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Kotlin MP BigNum library

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.

Notes & Roadmap

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.

Should I use this in production?

The library is still under development, but at the moment it is feature complete, further improvements will be optimizations and bug-fixing.

WASM

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.

Integration

Gradle

implementation("com.ionspin.kotlin:bignum:0.3.10")

Snapshot builds

repositories {
    maven {
        url = uri("https://oss.sonatype.org/content/repositories/snapshots")
    }
}
implementation("com.ionspin.kotlin:bignum:0.3.11-SNAPSHOT")

Serialization

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.

Usage

Integers

Creating Big Integers

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()

Basic Arithmetic Operations

Addition

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

Subtraction

val a = BigInteger.fromLong(Long.MIN_VALUE)
val b = BigInteger.fromLong(Long.MAX_VALUE)

val difference = a - b
println("Difference: $difference")
----- Output -----
Difference: -18446744073709551615

Multiplication

val a = BigInteger.fromLong(Long.MAX_VALUE)
val b = BigInteger.fromLong(Long.MIN_VALUE)

val product = a * b

println("Product: $product")
----- Output -----
Product: -85070591730234615856620279821087277056

Division - Quotient

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

Division - Remainder

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

Division - Quotient and Remainder

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

Bitwise Operations

Shift Left

val a = BigInteger.fromByte(1)

val shifted = a shl 215
println("Shifted: $shifted")
----- Output -----
Shifted: 52656145834278593348959013841835216159447547700274555627155488768

Shift Right

val a = BigInteger.parseString("100000000000000000000000000000000", 10)

val shifted = a shr 90
----- Output -----
Shifted: 80779

Xor

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

And

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

Or

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

Binary Not

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

Modular integers

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

Floating Point

Creating

Parsing

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

From Long, Int, Short, Byte

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

Extension functions

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()

toString

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

toByteArray and fromByteArray

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):

  • fromTwosComplementByteArray
val negativeInput = ubyteArrayOf(0xFFU, 0x55U, 0x44U, 0x34U)
val negativeBigInt = BigInteger.fromTwosComplementByteArray(negativeInput.asByteArray())
  • toTwosComplementByteArray
val negativeBigInt = BigInteger.parseString("-AABBCC", 16)
val negativeBigIntArray = negativeBigInt.toTwosComplementByteArray()

Arithmetic operations

Standard arithmetic operations that are present:

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Exponentiation
  • Increase by one
  • Decrease by one
  • Absolute value
  • Negate
  • Signum

(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

DecimalMode

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.

Decimal mode resolution

  • DecimalMode supplied to the operation always overrides all other DecimalModes set in BigDecimals

  • If 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.

Scale

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:

  • add, subtract - max of the two scales
  • multiply - sum of the two scales
  • divide - min of the two scales
Infinite precision

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()
            val b = 3.toBigDecimal()
            val result = a.div(b, DecimalMode(20, RoundingMode.ROUND_HALF_AWAY_FROM_ZERO))
            result.toString() == "3.3333333333333333333E-1"
        }
    }

Convenience rounding methods

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"
        }

Rounding modes

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 towards zero as tie breaker when significant digit being rounded is 5
ROUND_HALF_TOWARDS_ZERO Round towards nearest integer, using away from 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

Modular Integers

Modular arithmetic operations are supported only between integers with the same modulo.

Creating Modular Integers

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

Sources

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.

Development environment

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!