The value 1, with a scale of 0.

The value 2, with a scale of 0.

The value 10, with a scale of 0.

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.

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.

Rounding mode to round towards positive infinity. If the BigDecimal is positive, behaves as for ROUND_UP; if negative, behaves as for ROUND_DOWN. Note that this rounding mode never decreases the calculated value.

Rounding mode to round towards negative infinity. If the BigDecimal is positive, behave as for ROUND_DOWN; if negative, behave as for ROUND_UP. Note that this rounding mode never increases the calculated value.

Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round up. Behaves as for ROUND_UP if the discarded fraction is ≥ 0.5; otherwise, behaves as for ROUND_DOWN. Note that this is the rounding mode that most of us were taught in grade school.

Rounding mode to round towards "nearest neighbor" unless both neighbors are equidistant, in which case round down. Behaves as for ROUND_UP if the discarded fraction is > 0.5; otherwise, behaves as for ROUND_DOWN.

Rounding mode to round towards the "nearest neighbor" unless both neighbors are equidistant, in which case, round towards the even neighbor. Behaves as for ROUND_HALF_UP if the digit to the left of the discarded fraction is odd; behaves as for 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.

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 ArithmeticException is thrown.

Translates a character array representation of a BigDecimal into a BigDecimal, accepting the same sequence of characters as the BigDecimal(String) constructor, while allowing a sub-array to be specified and with rounding according to the context settings.

Translates a character array representation of a BigDecimal into a BigDecimal, accepting the same sequence of characters as the BigDecimal(String) constructor.

Translates a character array representation of a BigDecimal into a BigDecimal, accepting the same sequence of characters as the BigDecimal(String) constructor and with rounding according to the context settings.

Translates the string representation of a BigDecimal into a BigDecimal. The string representation consists of an optional sign, '+' ( '\u002B' ) or '-' ('\u002D'), followed by a sequence of zero or more decimal digits ("the integer"), optionally followed by a fraction, optionally followed by an exponent.

The fraction consists of a decimal point followed by zero or more decimal digits. The string must contain at least one digit in either the integer or the fraction. The number formed by the sign, the integer and the fraction is referred to as the significand.

The exponent consists of the character 'e' ('\u0065') or 'E' ('\u0045') followed by one or more decimal digits.

More formally, the strings this constructor accepts are described by the following grammar:

BigDecimalString:

Sign_opt Significand Exponent_opt

Sign:

+

-

Significand:

IntegerPart.FractionPart_opt

.FractionPart

IntegerPart

IntegerPart:

Digits

FractionPart:

Digits

Exponent:

ExponentIndicator SignedInteger

ExponentIndicator:

e

E

SignedInteger:

Sign_opt Digits

Digits:

Digit

Digits Digit

Digit:

any character for which Character.isDigit(char) returns true, including 0, 1, 2 ...

The scale of the returned 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 Integer.MIN_VALUE and Integer.MAX_VALUE, inclusive.

The character-to-digit mapping is provided by Character.digit(char, int) set to convert to radix 10. The String may not contain any extraneous characters (whitespace, for example).

Examples:
The value of the returned BigDecimal is equal to significand × 10 ^exponent. For each string on the left, the resulting representation [BigInteger, scale] is shown on the right.

 "0"            [0,0]
 "0.00"         [0,2]
 "123"          [123,0]
 "-123"         [-123,0]
 "1.23E3"       [123,-1]
 "1.23E+3"      [123,-1]
 "12.3E+7"      [123,-6]
 "12.0"         [120,1]
 "12.3"         [123,1]
 "0.00123"      [123,5]
 "-1.23E-12"    [-123,14]
 "1234.5E-4"    [12345,5]
 "0E+7"         [0,-7]
 "-0"           [0,0]
 

Translates the string representation of a BigDecimal into a BigDecimal, accepting the same strings as the BigDecimal(String) constructor, with rounding according to the context settings.

Translates a double into a BigDecimal which is the exact decimal representation of the double's binary floating-point value. The scale of the returned BigDecimal is the smallest value such that (10scale × val) is an integer.

Notes:

1. The results of this constructor can be somewhat unpredictable. One might assume that writing new BigDecimal(0.1) in Java creates a 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 double (or, for that matter, as a binary fraction of any finite length). Thus, the value that is being passed in to the constructor is not exactly equal to 0.1, appearances notwithstanding.
2. The String constructor, on the other hand, is perfectly predictable: writing new BigDecimal("0.1") creates a BigDecimal which is exactly equal to 0.1, as one would expect. Therefore, it is generally recommended that the String constructor be used in preference to this one.
3. When a double must be used as a source for a BigDecimal, note that this constructor provides an exact conversion; it does not give the same result as converting the double to a String using the Double.toString(double) method and then using the BigDecimal(String) constructor. To get that result, use the staticvalueOf(double) method.

Translates a double into a BigDecimal, with rounding according to the context settings. The scale of the BigDecimal is the smallest value such that (10scale × val) is an integer.

The results of this constructor can be somewhat unpredictable and its use is generally not recommended; see the notes under the BigDecimal(double) constructor.

Translates a BigInteger into a BigDecimal. The scale of the BigDecimal is zero.

Translates a BigInteger into a BigDecimal rounding according to the context settings. The scale of the BigDecimal is zero.

Translates a BigInteger unscaled value and an int scale into a BigDecimal. The value of the BigDecimal is (unscaledVal × 10-scale) .

Translates a BigInteger unscaled value and an int scale into a BigDecimal, with rounding according to the context settings. The value of the BigDecimal is (unscaledVal × 10-scale) , rounded according to the precision and rounding mode settings.

Translates an int into a BigDecimal. The scale of the BigDecimal is zero.

Translates an int into a BigDecimal, with rounding according to the context settings. The scale of the BigDecimal, before any rounding, is zero.

Translates a long into a BigDecimal. The scale of the BigDecimal is zero.

Translates a long into a BigDecimal, with rounding according to the context settings. The scale of the BigDecimal, before any rounding, is zero.

Translates a long value into a BigDecimal with a scale of zero.

Translates a double into a BigDecimal, using the double's canonical string representation provided by the Double.toString(double) method.

Returns a BigDecimal whose value is (this + augend) , and whose scale is max(this.scale(), augend.scale()) .

Returns a BigDecimal whose value is (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.

Returns a BigDecimal whose value is (this - subtrahend) , and whose scale is max(this.scale(), subtrahend.scale()) .

Returns a BigDecimal whose value is (this - subtrahend) , with rounding according to the context settings. If subtrahend is zero then this, rounded if necessary, is used as the result. If this is zero then the result is subtrahend.negate(mc).

Returns a BigDecimal whose value is (this × multiplicand) , and whose scale is (this.scale() + multiplicand.scale()) .

Returns a BigDecimal whose value is (this × multiplicand) , with rounding according to the context settings.

Returns a BigDecimal whose value is (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.

Returns a BigDecimal whose value is (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.

Returns a BigDecimal whose value is (this / divisor) , and whose scale is this.scale(). If rounding must be performed to generate a result with the given scale, the specified rounding mode is applied.

Returns a BigDecimal whose value is (this / divisor) , and whose scale is this.scale(). If rounding must be performed to generate a result with the given scale, the specified rounding mode is applied.

Returns a BigDecimal whose value is (this / divisor) , and whose preferred scale is (this.scale() - divisor.scale()) ; if the exact quotient cannot be represented (because it has a non-terminating decimal expansion) an ArithmeticException is thrown.

Returns a BigDecimal whose value is (this / divisor) , with rounding according to the context settings.

Returns a BigDecimal whose value is the integer part of the quotient (this / divisor) rounded down. The preferred scale of the result is (this.scale() - divisor.scale()) .

Returns a BigDecimal whose value is the integer part of (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 (this.scale() - divisor.scale()) . An ArithmeticException is thrown if the integer part of the exact quotient needs more than mc.precision digits.

Returns a BigDecimal whose value is (this % divisor) .

The remainder is given by this.subtract(this.divideToIntegralValue(divisor).multiply(divisor)). Note that this is not the modulo operation (the result can be negative).

Returns a BigDecimal whose value is (this % divisor) , with rounding according to the context settings. The 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 mc.getPrecision() digits.

The remainder is given by this.subtract(this.divideToIntegralValue(divisor, mc).multiply(divisor)) . Note that this is not the modulo operation (the result can be negative).

Returns a two-element BigDecimal array containing the result of divideToIntegralValue followed by the result of remainder on the two operands.

Note that if both the integer quotient and remainder are needed, this method is faster than using the divideToIntegralValue and remainder methods separately because the division need only be carried out once.

Returns a two-element BigDecimal array containing the result of divideToIntegralValue followed by the result of remainder on the two operands calculated with rounding according to the context settings.

Note that if both the integer quotient and remainder are needed, this method is faster than using the divideToIntegralValue and remainder methods separately because the division need only be carried out once.

Returns an approximation to the square root of this with rounding according to the context settings.

The preferred scale of the returned result is equal to this.scale()/2. The value of the returned result is always within one ulp of the exact decimal value for the precision in question. If the rounding mode is HALF_UP, HALF_DOWN, or HALF_EVEN, the result is within one half an ulp of the exact decimal value.

Special case:

• The square root of a number numerically equal to ZERO is numerically equal to ZERO with a preferred scale according to the general rule above. In particular, for ZERO, ZERO.sqrt(mc).equals(ZERO) is true with any MathContext as an argument.

Returns a BigDecimal whose value is (thisn), The power is computed exactly, to unlimited precision.

The parameter n must be in the range 0 through 999999999, inclusive. ZERO.pow(0) returns ONE. Note that future releases may expand the allowable exponent range of this method.

Returns a BigDecimal whose value is (thisn). The current implementation uses the core algorithm defined in ANSI standard X3.274-1996 with rounding according to the context settings. In general, the returned numerical value is within two ulps of the exact numerical value for the chosen precision. Note that future releases may use a different algorithm with a decreased allowable error bound and increased allowable exponent range.

The X3.274-1996 algorithm is:

• An ArithmeticException exception is thrown if
  • abs(n) > 999999999
  • mc.precision == 0 and n < 0
  • mc.precision > 0 and n has more than mc.precision decimal digits
• if n is zero, ONE is returned even if this is zero, otherwise
  • if 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 mc except for a precision increased to mc.precision + elength + 1 where elength is the number of decimal digits in n.
  • if n is negative, the result is calculated as if n were positive; this value is then divided into one using the working precision specified above.
  • The final value from either the positive or negative case is then rounded to the destination precision.

Returns a BigDecimal whose value is the absolute value of this BigDecimal, and whose scale is this.scale().

Returns a BigDecimal whose value is the absolute value of this BigDecimal, with rounding according to the context settings.

Returns a BigDecimal whose value is (-this), and whose scale is this.scale().

Returns a BigDecimal whose value is (-this), with rounding according to the context settings.

Returns a BigDecimal whose value is (+this), and whose scale is this.scale().

This method, which simply returns this BigDecimal is included for symmetry with the unary minus method negate().

Returns a BigDecimal whose value is (+this), with rounding according to the context settings.

The effect of this method is identical to that of the round(MathContext) method.

Returns the signum function of this BigDecimal.

Returns the scale of this 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 -3 means the unscaled value is multiplied by 1000.

Returns the precision of this BigDecimal. (The precision is the number of digits in the unscaled value.)

The precision of a zero value is 1.

Returns a BigInteger whose value is the unscaled value of this BigDecimal. (Computes (this * 10this.scale()) .)

Returns a BigDecimal rounded according to the MathContext settings. If the precision setting is 0 then no rounding takes place.

The effect of this method is identical to that of the plus(MathContext) method.

Returns a BigDecimal whose scale is the specified value, and whose unscaled value is determined by multiplying or dividing this 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.

Returns a BigDecimal whose scale is the specified value, and whose unscaled value is determined by multiplying or dividing this 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.

Returns a BigDecimal whose scale is the specified value, and whose value is numerically equal to this BigDecimal's. Throws an ArithmeticException if this is not possible.

This call is typically used to increase the scale, in which case it is guaranteed that there exists a 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 BigDecimal has sufficiently many zeros at the end of its fractional part (i.e., factors of ten in its integer value) to allow for the rescaling without changing its value.

This method returns the same result as the two-argument versions of setScale, but saves the caller the trouble of specifying a rounding mode in cases where it is irrelevant.

Returns a BigDecimal which is equivalent to this one with the decimal point moved n places to the left. If n is non-negative, the call merely adds n to the scale. If n is negative, the call is equivalent to movePointRight(-n). The BigDecimal returned by this call has value (this × 10-n) and scale max(this.scale()+n, 0) .

Returns a BigDecimal which is equivalent to this one with the decimal point moved n places to the right. If n is non-negative, the call merely subtracts n from the scale. If n is negative, the call is equivalent to movePointLeft(-n). The BigDecimal returned by this call has value (this × 10n) and scale max(this.scale()-n, 0) .

Returns a BigDecimal whose numerical value is equal to (this * 10ⁿ). The scale of the result is (this.scale() - n) .

Returns a 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 BigDecimal value 600.0, which has [BigInteger, scale] components equal to [6000, 1], yields 6E2 with [BigInteger, scale] components equal to [6, -2]. If this BigDecimal is numerically equal to zero, then BigDecimal.ZERO is returned.

Compares this BigDecimal numerically with the specified BigDecimal. Two BigDecimal objects that are equal in value but have a different scale (like 2.0 and 2.00) are considered equal by this method. Such values are in the same cohort. This method is provided in preference to individual methods for each of the six boolean comparison operators (<, ==, >, >=, !=, <=). The suggested idiom for performing these comparisons is: (x.compareTo(y) <op> 0), where <op> is one of the six comparison operators.

Compares this BigDecimal numerically with the specified BigDecimal. Two BigDecimal objects that are equal in value but have a different scale (like 2.0 and 2.00) are considered equal by this method. Such values are in the same cohort. This method is provided in preference to individual methods for each of the six boolean comparison operators (<, ==, >, >=, !=, <=). The suggested idiom for performing these comparisons is: (x.compareTo(y) <op> 0), where <op> is one of the six comparison operators.

Compares this BigDecimal numerically with the specified BigDecimal. Two BigDecimal objects that are equal in value but have a different scale (like 2.0 and 2.00) are considered equal by this method. Such values are in the same cohort. This method is provided in preference to individual methods for each of the six boolean comparison operators (<, ==, >, >=, !=, <=). The suggested idiom for performing these comparisons is: (x.compareTo(y) <op> 0), where <op> is one of the six comparison operators.

Compares this BigDecimal with the specified Object for equality. Unlike compareTo, this method considers two BigDecimal objects equal only if they are equal in value and scale. Therefore 2.0 is not equal to 2.00 when compared by this method since the former has [BigInteger, scale] components equal to [20, 1] while the latter has components equal to [200, 2].

Compares this BigDecimal with the specified Object for equality. Unlike compareTo, this method considers two BigDecimal objects equal only if they are equal in value and scale. Therefore 2.0 is not equal to 2.00 when compared by this method since the former has [BigInteger, scale] components equal to [20, 1] while the latter has components equal to [200, 2].

Compares this BigDecimal with the specified Object for equality. Unlike compareTo, this method considers two BigDecimal objects equal only if they are equal in value and scale. Therefore 2.0 is not equal to 2.00 when compared by this method since the former has [BigInteger, scale] components equal to [20, 1] while the latter has components equal to [200, 2].

Returns the minimum of this BigDecimal and val.

Returns the maximum of this BigDecimal and val.

Returns the hash code for this BigDecimal. The hash code is computed as a function of the unscaled value and the scale of this BigDecimal.

Returns the string representation of this BigDecimal, using scientific notation if an exponent is needed.

A standard canonical string form of the BigDecimal is created as though by the following steps: first, the absolute value of the unscaled value of the BigDecimal is converted to a string in base ten using the characters '0' through '9' with no leading zeros (except if its value is zero, in which case a single '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, -scale+(ulength-1), where 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 -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. '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 '0' character is prefixed.

Otherwise (that is, if the scale is negative, or the adjusted exponent is less than -6), the number will be converted to a character form using exponential notation. In this case, if the converted 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 'E' followed immediately by the adjusted exponent converted to a character form. The latter is in base ten, using the characters '0' through '9' with no leading zeros, and is always prefixed by a sign character '-' ('\u002D') if the adjusted exponent is negative, '+' ('\u002B') otherwise).

Finally, the entire string is prefixed by a minus sign character '-' ('\u002D') if the unscaled value is less than zero. No sign character is prefixed if the unscaled value is zero or positive.

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]     "1.23E-8"
 [-123,12]    "-1.23E-10"
 

Notes:

1. There is a one-to-one mapping between the distinguishable BigDecimal values and the result of this conversion. That is, every distinguishable BigDecimal value (unscaled value and scale) has a unique string representation as a result of using toString. If that string representation is converted back to a BigDecimal using the BigDecimal(String) constructor, then the original value will be recovered.
2. 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 NumberFormat class and its subclasses.
3. The toEngineeringString() method may be used for presenting numbers with exponents in engineering notation, and the setScale method may be used for rounding a BigDecimal so it has a known number of digits after the decimal point.
4. The digit-to-character mapping provided by Character.forDigit is used.

Returns a string representation of this BigDecimal, using engineering notation if an exponent is needed.

Returns a string that represents the 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 BigDecimal if the output string is converting back to a BigDecimal using the 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.

Returns a string representation of this BigDecimal without an exponent field. For values with a positive scale, the number of digits to the right of the decimal point is used to indicate scale. For values with a zero or negative scale, the resulting string is generated as if the value were converted to a numerically equal value with zero scale and as if all the trailing zeros of the zero scale value were present in the result. The entire string is prefixed by a minus sign character '-' ('\u002D') if the unscaled value is less than zero. No sign character is prefixed if the unscaled value is zero or positive. Note that if the result of this method is passed to the string constructor , only the numerical value of this BigDecimal will necessarily be recovered; the representation of the new BigDecimal may have a different scale. In particular, if this 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 toString method in 1.4 and earlier releases.)

Converts this BigDecimal to a BigInteger. This conversion is analogous to the narrowing primitive conversion from double to long as defined in The Java Language Specification : any fractional part of this BigDecimal will be discarded. Note that this conversion can lose information about the precision of the BigDecimal value.

To have an exception thrown if the conversion is inexact (in other words if a nonzero fractional part is discarded), use the toBigIntegerExact() method.

Converts this BigDecimal to a BigInteger, checking for lost information. An exception is thrown if this BigDecimal has a nonzero fractional part.

Converts this BigDecimal to a long. This conversion is analogous to the narrowing primitive conversion from double to short as defined in The Java Language Specification : any fractional part of this BigDecimal will be discarded, and if the resulting "BigInteger" is too big to fit in a long, only the low-order 64 bits are returned. Note that this conversion can lose information about the overall magnitude and precision of this BigDecimal value as well as return a result with the opposite sign.

Converts this BigDecimal to a long, checking for lost information. If this BigDecimal has a nonzero fractional part or is out of the possible range for a long result then an ArithmeticException is thrown.

Converts this BigDecimal to an int. This conversion is analogous to the narrowing primitive conversion from double to short as defined in The Java Language Specification : any fractional part of this BigDecimal will be discarded, and if the resulting "BigInteger" is too big to fit in an int, only the low-order 32 bits are returned. Note that this conversion can lose information about the overall magnitude and precision of this BigDecimal value as well as return a result with the opposite sign.

Converts this BigDecimal to an int, checking for lost information. If this BigDecimal has a nonzero fractional part or is out of the possible range for an int result then an ArithmeticException is thrown.

Converts this BigDecimal to a short, checking for lost information. If this BigDecimal has a nonzero fractional part or is out of the possible range for a short result then an ArithmeticException is thrown.

Converts this BigDecimal to a byte, checking for lost information. If this BigDecimal has a nonzero fractional part or is out of the possible range for a byte result then an ArithmeticException is thrown.

Converts this BigDecimal to a float. This conversion is similar to the narrowing primitive conversion from double to float as defined in The Java Language Specification : if this BigDecimal has too great a magnitude to represent as a float, it will be converted to Float.NEGATIVE_INFINITY or Float.POSITIVE_INFINITY as appropriate. Note that even when the return value is finite, this conversion can lose information about the precision of the BigDecimal value.

Converts this BigDecimal to a double. This conversion is similar to the narrowing primitive conversion from double to float as defined in The Java Language Specification : if this BigDecimal has too great a magnitude represent as a double, it will be converted to Double.NEGATIVE_INFINITY or Double.POSITIVE_INFINITY as appropriate. Note that even when the return value is finite, this conversion can lose information about the precision of the BigDecimal value.

Returns the size of an ulp, a unit in the last place, of this BigDecimal. An ulp of a nonzero BigDecimal value is the positive distance between this value and the 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 this. The result is stored with the same scale as this so the result for zero and nonzero values is equal to [1, this.scale()] .