=19, scale=2}
but
{@code 21/110 = 0.190 // integer=190, scale=3}
Note that for add, subtract, and multiply, the reduction in scale will equal the number of digit positions of the exact result which are discarded. If the rounding causes a carry propagation to create a new highorder digit position, an additional digit of the result is discarded than when no new digit position is created.
Other methods may have slightly different rounding semantics. For example, the result of the {@code pow} method using the {@linkplain #pow(int, MathContext) specified algorithm} can occasionally differ from the rounded mathematical result by more than one unit in the last place, one {@linkplain #ulp() ulp}.
Two types of operations are provided for manipulating the scale of a {@code BigDecimal}: scaling/rounding operations and decimal point motion operations. Scaling/rounding operations ( setScale and 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 ( movePointLeft and movePointRight ) return a {@code BigDecimal} created from the operand by moving the decimal point a specified distance in the specified direction.
For the sake of brevity and clarity, pseudocode is used throughout the descriptions of {@code BigDecimal} methods. The pseudocode 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 pseudocode 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 pseudocode expressions are interpreted similarly. Square brackets are used to represent the particular {@code BigInteger} and scale pair defining a {@code BigDecimal} value; for example [19, 2] is the {@code BigDecimal} numerically equal to 0.19 having a scale of 2.
Note: care should be exercised if {@code BigDecimal} objects are used as keys in a SortedMap or elements in a SortedSet since {@code BigDecimal}'s natural ordering is inconsistent with equals. See Comparable , java.util.SortedMap or java.util.SortedSet for more information.
All methods and constructors for this class throw {@code NullPointerException} when passed a {@code null} object reference for any input parameter.
Josh
 BlochMike
 CowlishawJoseph
 D. DarcyNested Class Summary:  

static class  BigDecimal.StringBuilderHelper 
Field Summary  

static final long  INFLATED  Sentinel value for #intCompact indicating the significand information is only available from {@code intVal}. 
public static final BigDecimal  ZERO  The value 0, with a scale of 0.

public static final BigDecimal  ONE  The value 1, with a scale of 0.

public static final BigDecimal  TEN  The value 10, with a scale of 0.

public static final int  ROUND_UP  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 static final int  ROUND_DOWN  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 static final int  ROUND_CEILING  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 static final int  ROUND_FLOOR  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 static final int  ROUND_HALF_UP  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 static final int  ROUND_HALF_DOWN  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 static final int  ROUND_HALF_EVEN  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 static final int  ROUND_UNNECESSARY  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. 
Constructor: 

public BigDecimal(char[] in){ this(in, 0, in.length); }
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 .

public BigDecimal(String val){ this(val.toCharArray(), 0, val.length()); }
The fraction consists of a decimal point followed by zero or more decimal digits. The string must contain at least one digit in either the integer or the fraction. The number formed by the sign, the integer and the fraction is referred to as the significand. The exponent consists of the character {@code 'e'} ('\u0065') or {@code 'E'} ('\u0045') followed by one or more decimal digits. The value of the exponent must lie between Integer#MAX_VALUE (Integer#MIN_VALUE +1) and Integer#MAX_VALUE , inclusive. More formally, the strings this constructor accepts are described by the following grammar: The scale of the returned {@code BigDecimal} will be the number of digits in the fraction, or zero if the string contains no decimal point, subject to adjustment for any exponent; if the string contains an exponent, the exponent is subtracted from the scale. The value of the resulting scale must lie between {@code Integer.MIN_VALUE} and {@code Integer.MAX_VALUE}, inclusive. The charactertodigit mapping is provided by java.lang.Character#digit set to convert to radix 10. The String may not contain any extraneous characters (whitespace, for example). Examples: "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] "1.23E12" [123,14] "1234.5E4" [12345,5] "0E+7" [0,7] "0" [0,0] Note: For values other than {@code float} and {@code double} NaN and ±Infinity, this constructor is compatible with the values returned by Float#toString and 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 #BigDecimal(double) constructor.

public BigDecimal(double val){ if (Double.isInfinite(val)  Double.isNaN(val)) throw new NumberFormatException("Infinite or NaN"); // Translate the double into sign, exponent and significand, according // to the formulae in JLS, Section 20.10.22. long valBits = Double.doubleToLongBits(val); int sign = ((valBits > > 63)==0 ? 1 : 1); int exponent = (int) ((valBits > > 52) & 0x7ffL); long significand = (exponent==0 ? (valBits & ((1L< < 52)  1)) < < 1 : (valBits & ((1L< < 52)  1))  (1L< < 52)); exponent = 1075; // At this point, val == sign * significand * 2**exponent. /* * Special case zero to supress nonterminating normalization * and bogus scale calculation. */ if (significand == 0) { intVal = BigInteger.ZERO; intCompact = 0; precision = 1; return; } // Normalize while((significand & 1) == 0) { // i.e., significand is even significand > >= 1; exponent++; } // Calculate intVal and scale long s = sign * significand; BigInteger b; if (exponent < 0) { b = BigInteger.valueOf(5).pow(exponent).multiply(s); scale = exponent; } else if (exponent > 0) { b = BigInteger.valueOf(2).pow(exponent).multiply(s); } else { b = BigInteger.valueOf(s); } intCompact = compactValFor(b); intVal = (intCompact != INFLATED) ? null : b; }
Notes:

public BigDecimal(BigInteger val){ intCompact = compactValFor(val); intVal = (intCompact != INFLATED) ? null : val; }

public BigDecimal(int val){ intCompact = val; } 
public BigDecimal(long val){ this.intCompact = val; this.intVal = (val == INFLATED) ? BigInteger.valueOf(val) : null; } 
public BigDecimal(char[] in, MathContext mc){ this(in, 0, in.length, mc); }
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 .

public BigDecimal(String val, MathContext mc){ this(val.toCharArray(), 0, val.length()); if (mc.precision > 0) roundThis(mc); }

public BigDecimal(double val, MathContext mc){ this(val); if (mc.precision > 0) roundThis(mc); }
The results of this constructor can be somewhat unpredictable and its use is generally not recommended; see the notes under the #BigDecimal(double) constructor.

public BigDecimal(BigInteger val, MathContext mc){ this(val); if (mc.precision > 0) roundThis(mc); }

public BigDecimal(BigInteger unscaledVal, int scale){ // Negative scales are now allowed this(unscaledVal); this.scale = scale; }

public BigDecimal(int val, MathContext mc){ intCompact = val; if (mc.precision > 0) roundThis(mc); }

public BigDecimal(long val, MathContext mc){ this(val); if (mc.precision > 0) roundThis(mc); }

public BigDecimal(char[] in, int offset, int len){ // protect against huge length. if (offset+len > in.length  offset < 0) throw new NumberFormatException(); // This is the primary string to BigDecimal constructor; all // incoming strings end up here; it uses explicit (inline) // parsing for speed and generates at most one intermediate // (temporary) object (a char[] array) for noncompact 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 toolong, len == 0, // bad offset, etc. try { // handle the sign boolean isneg = false; // assume positive if (in[offset] == '') { isneg = true; // leading minus means negative offset++; len; } else if (in[offset] == '+') { // leading + allowed offset++; len; } // should now be at numeric part of the significand boolean dot = false; // true when there is a '.' int cfirst = offset; // record start of integer long exp = 0; // exponent char c; // current character boolean isCompact = (len < = MAX_COMPACT_DIGITS); // integer significand array & idx is the index to it. The array // is ONLY used when we can't use a compact representation. char coeff[] = isCompact ? null : new char[len]; int idx = 0; for (; len > 0; offset++, len) { c = in[offset]; // have digit if ((c >= '0' && c < = '9')  Character.isDigit(c)) { // First compact case, we need not to preserve the character // and we can just compute the value in place. if (isCompact) { int digit = Character.digit(c, 10); if (digit == 0) { if (prec == 0) prec = 1; else if (rs != 0) { rs *= 10; ++prec; } // else digit is a redundant leading zero } else { if (prec != 1  rs != 0) ++prec; // prec unchanged if preceded by 0s rs = rs * 10 + digit; } } else { // the unscaled value is likely a BigInteger object. if (c == '0'  Character.digit(c, 10) == 0) { if (prec == 0) { coeff[idx] = c; prec = 1; } else if (idx != 0) { coeff[idx++] = c; ++prec; } // else c must be a redundant leading zero } else { if (prec != 1  idx != 0) ++prec; // prec unchanged if preceded by 0s coeff[idx++] = c; } } if (dot) ++scl; continue; } // have dot if (c == '.') { // have dot if (dot) // two dots throw new NumberFormatException(); dot = true; continue; } // exponent expected if ((c != 'e') && (c != 'E')) throw new NumberFormatException(); offset++; c = in[offset]; len; boolean negexp = (c == ''); // optional sign if (negexp  c == '+') { offset++; c = in[offset]; len; } if (len < = 0) // no exponent digits throw new NumberFormatException(); // skip leading zeros in the exponent while (len > 10 && Character.digit(c, 10) == 0) { offset++; c = in[offset]; len; } if (len > 10) // too many nonzero exponent digits throw new NumberFormatException(); // c now holds first digit of exponent for (;; len) { int v; if (c >= '0' && c < = '9') { v = c  '0'; } else { v = Character.digit(c, 10); if (v < 0) // not a digit throw new NumberFormatException(); } exp = exp * 10 + v; if (len == 1) break; // that was final character offset++; c = in[offset]; } if (negexp) // apply sign exp = exp; // Next test is required for backwards compatibility if ((int)exp != exp) // overflow throw new NumberFormatException(); break; // [saves a test] } // here when no characters left if (prec == 0) // no digits found throw new NumberFormatException(); // Adjust scale if exp is not zero. if (exp != 0) { // had significant exponent // Can't call checkScale which relies on proper fields value long adjustedScale = scl  exp; if (adjustedScale > Integer.MAX_VALUE  adjustedScale < Integer.MIN_VALUE) throw new NumberFormatException("Scale out of range."); scl = (int)adjustedScale; } // Remove leading zeros from precision (digits count) if (isCompact) { rs = isneg ? rs : rs; } else { char quick[]; if (!isneg) { quick = (coeff.length != prec) ? Arrays.copyOf(coeff, prec) : coeff; } else { quick = new char[prec + 1]; quick[0] = ''; System.arraycopy(coeff, 0, quick, 1, prec); } rb = new BigInteger(quick); rs = compactValFor(rb); } } catch (ArrayIndexOutOfBoundsException e) { throw new NumberFormatException(); } catch (NegativeArraySizeException e) { throw new NumberFormatException(); } this.scale = scl; this.precision = prec; this.intCompact = rs; this.intVal = (rs != INFLATED) ? null : rb; }
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 .

public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc){ this(unscaledVal); this.scale = scale; if (mc.precision > 0) roundThis(mc); }

BigDecimal(BigInteger intVal, long val, int scale, int prec){ this.scale = scale; this.precision = prec; this.intCompact = val; this.intVal = intVal; }

public BigDecimal(char[] in, int offset, int len, MathContext mc){ this(in, offset, len); if (mc.precision > 0) roundThis(mc); }
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 .

Method from java.math.BigDecimal Summary: 

abs, abs, add, add, byteValueExact, compareTo, divide, divide, divide, divide, divide, divide, divideAndRemainder, divideAndRemainder, divideToIntegralValue, divideToIntegralValue, doubleValue, equals, floatValue, hashCode, intValue, intValueExact, longValue, longValueExact, max, min, movePointLeft, movePointRight, multiply, multiply, negate, negate, plus, plus, pow, pow, precision, remainder, remainder, round, scale, scaleByPowerOfTen, setScale, setScale, setScale, shortValueExact, signum, stripTrailingZeros, subtract, subtract, toBigInteger, toBigIntegerExact, toEngineeringString, toPlainString, toString, ulp, unscaledValue, valueOf, valueOf, valueOf 
Methods from java.lang.Number: 

byteValue, doubleValue, floatValue, intValue, longValue, shortValue 
Methods from java.lang.Object: 

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Method from java.math.BigDecimal Detail: 

public BigDecimal abs(){ return (signum() < 0 ? negate() : this); }

public BigDecimal abs(MathContext mc){ return (signum() < 0 ? negate(mc) : plus(mc)); }

public BigDecimal add(BigDecimal augend){ long xs = this.intCompact; long ys = augend.intCompact; BigInteger fst = (xs != INFLATED) ? null : this.intVal; BigInteger snd = (ys != INFLATED) ? null : augend.intVal; int rscale = this.scale; long sdiff = (long)rscale  augend.scale; if (sdiff != 0) { if (sdiff < 0) { int raise = checkScale(sdiff); rscale = augend.scale; if (xs == INFLATED  (xs = longMultiplyPowerTen(xs, raise)) == INFLATED) fst = bigMultiplyPowerTen(raise); } else { int raise = augend.checkScale(sdiff); if (ys == INFLATED  (ys = longMultiplyPowerTen(ys, raise)) == INFLATED) snd = augend.bigMultiplyPowerTen(raise); } } if (xs != INFLATED && ys != INFLATED) { long sum = xs + ys; // See "Hacker's Delight" section 212 for explanation of // the overflow test. if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) // not overflowed return BigDecimal.valueOf(sum, rscale); } if (fst == null) fst = BigInteger.valueOf(xs); if (snd == null) snd = BigInteger.valueOf(ys); BigInteger sum = fst.add(snd); return (fst.signum == snd.signum) ? new BigDecimal(sum, INFLATED, rscale, 0) : new BigDecimal(sum, rscale); }

public BigDecimal add(BigDecimal augend, MathContext mc){ if (mc.precision == 0) return add(augend); BigDecimal lhs = this; // Could optimize if values are compact this.inflate(); augend.inflate(); // If either number is zero then the other number, rounded and // scaled if necessary, is used as the result. { boolean lhsIsZero = lhs.signum() == 0; boolean augendIsZero = augend.signum() == 0; if (lhsIsZero  augendIsZero) { int preferredScale = Math.max(lhs.scale(), augend.scale()); BigDecimal result; // Could use a factory for zero instead of a new object if (lhsIsZero && augendIsZero) return new BigDecimal(BigInteger.ZERO, 0, preferredScale, 0); result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc); if (result.scale() == preferredScale) return result; else if (result.scale() > preferredScale) { BigDecimal scaledResult = new BigDecimal(result.intVal, result.intCompact, result.scale, 0); scaledResult.stripZerosToMatchScale(preferredScale); return scaledResult; } else { // result.scale < preferredScale int precisionDiff = mc.precision  result.precision(); int scaleDiff = preferredScale  result.scale(); if (precisionDiff >= scaleDiff) return result.setScale(preferredScale); // can achieve target scale else return result.setScale(result.scale() + precisionDiff); } } } long padding = (long)lhs.scale  augend.scale; if (padding != 0) { // scales differ; alignment needed BigDecimal arg[] = preAlign(lhs, augend, padding, mc); matchScale(arg); lhs = arg[0]; augend = arg[1]; } BigDecimal d = new BigDecimal(lhs.inflate().add(augend.inflate()), lhs.scale); return doRound(d, mc); }

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; }

public int compareTo(BigDecimal val){ // Quick path for equal scale and noninflated 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; }

public BigDecimal divide(BigDecimal divisor){ /* * Handle zero cases first. */ if (divisor.signum() == 0) { // x/0 if (this.signum() == 0) // 0/0 throw new ArithmeticException("Division undefined"); // NaN throw new ArithmeticException("Division by zero"); } // Calculate preferred scale int preferredScale = saturateLong((long)this.scale  divisor.scale); if (this.signum() == 0) // 0/y return (preferredScale >= 0 && preferredScale < ZERO_SCALED_BY.length) ? ZERO_SCALED_BY[preferredScale] : BigDecimal.valueOf(0, preferredScale); else { this.inflate(); divisor.inflate(); /* * If the quotient this/divisor has a terminating decimal * expansion, the expansion can have no more than * (a.precision() + ceil(10*b.precision)/3) digits. * Therefore, create a MathContext object with this * precision and do a divide with the UNNECESSARY rounding * mode. */ MathContext mc = new MathContext( (int)Math.min(this.precision() + (long)Math.ceil(10.0*divisor.precision()/3.0), Integer.MAX_VALUE), RoundingMode.UNNECESSARY); BigDecimal quotient; try { quotient = this.divide(divisor, mc); } catch (ArithmeticException e) { throw new ArithmeticException("Nonterminating 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; } }

public BigDecimal divide(BigDecimal divisor, int roundingMode){ return this.divide(divisor, scale, roundingMode); }
The new #divide(BigDecimal, RoundingMode) method should be used in preference to this legacy method. 
public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode){ return this.divide(divisor, scale, roundingMode.oldMode); }

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 // divideandround method, but as this rounds to scale we have // to normalize the values here to achieve the desired result. // For x/y we first handle y=0 and x=0, and then normalize x and // y to give x' and y' with the following constraints: // (a) 0.1 < = x' < 1 // (b) x' < = y' < 10*x' // Dividing x'/y' with the required scale set to mc.precision then // will give a result in the range 0.1 to 1 rounded to exactly // the right number of digits (except in the case of a result of // 1.000... which can arise when x=y, or when rounding overflows // The 1.000... case will reduce properly to 1. if (divisor.signum() == 0) { // x/0 if (dividend.signum() == 0) // 0/0 throw new ArithmeticException("Division undefined"); // NaN throw new ArithmeticException("Division by zero"); } if (dividend.signum() == 0) // 0/y return new BigDecimal(BigInteger.ZERO, 0, saturateLong(preferredScale), 1); // Normalize dividend & divisor so that both fall into [0.1, 0.999...] int xscale = dividend.precision(); int yscale = divisor.precision(); dividend = new BigDecimal(dividend.intVal, dividend.intCompact, xscale, xscale); divisor = new BigDecimal(divisor.intVal, divisor.intCompact, yscale, yscale); if (dividend.compareMagnitude(divisor) > 0) // satisfy constraint (b) yscale = divisor.scale = 1; // [that is, divisor *= 10] // In order to find out whether the divide generates the exact result, // we avoid calling the above divide method. 'quotient' holds the // return BigDecimal object whose scale will be set to 'scl'. BigDecimal quotient; int scl = checkScale(preferredScale + yscale  xscale + mcp); if (checkScale((long)mcp + yscale) > xscale) dividend = dividend.setScale(mcp + yscale, ROUND_UNNECESSARY); else divisor = divisor.setScale(checkScale((long)xscale  mcp), ROUND_UNNECESSARY); quotient = divideAndRound(dividend.intCompact, dividend.intVal, divisor.intCompact, divisor.intVal, scl, mc.roundingMode.oldMode, checkScale(preferredScale)); // doRound, here, only affects 1000000000 case. quotient = doRound(quotient, mc); return quotient; }

public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode){ /* * IMPLEMENTATION NOTE: This method *must* return a new object * since divideAndRound uses divide to generate a value whose * scale is then modified. */ if (roundingMode < ROUND_UP  roundingMode > ROUND_UNNECESSARY) throw new IllegalArgumentException("Invalid rounding mode"); /* * Rescale dividend or divisor (whichever can be "upscaled" to * produce correctly scaled quotient). * Take care to detect outofrange scales */ BigDecimal dividend = this; if (checkScale((long)scale + divisor.scale) > this.scale) dividend = this.setScale(scale + divisor.scale, ROUND_UNNECESSARY); else divisor = divisor.setScale(checkScale((long)this.scale  scale), ROUND_UNNECESSARY); return divideAndRound(dividend.intCompact, dividend.intVal, divisor.intCompact, divisor.intVal, scale, roundingMode, scale); }
The new #divide(BigDecimal, int, RoundingMode) method should be used in preference to this legacy method. 
public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode){ return divide(divisor, scale, roundingMode.oldMode); }

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; }
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. 
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; }
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. 
public BigDecimal divideToIntegralValue(BigDecimal divisor){ // Calculate preferred scale int preferredScale = saturateLong((long)this.scale  divisor.scale); if (this.compareMagnitude(divisor) < 0) { // much faster when this < < divisor return BigDecimal.valueOf(0, preferredScale); } if(this.signum() == 0 && divisor.signum() != 0) return this.setScale(preferredScale, ROUND_UNNECESSARY); // Perform a divide with enough digits to round to a correct // integer value; then remove any fractional digits int maxDigits = (int)Math.min(this.precision() + (long)Math.ceil(10.0*divisor.precision()/3.0) + Math.abs((long)this.scale()  divisor.scale()) + 2, Integer.MAX_VALUE); BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits, RoundingMode.DOWN)); if (quotient.scale > 0) { quotient = quotient.setScale(0, RoundingMode.DOWN); quotient.stripZerosToMatchScale(preferredScale); } if (quotient.scale < preferredScale) { // pad with zeros if necessary quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY); } return quotient; }

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, // dividendproduct < divisor. if (this.subtract(product).compareMagnitude(divisor) >= 0) { throw new ArithmeticException("Division impossible"); } } else if (result.scale() > 0) { /* * Integer portion of quotient will fit into precision * digits; recompute quotient to scale 0 to avoid double * rounding and then try to adjust, if necessary. */ result = result.setScale(0, RoundingMode.DOWN); } // else result.scale() == 0; int precisionDiff; if ((preferredScale > result.scale()) && (precisionDiff = mc.precision  result.precision()) > 0) { return result.setScale(result.scale() + Math.min(precisionDiff, preferredScale  result.scale) ); } else { result.stripZerosToMatchScale(preferredScale); return result; } }

public double doubleValue(){ if (scale == 0 && intCompact != INFLATED) return (double)intCompact; // Somewhat inefficient, but guaranteed to work. return Double.parseDouble(this.toString()); }

public boolean equals(Object x){ if (!(x instanceof BigDecimal)) return false; BigDecimal xDec = (BigDecimal) x; if (x == this) return true; if (scale != xDec.scale) return false; long s = this.intCompact; long xs = xDec.intCompact; if (s != INFLATED) { if (xs == INFLATED) xs = compactValFor(xDec.intVal); return xs == s; } else if (xs != INFLATED) return xs == compactValFor(this.intVal); return this.inflate().equals(xDec.inflate()); }

public float floatValue(){ if (scale == 0 && intCompact != INFLATED) return (float)intCompact; // Somewhat inefficient, but guaranteed to work. return Float.parseFloat(this.toString()); }

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; }

public int intValue(){ return (intCompact != INFLATED && scale == 0) ? (int)intCompact : toBigInteger().intValue(); }

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; }

public long longValue(){ return (intCompact != INFLATED && scale == 0) ? intCompact: toBigInteger().longValue(); }

public long longValueExact(){ if (intCompact != INFLATED && scale == 0) return intCompact; // If more than 19 digits in integer part it cannot possibly fit if ((precision()  scale) > 19) // [OK for negative scale too] throw new java.lang.ArithmeticException("Overflow"); // Fastpath zero and < 1.0 numbers (the latter can be very slow // to round if very small) if (this.signum() == 0) return 0; if ((this.precision()  this.scale) < = 0) throw new ArithmeticException("Rounding necessary"); // round to an integer, with Exception if decimal part non0 BigDecimal num = this.setScale(0, ROUND_UNNECESSARY); if (num.precision() >= 19) // need to check carefully LongOverflow.check(num); return num.inflate().longValue(); }

public BigDecimal max(BigDecimal val){ return (compareTo(val) >= 0 ? this : val); }

public BigDecimal min(BigDecimal val){ return (compareTo(val) < = 0 ? this : val); }

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; }

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; }

public BigDecimal multiply(BigDecimal multiplicand){ long x = this.intCompact; long y = multiplicand.intCompact; int productScale = checkScale((long)scale + multiplicand.scale); // Might be able to do a more clever check incorporating the // inflated check into the overflow computation. if (x != INFLATED && y != INFLATED) { /* * If the product is not an overflowed value, continue * to use the compact representation. if either of x or y * is INFLATED, the product should also be regarded as * an overflow. Before using the overflow test suggested in * "Hacker's Delight" section 212, we perform quick checks * using the precision information to see whether the overflow * would occur since division is expensive on most CPUs. */ long product = x * y; long prec = this.precision() + multiplicand.precision(); if (prec < 19  (prec < 21 && (y == 0  product / y == x))) return BigDecimal.valueOf(product, productScale); return new BigDecimal(BigInteger.valueOf(x).multiply(y), INFLATED, productScale, 0); } BigInteger rb; if (x == INFLATED && y == INFLATED) rb = this.intVal.multiply(multiplicand.intVal); else if (x != INFLATED) rb = multiplicand.intVal.multiply(x); else rb = this.intVal.multiply(y); return new BigDecimal(rb, INFLATED, productScale, 0); }

public BigDecimal multiply(BigDecimal multiplicand, MathContext mc){ if (mc.precision == 0) return multiply(multiplicand); return doRound(this.multiply(multiplicand), mc); }

public BigDecimal negate(){ BigDecimal result; if (intCompact != INFLATED) result = BigDecimal.valueOf(intCompact, scale); else { result = new BigDecimal(intVal.negate(), scale); result.precision = precision; } return result; }

public BigDecimal negate(MathContext mc){ return negate().plus(mc); }

public BigDecimal plus(){ return this; }
This method, which simply returns this {@code BigDecimal} is included for symmetry with the unary minus method #negate() . 
public BigDecimal plus(MathContext mc){ if (mc.precision == 0) // no rounding please return this; return doRound(this, mc); }
The effect of this method is identical to that of the #round(MathContext) method. 
public BigDecimal pow(int n){ if (n < 0  n > 999999999) throw new ArithmeticException("Invalid operation"); // No need to calculate pow(n) if result will over/underflow. // Don't attempt to support "supernormal" numbers. int newScale = checkScale((long)scale * n); this.inflate(); return new BigDecimal(intVal.pow(n), newScale); }
The parameter {@code n} must be in the range 0 through 999999999, inclusive. {@code ZERO.pow(0)} returns #ONE . Note that future releases may expand the allowable exponent range of this method. 
public BigDecimal pow(int n, MathContext mc){ if (mc.precision == 0) return pow(n); if (n < 999999999  n > 999999999) throw new ArithmeticException("Invalid operation"); if (n == 0) return ONE; // x**0 == 1 in X3.274 this.inflate(); BigDecimal lhs = this; MathContext workmc = mc; // working settings int mag = Math.abs(n); // magnitude of n if (mc.precision > 0) { int elength = longDigitLength(mag); // length of n in digits if (elength > mc.precision) // X3.274 rule throw new ArithmeticException("Invalid operation"); workmc = new MathContext(mc.precision + elength + 1, mc.roundingMode); } // ready to carry out power calculation... BigDecimal acc = ONE; // accumulator boolean seenbit = false; // set once we've seen a 1bit 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); }
The X3.2741996 algorithm is: 
public int precision(){ int result = precision; if (result == 0) { long s = intCompact; if (s != INFLATED) result = longDigitLength(s); else result = bigDigitLength(inflate()); precision = result; } return result; }
The precision of a zero value is 1. 
public BigDecimal remainder(BigDecimal divisor){ BigDecimal divrem[] = this.divideAndRemainder(divisor); return divrem[1]; }
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). 
public BigDecimal remainder(BigDecimal divisor, MathContext mc){ BigDecimal divrem[] = this.divideAndRemainder(divisor, mc); return divrem[1]; }
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). 
public BigDecimal round(MathContext mc){ return plus(mc); }
The effect of this method is identical to that of the #plus(MathContext) method. 
public int scale(){ return scale; }

public BigDecimal scaleByPowerOfTen(int n){ return new BigDecimal(intVal, intCompact, checkScale((long)scale  n), precision); }

public BigDecimal setScale(int newScale){ return setScale(newScale, ROUND_UNNECESSARY); }
This call is typically used to increase the scale, in which case it is guaranteed that there exists a {@code BigDecimal} of the specified scale and the correct value. The call can also be used to reduce the scale if the caller knows that the {@code BigDecimal} has sufficiently many zeros at the end of its fractional part (i.e., factors of ten in its integer value) to allow for the rescaling without changing its value. This method returns the same result as the twoargument versions of {@code setScale}, but saves the caller the trouble of specifying a rounding mode in cases where it is irrelevant. Note that since {@code BigDecimal} objects are immutable, calls of this method do not result in the original object being modified, contrary to the usual convention of having methods named setX mutate field {@code X}. Instead, {@code setScale} returns an object with the proper scale; the returned object may or may not be newly allocated. 
public BigDecimal setScale(int newScale, RoundingMode roundingMode){ return setScale(newScale, roundingMode.oldMode); }
Note that since BigDecimal objects are immutable, calls of this method do not result in the original object being modified, contrary to the usual convention of having methods named setX mutate field {@code X}. Instead, {@code setScale} returns an object with the proper scale; the returned object may or may not be newly allocated. 
public BigDecimal setScale(int newScale, int roundingMode){ if (roundingMode < ROUND_UP  roundingMode > ROUND_UNNECESSARY) throw new IllegalArgumentException("Invalid rounding mode"); int oldScale = this.scale; if (newScale == oldScale) // easy case return this; if (this.signum() == 0) // zero can have any scale return BigDecimal.valueOf(0, newScale); long rs = this.intCompact; if (newScale > oldScale) { int raise = checkScale((long)newScale  oldScale); BigInteger rb = null; if (rs == INFLATED  (rs = longMultiplyPowerTen(rs, raise)) == INFLATED) rb = bigMultiplyPowerTen(raise); return new BigDecimal(rb, rs, newScale, (precision > 0) ? precision + raise : 0); } else { // newScale < oldScale  drop some digits // Can't predict the precision due to the effect of rounding. int drop = checkScale((long)oldScale  newScale); if (drop < LONG_TEN_POWERS_TABLE.length) return divideAndRound(rs, this.intVal, LONG_TEN_POWERS_TABLE[drop], null, newScale, roundingMode, newScale); else return divideAndRound(rs, this.intVal, INFLATED, bigTenToThe(drop), newScale, roundingMode, newScale); } }
Note that since BigDecimal objects are immutable, calls of this method do not result in the original object being modified, contrary to the usual convention of having methods named setX mutate field {@code X}. Instead, {@code setScale} returns an object with the proper scale; the returned object may or may not be newly allocated. The new #setScale(int, RoundingMode) method should be used in preference to this legacy method. 
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; }

public int signum(){ return (intCompact != INFLATED)? Long.signum(intCompact): intVal.signum(); }

public BigDecimal stripTrailingZeros(){ this.inflate(); BigDecimal result = new BigDecimal(intVal, scale); result.stripZerosToMatchScale(Long.MIN_VALUE); return result; }

public BigDecimal subtract(BigDecimal subtrahend){ return add(subtrahend.negate()); }

public BigDecimal subtract(BigDecimal subtrahend, MathContext mc){ BigDecimal nsubtrahend = subtrahend.negate(); if (mc.precision == 0) return add(nsubtrahend); // share the special rounding code in add() return add(nsubtrahend, mc); }

public BigInteger toBigInteger(){ // force to an integer, quietly return this.setScale(0, ROUND_DOWN).inflate(); }
To have an exception thrown if the conversion is inexact (in other words if a nonzero fractional part is discarded), use the #toBigIntegerExact() method. 
public BigInteger toBigIntegerExact(){ // round to an integer, with Exception if decimal part non0 return this.setScale(0, ROUND_UNNECESSARY).inflate(); }

public String toEngineeringString(){ return layoutChars(false); }
Returns a string that represents the {@code BigDecimal} as described in the #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 #toString() , the output of this method is not guaranteed to recover the same [integer, scale] pair of this {@code BigDecimal} if the output string is converting back to a {@code BigDecimal} using the {@linkplain #BigDecimal(String) string constructor}. The result of this method meets the weaker constraint of always producing a numerically equal result from applying the string constructor to the method's output. 
public String toPlainString(){ BigDecimal bd = this; if (bd.scale < 0) bd = bd.setScale(0); bd.inflate(); if (bd.scale == 0) // No decimal point return bd.intVal.toString(); return bd.getValueString(bd.signum(), bd.intVal.abs().toString(), bd.scale); }

public String toString(){ String sc = stringCache; if (sc == null) stringCache = sc = layoutChars(true); return sc; }
A standard canonical string form of the {@code BigDecimal} is created as though by the following steps: first, the absolute value of the unscaled value of the {@code BigDecimal} is converted to a string in base ten using the characters {@code '0'} through {@code '9'} with no leading zeros (except if its value is zero, in which case a single {@code '0'} character is used). Next, an adjusted exponent is calculated; this is the negated scale, plus the number of characters in the converted unscaled value, less one. That is, {@code scale+(ulength1)}, where {@code ulength} is the length of the absolute value of the unscaled value in decimal digits (its precision). If the scale is greater than or equal to zero and the adjusted exponent is greater than or equal to {@code 6}, the number will be converted to a character form without using exponential notation. In this case, if the scale is zero then no decimal point is added and if the scale is positive a decimal point will be inserted with the scale specifying the number of characters to the right of the decimal point. {@code '0'} characters are added to the left of the converted unscaled value as necessary. If no character precedes the decimal point after this insertion then a conventional {@code '0'} character is prefixed. Otherwise (that is, if the scale is negative, or the adjusted exponent is less than {@code 6}), the number will be converted to a character form using exponential notation. In this case, if the converted {@code BigInteger} has more than one digit a decimal point is inserted after the first digit. An exponent in character form is then suffixed to the converted unscaled value (perhaps with inserted decimal point); this comprises the letter {@code 'E'} followed immediately by the adjusted exponent converted to a character form. The latter is in base ten, using the characters {@code '0'} through {@code '9'} with no leading zeros, and is always prefixed by a sign character {@code ''} ('\u002D') if the adjusted exponent is negative, {@code '+'} ('\u002B') otherwise). Finally, the entire string is prefixed by a minus sign character {@code ''} ('\u002D') if the unscaled value is less than zero. No sign character is prefixed if the unscaled value is zero or positive. Examples: For each representation [unscaled value, scale] on the left, the resulting string is shown on the right. [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] "1.23E8" [123,12] "1.23E10"Notes:

public BigDecimal ulp(){ return BigDecimal.valueOf(1, this.scale()); }

public BigInteger unscaledValue(){ return this.inflate(); }

public static BigDecimal valueOf(long val){ if (val >= 0 && val < zeroThroughTen.length) return zeroThroughTen[(int)val]; else if (val != INFLATED) return new BigDecimal(null, val, 0, 0); return new BigDecimal(BigInteger.valueOf(val), val, 0, 0); }

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)); }
Note: This is generally the preferred way to convert a {@code double} (or {@code float}) into a {@code BigDecimal}, as the value returned is equal to that resulting from constructing a {@code BigDecimal} from the result of using Double#toString(double) . 
public static BigDecimal valueOf(long unscaledVal, int scale){ if (scale == 0) return valueOf(unscaledVal); else if (unscaledVal == 0) { if (scale > 0 && scale < ZERO_SCALED_BY.length) return ZERO_SCALED_BY[scale]; else return new BigDecimal(BigInteger.ZERO, 0, scale, 1); } return new BigDecimal(unscaledVal == INFLATED ? BigInteger.valueOf(unscaledVal) : null, unscaledVal, scale, 0); }
