Implements arbitrary precision arithmetic operations, including integers and floating-point numbers. Offers extensive functionality like basic arithmetic, bitwise operations, and modular arithmetic. Also supports serialization and various rounding modes.
Kotlin Multiplatform BigNum library is a pure kotlin implementation of arbitrary precision arithmetic operations. It follows the same approach as Kotlin does on JVM to keep the interface familiar.
This is an implementation of pure kotlin arbitrary integer and floating-point arithmetic support.
The APIs might change until v1.0
Version 0.3.0 brings API changes to BigDecimal API see changelog for full list.
Also, there is a plan to implement platform native versions.
Testing to verify that the library works properly is mostly done against Java BigInteger and BigDecimal implementations.
The library is still under development, but at the moment it is feature complete, further improvements will be optimizations and bug-fixing.
WASM platform is experimental, use with caution, tests for wasm are not run on Windows and Mac at the moment. Note that currently wasm returns a value after converting to IEEE-754 number, unlike other platforms (JVM, JS, Native), so if you use:
val a = BigDecimal.fromFloat(0.000000000000123f)
expect a to be 1.2299999885799495E-13.
implementation("com.ionspin.kotlin:bignum:0.3.10")
repositories {
maven {
url = uri("https://oss.sonatype.org/content/repositories/snapshots")
}
}
implementation("com.ionspin.kotlin:bignum:0.3.11-SNAPSHOT")
Serializers for KotlinX Serializtion library are provided, see more here kotlinx serialization support
Note that because kotlinx doesn't support linux ARM targets as well as MinGW x86, serialization support library doesn't either. Additionally, because of a bug when building serialization support library only JS IR variant is provided.
To create a big integer you can parse a string:
BigInteger.parse("-1122334455667788990011223344556677889900", 10)
Or use the extensions or companion function for Long, Int, Byte or Short
val bigIntegerExtension = 234L.toBigInteger()
val bigIntegerCompanion = BigInteger.fromLong(234L)
Or use extensions functions for String
"12345678".toBigInteger()
val a = BigInteger.fromLong(Long.MAX_VALUE)
val b = BigInteger.fromInt(Integer.MAX_VALUE)
val sum = a + b
println("Sum: $sum")
----- Output -----
Sum: Sum: 9223372039002259454
val a = BigInteger.fromLong(Long.MIN_VALUE)
val b = BigInteger.fromLong(Long.MAX_VALUE)
val difference = a - b
println("Difference: $difference")
----- Output -----
Difference: -18446744073709551615
val a = BigInteger.fromLong(Long.MAX_VALUE)
val b = BigInteger.fromLong(Long.MIN_VALUE)
val product = a * b
println("Product: $product")
----- Output -----
Product: -85070591730234615856620279821087277056
val a = BigInteger.fromLong(Long.MAX_VALUE)
val b = BigInteger.fromInt(Int.MAX_VALUE)
val dividend = a + b
val divisor = BigInteger.fromLong(Long.MAX_VALUE)
val quotient = dividend / divisor
println("Quotient: $quotient")
----- Output -----
Quotient: 1
val a = BigInteger.fromLong(Long.MAX_VALUE)
val b = BigInteger.fromInt(Int.MAX_VALUE)
val dividend = a + b
val divisor = BigInteger.fromLong(Long.MAX_VALUE)
val remainder = dividend % divisor
println("Remainder: $remainder")
----- Output -----
Remainder: 2147483647
val a = BigInteger.fromLong(Long.MAX_VALUE)
val b = BigInteger.fromInt(Int.MAX_VALUE)
val dividend = a + b
val divisor = BigInteger.fromLong(Long.MAX_VALUE)
val quotientAndRemainder = dividend divrem divisor
println("Quotient: ${quotientAndRemainder.quotient} \nRemainder: ${quotientAndRemainder.remainder}")
----- Output -----
Quotient: 1
Remainder: 2147483647
val a = BigInteger.fromByte(1)
val shifted = a shl 215
println("Shifted: $shifted")
----- Output -----
Shifted: 52656145834278593348959013841835216159447547700274555627155488768
val a = BigInteger.parseString("100000000000000000000000000000000", 10)
val shifted = a shr 90
----- Output -----
Shifted: 80779
val operand = BigInteger.parseString("11110000", 2)
val mask = BigInteger.parseString("00111100", 2)
val xorResult = operand xor mask
println("Xor result: ${xorResult.toString(2)}")
----- Output -----
Xor result: 11001100
val operand = BigInteger.parseString("FFFFFFFFFF000000000000", 16)
val mask = BigInteger.parseString("00000000FFFF0000000000", 16)
val andResult = operand and mask
println("And result: ${andResult.toString(16)}")
----- Output -----
And result: ff000000000000
val operand = BigInteger.parseString("FFFFFFFFFF000000000000", 16)
val mask = BigInteger.parseString("00000000FFFF0000000000", 16)
val orResult = operand or mask
println("Or result: ${orResult.toString(16)}")
----- Output -----
Or result: ffffffffffff0000000000
Unlike Java BigInteger which does two's complement inversion, this method does bitwise inversion,
i.e.:
If the number was "1100" binary, not() returns "0011" => "11" => 4 in base 10
In the same case Java BigInteger would return "1011" => -13 two's complement base 10
val operand = BigInteger.parseString("11110000", 2)
val result = operand.not()
println("Not operation result: ${result.toString(2)}")
----- Output -----
Inv result: 1111
A modInverse function that is equivalent to java BigInteger modInverse is available. Note that this method will
produce a BigInteger not a ModularBigInteger
Big integers can be converted to modularIntegers with same modulo, and then inverse() method is available. This method
will return ModularBigInteger
val a = 100_002.toBigInteger()
val modularA = a.toModularBigInteger(500.toBigInteger())
println("ModularBigInteger: ${modularA.toStringWithModulo()}")
----- Output -----
ModularBigInteger: 2 mod 500
If you want to create more ModularBigIntegers with the same module, you can retrieve creator by calling getCreator
More inforamtion about the ModularBigIntegers can be found in the third section
To create a BigDecimal you can parse a string in expanded or scientific notation
Scientific
val bigDecimal = BigDecimal.parseString("1.23E-6)")
println("BigDecimal: $bigDecimal")
----- Output -----
BigDecimal: 1.23E-6
Expanded
val bigDecimal = BigDecimal.parseString("0.00000123")
println("BigDecimal: $bigDecimal")
----- Output -----
BigDecimal: 1.23E-6
You can convert standard types to BigDecimal, i.e. Long
val bigDecimal = BigDecimal.fromLong(7111)
println("BigDecimal: $bigDecimal")
----- Output -----
BigDecimal: 7.111E+3
Or you can specify an exponent. when you do specify an exponent, input value (long, int, short, byte) is considered to be in scientific notation.
val bigDecimal = BigDecimal.fromLongWithExponent(1, -5L)
println("BigDecimal: $bigDecimal")
println("BigDecimalExpanded: ${bigDecimal.toStringExpanded()}")
----- Output -----
BigDecimal: 1.0E-5
BigDecimalExpanded: 0.00001
For String
val bigDecimal = "12345678.123".toBigInteger
Or for Double of Float
val bigDecimalFromFloat = 123.456f.toBigDecimal()
val bigDecimalFromDouble = 123.456.toBigDecimal()
Long, Int, Short, Byte
val bigDecimalFromLong = 10.toLong().toBigDecimal()
val bigDecimalFromInt = 10.toInt().toBigDecimal()
val bigDecimalFromShort = 10.toShort().toBigDecimal()
val bigDecimalFromByte = 10.toByte().toBigDecimal()
By default toString() is returned in scientific output, but expanded output is also available
val bigDecimal = BigDecimal.parseString("123.456")
println("BigDecimal: ${bigDecimal.toStringExpanded()}")
bigDecimal.toStringExpanded() == "123.456"
----- Output -----
BigDecimal: 123.456
Converts the BigInteger to and from big endian byte array.
val bigIntOriginal = BigInteger.fromULong(ULong.MAX_VALUE)
val byteArray = bigIntOriginal.toByteArray()
val reconstructed = BigInteger.fromByteArray(byteArray)
println("${bigIntOriginal == reconstructed}")
----- Output -----
true
There are two helper methods when converting from two's complement array (the same form that Java BigInteger provides):
fromTwosComplementByteArrayval negativeInput = ubyteArrayOf(0xFFU, 0x55U, 0x44U, 0x34U)
val negativeBigInt = BigInteger.fromTwosComplementByteArray(negativeInput.asByteArray())
toTwosComplementByteArrayval negativeBigInt = BigInteger.parseString("-AABBCC", 16)
val negativeBigIntArray = negativeBigInt.toTwosComplementByteArray()
Standard arithmetic operations that are present:
(Suspiciously missing is square root, should be added soon™)
Operations are executed with existing significands and then rounded down afterwards. Decimal mode parameter controls the precision and rounding mode
This is a counterpart to the Java BigDecimal MathContext and scale at the same time. Decimal mode API is under revision and will be improved during 0.3.0-0.4.0 library lifecycle
data class DecimalMode(val decimalPrecision : Long = 0, val roundingMode : RoundingMode = RoundingMode.NONE, val scale: Long = -1)
decimalPrecision defines how many digits should significand have
roundingMode defines rounding mode.
supplied to the operation always overrides all other set in s
Scale, or the number of digits to the right of the decimal, can also be specified. Default is no
scale, which puts no restriction on number of digits to the right of the decimal. When scale is
specified, a RoundingMode other than RoundingMode.NONE is also required.
When arithmetic operations have both operands unlimited precision and no scaling, the result is
also unlimited precision and no scale. When an operation mixes an unlimited precision operand
and a scaled operand, the result is unlimited precision. WHen both operands have scale,
whether unlimited precision or limited precision, then these rules for scale of the result are used:
Precision 0 and roundingMode none attempt to provide infinite precisions. Exception is division (and exponentiation with negative parameter), where default precision is the sum of precisions of operands (or 6, if the sum is below 6). If result of the operation cannot fit inside precision and RoundingMode is NONE, ArithmeticException
will be thrown.
Example from the tests:
fun readmeDivisionTest() {
assertFailsWith(ArithmeticException::class) {
val a = 1.toBigDecimal()
val b = 3.toBigDecimal()
val result = a/b
}
assertTrue {
val a = 1.toBigDecimal()
b = toBigDecimal()
result = a.div(b, DecimalMode(, RoundingMode.ROUND_HALF_AWAY_FROM_ZERO))
result.toString() ==
}
}
BigDecimal class contains two convenience rounding methods, the roundToDigitPositionAfterDecimalPoint(digitPosition: Long, roundingMode: RoundingMode)
which rounds to a specific position after the decimal point, like in the following example:
assertTrue {
val rounded = BigDecimal.fromIntWithExponent(123456789, 3)
.roundToDigitPositionAfterDecimalPoint(3, RoundingMode.CEILING)
rounded.toStringExpanded() == "1234.568"
}
and roundToDigitPosition(digitPosition: Long, roundingMode: RoundingMode) which rounds to a specifi digit precision
regardless of decimal point, like in the following example:
assertTrue {
val rounded = BigDecimal.parseString("1234.5678")
.roundToDigitPosition(3, RoundingMode.ROUND_HALF_TOWARDS_ZERO)
rounded.toStringExpanded() == "1230"
}
assertTrue {
val rounded = BigDecimal.parseString("0.0012345678")
.roundToDigitPosition(4, RoundingMode.ROUND_HALF_TOWARDS_ZERO)
rounded.toStringExpanded() == "0.001"
}
Modular arithmetic operations are supported only between integers with the same modulo.
First define the modulo you are going to use by getting an instance of the creator, and than use that creator to create instances of modular integers
val creator = ModularBigInteger.creatorForModulo(100)
val modularBigInteger = creator.fromLong(150)
println("ModularBigInteger: ${modularBigInteger.toStringWithModulo()}")
----- Output -----
ModularBigInteger: 50 mod 100
Otherwise, behavior is similar to normal integers
For examples of rounding modes consult Comparison of approaches for rounding to an integer on Wikipedia
This library draws inspiration from libraries like Java BigInteger, GNU MP Arithmetic Library, Javolution JScience, as well as following literature
Modern Computer Arithmetic
Richard P. Brent and Paul Zimmermann
Version 0.5.9 of 7 October 2010
Hacker`s Delight
Henry S. Warren, Jr.
Second Edition
Art of Computer Programming, Volume 2: Seminumerical Algorithms
Donald E. Knuth
3rd Edition
Refinement of a newton reciprocal algorithm for arbitrary precision numbers
Yiping Cheng, Ze Liu
And many other blogs and posts scattered over the internet.
If you want to try building BigNum library yourself, those are the sources I would recommend to start with.
If you are planning on contributing to the development of the library, you can set a local gradle variable
in gradle.properties in your gradle home directory (i.e. on Linux ~/.gradle/gradle.properties) called
bignumPrimaryDevelopmentOs to linux, windows or mac so that the gradle builds JVM and JS targets on your
platform. The reason for this switch is that most of the test are run on JVM by comparing results to Java BigInteger/Decimal
so they should be run on your main development OS to verify proper results, and can be skipped on other operating systems
where you are developing that platform specific features.
And thank you for contributing!
DecimalModeDecimalModesBigDecimalIf a DecimalMode is set when creating a BigDecimal that mode will be used for all operations.
If two BigDecimals have different DecimalModes with different RoundingModes an ArithmeticException will be thrown.
If the modes are same, but the precision is different, larger precision will be used.
| Name | Description |
|---|
| FLOOR | Towards negative infinity |
| CEILING | Towards positive infinity |
| AWAY_FROM_ZERO | Away from zero |
| TOWARDS_ZERO | Towards zero |
| NONE | Infinite decimalPrecision, and beyond |
| ROUND_HALF_AWAY_FROM_ZERO | Round towards nearest integer, using away from zero as tie breaker when significant digit being rounded is 5 |
| ROUND_HALF_TOWARDS_ZERO | Round towards nearest integer, using towards zero as tie breaker when significant digit being rounded is 5 |
| ROUND_HALF_CEILING | Round towards nearest integer, using towards infinity as tie breaker when significant digit being rounded is 5 |
| ROUND_HALF_FLOOR | Round towards nearest integer, using towards negative infinity as tie breaker when significant digit being rounded is 5 |
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