Packages

final class BigInt extends ScalaNumber with ScalaNumericConversions with Serializable with Ordered[BigInt]

Source
BigInt.scala
Version

1.0, 15/07/2003

Linear Supertypes
Ordered[BigInt], Comparable[BigInt], Serializable, ScalaNumericConversions, ScalaNumericAnyConversions, ScalaNumber, Number, java.io.Serializable, AnyRef, Any
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Inherited
  1. BigInt
  2. Ordered
  3. Comparable
  4. Serializable
  5. ScalaNumericConversions
  6. ScalaNumericAnyConversions
  7. ScalaNumber
  8. Number
  9. Serializable
  10. AnyRef
  11. Any
Implicitly
  1. by orderingToOrdered
  2. by any2stringadd
  3. by StringFormat
  4. by Ensuring
  5. by ArrowAssoc
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new BigInt(bigInteger: BigInteger)

Value Members

  1. final def !=(arg0: Any): Boolean

    Test two objects for inequality.

    Test two objects for inequality.

    returns

    true if !(this == that), false otherwise.

    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

    Equivalent to x.hashCode except for boxed numeric types and null.

    Equivalent to x.hashCode except for boxed numeric types and null. For numerics, it returns a hash value which is consistent with value equality: if two value type instances compare as true, then ## will produce the same hash value for each of them. For null returns a hashcode where null.hashCode throws a NullPointerException.

    returns

    a hash value consistent with ==

    Definition Classes
    AnyRef → Any
  3. def %(that: BigInt): BigInt

    Remainder of BigInts

  4. def &(that: BigInt): BigInt

    Bitwise and of BigInts

  5. def &~(that: BigInt): BigInt

    Bitwise and-not of BigInts.

    Bitwise and-not of BigInts. Returns a BigInt whose value is (this & ~that).

  6. def *(that: BigInt): BigInt

    Multiplication of BigInts

  7. def +(that: BigInt): BigInt

    Addition of BigInts

  8. def -(that: BigInt): BigInt

    Subtraction of BigInts

  9. def ->[B](y: B): (BigInt, B)
    Implicit
    This member is added by an implicit conversion from BigInt to ArrowAssoc[BigInt] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  10. def /(that: BigInt): BigInt

    Division of BigInts

  11. def /%(that: BigInt): (BigInt, BigInt)

    Returns a pair of two BigInts containing (this / that) and (this % that).

  12. def <(that: BigInt): Boolean

    Returns true if this is less than that

    Returns true if this is less than that

    Definition Classes
    Ordered
  13. def <<(n: Int): BigInt

    Leftshift of BigInt

  14. def <=(that: BigInt): Boolean

    Returns true if this is less than or equal to that.

    Returns true if this is less than or equal to that.

    Definition Classes
    Ordered
  15. final def ==(arg0: Any): Boolean

    The expression x == that is equivalent to if (x eq null) that eq null else x.equals(that).

    The expression x == that is equivalent to if (x eq null) that eq null else x.equals(that).

    returns

    true if the receiver object is equivalent to the argument; false otherwise.

    Definition Classes
    AnyRef → Any
  16. def >(that: BigInt): Boolean

    Returns true if this is greater than that.

    Returns true if this is greater than that.

    Definition Classes
    Ordered
  17. def >=(that: BigInt): Boolean

    Returns true if this is greater than or equal to that.

    Returns true if this is greater than or equal to that.

    Definition Classes
    Ordered
  18. def >>(n: Int): BigInt

    (Signed) rightshift of BigInt

  19. def ^(that: BigInt): BigInt

    Bitwise exclusive-or of BigInts

  20. def abs: BigInt

    Returns the absolute value of this BigInt

  21. final def asInstanceOf[T0]: T0

    Cast the receiver object to be of type T0.

    Cast the receiver object to be of type T0.

    Note that the success of a cast at runtime is modulo Scala's erasure semantics. Therefore the expression 1.asInstanceOf[String] will throw a ClassCastException at runtime, while the expression List(1).asInstanceOf[List[String]] will not. In the latter example, because the type argument is erased as part of compilation it is not possible to check whether the contents of the list are of the requested type.

    returns

    the receiver object.

    Definition Classes
    Any
    Exceptions thrown

    ClassCastException if the receiver object is not an instance of the erasure of type T0.

  22. val bigInteger: BigInteger
  23. def bitCount: Int

    Returns the number of bits in the two's complement representation of this BigInt that differ from its sign bit.

  24. def bitLength: Int

    Returns the number of bits in the minimal two's-complement representation of this BigInt, excluding a sign bit.

  25. def byteValue(): Byte

    Converts this BigInt to a byte.

    Converts this BigInt to a byte. If the BigInt is too big to fit in a byte, only the low-order 8 bits are returned. Note that this conversion can lose information about the overall magnitude of the BigInt value as well as return a result with the opposite sign.

    Definition Classes
    BigInt → ScalaNumericAnyConversions → Number
  26. def charValue: Char

    Converts this BigInt to a char.

    Converts this BigInt to a char. If the BigInt is too big to fit in a char, only the low-order 16 bits are returned. Note that this conversion can lose information about the overall magnitude of the BigInt value and that it always returns a positive result.

  27. def clearBit(n: Int): BigInt

    Returns a BigInt whose value is equivalent to this BigInt with the designated bit cleared.

  28. def clone(): AnyRef

    Create a copy of the receiver object.

    Create a copy of the receiver object.

    The default implementation of the clone method is platform dependent.

    returns

    a copy of the receiver object.

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
    Note

    not specified by SLS as a member of AnyRef

  29. def compare(that: BigInt): Int

    Compares this BigInt with the specified BigInt

    Compares this BigInt with the specified BigInt

    Definition Classes
    BigInt → Ordered
  30. def compareTo(that: BigInt): Int

    Result of comparing this with operand that.

    Result of comparing this with operand that.

    Definition Classes
    Ordered → Comparable
  31. def doubleValue(): Double

    Converts this BigInt to a double.

    Converts this BigInt to a double. if this BigInt has too great a magnitude to represent as a double, it will be converted to Double.NEGATIVE_INFINITY or Double.POSITIVE_INFINITY as appropriate.

    Definition Classes
    BigInt → ScalaNumericAnyConversions → Number
  32. def ensuring(cond: (BigInt) ⇒ Boolean, msg: ⇒ Any): BigInt
    Implicit
    This member is added by an implicit conversion from BigInt to Ensuring[BigInt] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  33. def ensuring(cond: (BigInt) ⇒ Boolean): BigInt
    Implicit
    This member is added by an implicit conversion from BigInt to Ensuring[BigInt] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  34. def ensuring(cond: Boolean, msg: ⇒ Any): BigInt
    Implicit
    This member is added by an implicit conversion from BigInt to Ensuring[BigInt] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  35. def ensuring(cond: Boolean): BigInt
    Implicit
    This member is added by an implicit conversion from BigInt to Ensuring[BigInt] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  36. final def eq(arg0: AnyRef): Boolean

    Tests whether the argument (that) is a reference to the receiver object (this).

    Tests whether the argument (that) is a reference to the receiver object (this).

    The eq method implements an equivalence relation on non-null instances of AnyRef, and has three additional properties:

    • It is consistent: for any non-null instances x and y of type AnyRef, multiple invocations of x.eq(y) consistently returns true or consistently returns false.
    • For any non-null instance x of type AnyRef, x.eq(null) and null.eq(x) returns false.
    • null.eq(null) returns true.

    When overriding the equals or hashCode methods, it is important to ensure that their behavior is consistent with reference equality. Therefore, if two objects are references to each other (o1 eq o2), they should be equal to each other (o1 == o2) and they should hash to the same value (o1.hashCode == o2.hashCode).

    returns

    true if the argument is a reference to the receiver object; false otherwise.

    Definition Classes
    AnyRef
  37. def equals(that: BigInt): Boolean

    Compares this BigInt with the specified BigInt for equality.

  38. def equals(that: Any): Boolean

    Compares this BigInt with the specified value for equality.

    Compares this BigInt with the specified value for equality.

    that

    the object to compare against this object for equality.

    returns

    true if the receiver object is equivalent to the argument; false otherwise.

    Definition Classes
    BigInt → AnyRef → Any
  39. def finalize(): Unit

    Called by the garbage collector on the receiver object when there are no more references to the object.

    Called by the garbage collector on the receiver object when there are no more references to the object.

    The details of when and if the finalize method is invoked, as well as the interaction between finalize and non-local returns and exceptions, are all platform dependent.

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
    Note

    not specified by SLS as a member of AnyRef

  40. def flipBit(n: Int): BigInt

    Returns a BigInt whose value is equivalent to this BigInt with the designated bit flipped.

  41. def floatValue(): Float

    Converts this BigInt to a float.

    Converts this BigInt to a float. If this BigInt has too great a magnitude to represent as a float, it will be converted to Float.NEGATIVE_INFINITY or Float.POSITIVE_INFINITY as appropriate.

    Definition Classes
    BigInt → ScalaNumericAnyConversions → Number
  42. def formatted(fmtstr: String): String

    Returns string formatted according to given format string.

    Returns string formatted according to given format string. Format strings are as for String.format (@see java.lang.String.format).

    Implicit
    This member is added by an implicit conversion from BigInt to StringFormat[BigInt] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  43. def gcd(that: BigInt): BigInt

    Returns the greatest common divisor of abs(this) and abs(that)

  44. final def getClass(): Class[_]

    Returns the runtime class representation of the object.

    Returns the runtime class representation of the object.

    returns

    a class object corresponding to the runtime type of the receiver.

    Definition Classes
    AnyRef → Any
  45. def hashCode(): Int

    Returns the hash code for this BigInt.

    Returns the hash code for this BigInt.

    returns

    the hash code value for this object.

    Definition Classes
    BigInt → AnyRef → Any
  46. def intValue(): Int

    Converts this BigInt to an int.

    Converts this BigInt to an int. If the BigInt 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 of the BigInt value as well as return a result with the opposite sign.

    Definition Classes
    BigInt → ScalaNumericAnyConversions → Number
  47. final def isInstanceOf[T0]: Boolean

    Test whether the dynamic type of the receiver object is T0.

    Test whether the dynamic type of the receiver object is T0.

    Note that the result of the test is modulo Scala's erasure semantics. Therefore the expression 1.isInstanceOf[String] will return false, while the expression List(1).isInstanceOf[List[String]] will return true. In the latter example, because the type argument is erased as part of compilation it is not possible to check whether the contents of the list are of the specified type.

    returns

    true if the receiver object is an instance of erasure of type T0; false otherwise.

    Definition Classes
    Any
  48. def isProbablePrime(certainty: Int): Boolean

    Returns true if this BigInt is probably prime, false if it's definitely composite.

    Returns true if this BigInt is probably prime, false if it's definitely composite.

    certainty

    a measure of the uncertainty that the caller is willing to tolerate: if the call returns true the probability that this BigInt is prime exceeds (1 - 1/2 ^ certainty). The execution time of this method is proportional to the value of this parameter.

  49. def isValidByte: Boolean

    Returns true iff this has a zero fractional part, and is within the range of scala.Byte MinValue and MaxValue; otherwise returns false.

    Returns true iff this has a zero fractional part, and is within the range of scala.Byte MinValue and MaxValue; otherwise returns false.

    Definition Classes
    BigInt → ScalaNumericAnyConversions
  50. def isValidChar: Boolean

    Returns true iff this has a zero fractional part, and is within the range of scala.Char MinValue and MaxValue; otherwise returns false.

    Returns true iff this has a zero fractional part, and is within the range of scala.Char MinValue and MaxValue; otherwise returns false.

    Definition Classes
    BigInt → ScalaNumericAnyConversions
  51. def isValidDouble: Boolean

    Returns true iff this can be represented exactly by scala.Double; otherwise returns false.

  52. def isValidFloat: Boolean

    Returns true iff this can be represented exactly by scala.Float; otherwise returns false.

  53. def isValidInt: Boolean

    Returns true iff this has a zero fractional part, and is within the range of scala.Int MinValue and MaxValue; otherwise returns false.

    Returns true iff this has a zero fractional part, and is within the range of scala.Int MinValue and MaxValue; otherwise returns false.

    Definition Classes
    BigInt → ScalaNumericAnyConversions
  54. def isValidLong: Boolean
  55. def isValidShort: Boolean

    Returns true iff this has a zero fractional part, and is within the range of scala.Short MinValue and MaxValue; otherwise returns false.

    Returns true iff this has a zero fractional part, and is within the range of scala.Short MinValue and MaxValue; otherwise returns false.

    Definition Classes
    BigInt → ScalaNumericAnyConversions
  56. def isWhole(): Boolean

    returns

    true if this number has no decimal component, false otherwise.

    Definition Classes
    BigInt → ScalaNumericAnyConversions → ScalaNumber
  57. def longValue(): Long

    Converts this BigInt to a long.

    Converts this BigInt to a long. If the BigInt 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 of the BigInt value as well as return a result with the opposite sign.

    Definition Classes
    BigInt → ScalaNumericAnyConversions → Number
  58. def lowestSetBit: Int

    Returns the index of the rightmost (lowest-order) one bit in this BigInt (the number of zero bits to the right of the rightmost one bit).

  59. def max(that: BigInt): BigInt

    Returns the maximum of this and that

  60. def min(that: BigInt): BigInt

    Returns the minimum of this and that

  61. def mod(that: BigInt): BigInt

    Returns a BigInt whose value is (this mod that).

    Returns a BigInt whose value is (this mod that). This method differs from % in that it always returns a non-negative BigInt.

  62. def modInverse(m: BigInt): BigInt

    Returns a BigInt whose value is (the inverse of this modulo m).

  63. def modPow(exp: BigInt, m: BigInt): BigInt

    Returns a BigInt whose value is (this raised to the power of exp modulo m).

  64. final def ne(arg0: AnyRef): Boolean

    Equivalent to !(this eq that).

    Equivalent to !(this eq that).

    returns

    true if the argument is not a reference to the receiver object; false otherwise.

    Definition Classes
    AnyRef
  65. final def notify(): Unit

    Wakes up a single thread that is waiting on the receiver object's monitor.

    Wakes up a single thread that is waiting on the receiver object's monitor.

    Definition Classes
    AnyRef
    Note

    not specified by SLS as a member of AnyRef

  66. final def notifyAll(): Unit

    Wakes up all threads that are waiting on the receiver object's monitor.

    Wakes up all threads that are waiting on the receiver object's monitor.

    Definition Classes
    AnyRef
    Note

    not specified by SLS as a member of AnyRef

  67. def pow(exp: Int): BigInt

    Returns a BigInt whose value is (this raised to the power of exp).

  68. def setBit(n: Int): BigInt

    Returns a BigInt whose value is equivalent to this BigInt with the designated bit set.

  69. def shortValue(): Short

    Converts this BigInt to a short.

    Converts this BigInt to a short. If the BigInt is too big to fit in a short, only the low-order 16 bits are returned. Note that this conversion can lose information about the overall magnitude of the BigInt value as well as return a result with the opposite sign.

    Definition Classes
    BigInt → ScalaNumericAnyConversions → Number
  70. def signum: Int

    Returns the sign of this BigInt; -1 if it is less than 0, +1 if it is greater than 0, 0 if it is equal to 0.

  71. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  72. def testBit(n: Int): Boolean

    Returns true if and only if the designated bit is set.

  73. def to(end: BigInt, step: BigInt = BigInt(1)): Inclusive[scala.BigInt]

    Like until, but inclusive of the end value.

  74. def toByte: Byte

    Returns the value of this as a scala.Byte.

    Returns the value of this as a scala.Byte. This may involve rounding or truncation.

    Definition Classes
    ScalaNumericAnyConversions
  75. def toByteArray: Array[Byte]

    Returns a byte array containing the two's-complement representation of this BigInt.

    Returns a byte array containing the two's-complement representation of this BigInt. The byte array will be in big-endian byte-order: the most significant byte is in the zeroth element. The array will contain the minimum number of bytes required to represent this BigInt, including at least one sign bit.

  76. def toChar: Char

    Returns the value of this as a scala.Char.

    Returns the value of this as a scala.Char. This may involve rounding or truncation.

    Definition Classes
    ScalaNumericAnyConversions
  77. def toDouble: Double

    Returns the value of this as a scala.Double.

    Returns the value of this as a scala.Double. This may involve rounding or truncation.

    Definition Classes
    ScalaNumericAnyConversions
  78. def toFloat: Float

    Returns the value of this as a scala.Float.

    Returns the value of this as a scala.Float. This may involve rounding or truncation.

    Definition Classes
    ScalaNumericAnyConversions
  79. def toInt: Int

    Returns the value of this as an scala.Int.

    Returns the value of this as an scala.Int. This may involve rounding or truncation.

    Definition Classes
    ScalaNumericAnyConversions
  80. def toLong: Long

    Returns the value of this as a scala.Long.

    Returns the value of this as a scala.Long. This may involve rounding or truncation.

    Definition Classes
    ScalaNumericAnyConversions
  81. def toShort: Short

    Returns the value of this as a scala.Short.

    Returns the value of this as a scala.Short. This may involve rounding or truncation.

    Definition Classes
    ScalaNumericAnyConversions
  82. def toString(radix: Int): String

    Returns the String representation in the specified radix of this BigInt.

  83. def toString(): String

    Returns the decimal String representation of this BigInt.

    Returns the decimal String representation of this BigInt.

    returns

    a String representation of the object.

    Definition Classes
    BigInt → AnyRef → Any
  84. def unary_-: BigInt

    Returns a BigInt whose value is the negation of this BigInt

  85. def unary_~: BigInt

    Returns the bitwise complement of this BigInt

  86. def underlying(): BigInteger
    Definition Classes
    BigInt → ScalaNumericConversions → ScalaNumericAnyConversions → ScalaNumber
  87. def unifiedPrimitiveEquals(x: Any): Boolean

    Should only be called after all known non-primitive types have been excluded.

    Should only be called after all known non-primitive types have been excluded. This method won't dispatch anywhere else after checking against the primitives to avoid infinite recursion between equals and this on unknown "Number" variants.

    Additionally, this should only be called if the numeric type is happy to be converted to Long, Float, and Double. If for instance a BigInt much larger than the Long range is sent here, it will claim equality with whatever Long is left in its lower 64 bits. Or a BigDecimal with more precision than Double can hold: same thing. There's no way given the interface available here to prevent this error.

    Attributes
    protected
    Definition Classes
    ScalaNumericAnyConversions
  88. def unifiedPrimitiveHashcode(): Int
    Attributes
    protected
    Definition Classes
    ScalaNumericAnyConversions
  89. def until(end: BigInt, step: BigInt = BigInt(1)): Exclusive[scala.BigInt]

    Create a NumericRange[BigInt] in range [start;end) with the specified step, where start is the target BigInt.

    Create a NumericRange[BigInt] in range [start;end) with the specified step, where start is the target BigInt.

    end

    the end value of the range (exclusive)

    step

    the distance between elements (defaults to 1)

    returns

    the range

  90. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  91. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  92. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  93. def |(that: BigInt): BigInt

    Bitwise or of BigInts

  94. def →[B](y: B): (BigInt, B)
    Implicit
    This member is added by an implicit conversion from BigInt to ArrowAssoc[BigInt] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Shadowed Implicit Value Members

  1. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from BigInt to any2stringadd[BigInt] performed by method any2stringadd in scala.Predef.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (bigInt: any2stringadd[BigInt]).+(other)
    Definition Classes
    any2stringadd
  2. def <(that: BigInt): Boolean

    Returns true if this is less than that

    Returns true if this is less than that

    Implicit
    This member is added by an implicit conversion from BigInt to Ordered[BigInt] performed by method orderingToOrdered in scala.math.Ordered.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (bigInt: Ordered[BigInt]).<(that)
    Definition Classes
    Ordered
  3. def <=(that: BigInt): Boolean

    Returns true if this is less than or equal to that.

    Returns true if this is less than or equal to that.

    Implicit
    This member is added by an implicit conversion from BigInt to Ordered[BigInt] performed by method orderingToOrdered in scala.math.Ordered.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (bigInt: Ordered[BigInt]).<=(that)
    Definition Classes
    Ordered
  4. def >(that: BigInt): Boolean

    Returns true if this is greater than that.

    Returns true if this is greater than that.

    Implicit
    This member is added by an implicit conversion from BigInt to Ordered[BigInt] performed by method orderingToOrdered in scala.math.Ordered.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (bigInt: Ordered[BigInt]).>(that)
    Definition Classes
    Ordered
  5. def >=(that: BigInt): Boolean

    Returns true if this is greater than or equal to that.

    Returns true if this is greater than or equal to that.

    Implicit
    This member is added by an implicit conversion from BigInt to Ordered[BigInt] performed by method orderingToOrdered in scala.math.Ordered.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (bigInt: Ordered[BigInt]).>=(that)
    Definition Classes
    Ordered
  6. def compare(that: BigInt): Int

    Result of comparing this with operand that.

    Result of comparing this with operand that.

    Implement this method to determine how instances of A will be sorted.

    Returns x where:

    • x < 0 when this < that
    • x == 0 when this == that
    • x > 0 when this > that
    Implicit
    This member is added by an implicit conversion from BigInt to Ordered[BigInt] performed by method orderingToOrdered in scala.math.Ordered.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (bigInt: Ordered[BigInt]).compare(that)
    Definition Classes
    Ordered
  7. def compareTo(that: BigInt): Int

    Result of comparing this with operand that.

    Result of comparing this with operand that.

    Implicit
    This member is added by an implicit conversion from BigInt to Ordered[BigInt] performed by method orderingToOrdered in scala.math.Ordered.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (bigInt: Ordered[BigInt]).compareTo(that)
    Definition Classes
    Ordered → Comparable

Inherited from Ordered[BigInt]

Inherited from Comparable[BigInt]

Inherited from Serializable

Inherited from ScalaNumericConversions

Inherited from ScalaNumericAnyConversions

Inherited from ScalaNumber

Inherited from Number

Inherited from java.io.Serializable

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion orderingToOrdered from BigInt to Ordered[BigInt]

Inherited by implicit conversion any2stringadd from BigInt to any2stringadd[BigInt]

Inherited by implicit conversion StringFormat from BigInt to StringFormat[BigInt]

Inherited by implicit conversion Ensuring from BigInt to Ensuring[BigInt]

Inherited by implicit conversion ArrowAssoc from BigInt to ArrowAssoc[BigInt]

Ungrouped