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bigint.dart
568 lines (525 loc) · 20.2 KB
/
bigint.dart
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// Copyright (c) 2017, the Dart project authors. Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.
part of dart.core;
/// An arbitrarily large integer value.
///
/// Big integers are signed and can have an arbitrary number of
/// significant digits, only limited by memory.
///
/// To create a big integer from the provided number, use [BigInt.from].
/// ```dart
/// var bigInteger = BigInt.from(-1); // -1
/// bigInteger = BigInt.from(0.9999); // 0
/// bigInteger = BigInt.from(-10.99); // -10
/// bigInteger = BigInt.from(0x7FFFFFFFFFFFFFFF); // 9223372036854775807
/// bigInteger = BigInt.from(1e+30); // 1000000000000000019884624838656
/// ```
/// To parse a large integer value from a string, use [parse] or [tryParse].
/// ```dart
/// var value = BigInt.parse('0x1ffffffffffffffff'); // 36893488147419103231
/// value = BigInt.parse('12345678901234567890'); // 12345678901234567890
/// ```
/// To check whether a big integer can be represented as an [int] without losing
/// precision, use [isValidInt].
/// ```dart continued
/// print(bigNumber.isValidInt); // false
/// ```
/// To convert a big integer into an [int], use [toInt].
/// To convert a big integer into an [double], use [toDouble].
/// ```dart
/// var bigValue = BigInt.from(10).pow(3);
/// print(bigValue.isValidInt); // true
/// print(bigValue.toInt()); // 1000
/// print(bigValue.toDouble()); // 1000.0
/// ```
/// **See also:**
/// * [int]: An integer number.
/// * [double]: A double-precision floating point number.
/// * [num]: The super class for [int] and [double].
/// * [Numbers](https://dart.dev/guides/language/numbers) in
/// [A tour of the Dart language](https://dart.dev/guides/language/language-tour).
abstract class BigInt implements Comparable<BigInt> {
/// A big integer with the numerical value 0.
external static BigInt get zero;
/// A big integer with the numerical value 1.
external static BigInt get one;
/// A big integer with the numerical value 2.
external static BigInt get two;
/// Parses [source] as a, possibly signed, integer literal and returns its
/// value.
///
/// The [source] must be a non-empty sequence of base-[radix] digits,
/// optionally prefixed with a minus or plus sign ('-' or '+').
///
/// The [radix] must be in the range 2..36. The digits used are
/// first the decimal digits 0..9, and then the letters 'a'..'z' with
/// values 10 through 35. Also accepts upper-case letters with the same
/// values as the lower-case ones.
///
/// If no [radix] is given then it defaults to 10. In this case, the [source]
/// digits may also start with `0x`, in which case the number is interpreted
/// as a hexadecimal literal, which effectively means that the `0x` is ignored
/// and the radix is instead set to 16.
///
/// For any int `n` and radix `r`, it is guaranteed that
/// `n == int.parse(n.toRadixString(r), radix: r)`.
///
/// Throws a [FormatException] if the [source] is not a valid integer literal,
/// optionally prefixed by a sign.
/// Examples:
/// ```dart
/// print(BigInt.parse('-12345678901234567890')); // -12345678901234567890
/// print(BigInt.parse('0xFF')); // 255
/// print(BigInt.parse('0xffffffffffffffff')); // 18446744073709551615
///
/// // From binary (base 2) value.
/// print(BigInt.parse('1100', radix: 2)); // 12
/// print(BigInt.parse('00011111', radix: 2)); // 31
/// print(BigInt.parse('011111100101', radix: 2)); // 2021
/// // From octal (base 8) value.
/// print(BigInt.parse('14', radix: 8)); // 12
/// print(BigInt.parse('37', radix: 8)); // 31
/// print(BigInt.parse('3745', radix: 8)); // 2021
/// // From hexadecimal (base 16) value.
/// print(BigInt.parse('c', radix: 16)); // 12
/// print(BigInt.parse('1f', radix: 16)); // 31
/// print(BigInt.parse('7e5', radix: 16)); // 2021
/// // From base 35 value.
/// print(BigInt.parse('y1', radix: 35)); // 1191 == 34 * 35 + 1
/// print(BigInt.parse('z1', radix: 35)); // Throws.
/// // From base 36 value.
/// print(BigInt.parse('y1', radix: 36)); // 1225 == 34 * 36 + 1
/// print(BigInt.parse('z1', radix: 36)); // 1261 == 35 * 36 + 1
/// ```
external static BigInt parse(String source, {int? radix});
/// Parses [source] as a, possibly signed, integer literal and returns its
/// value.
///
/// As [parse] except that this method returns `null` if the input is not
/// valid
///
/// Examples:
/// ```dart
/// print(BigInt.tryParse('-12345678901234567890')); // -12345678901234567890
/// print(BigInt.tryParse('0xFF')); // 255
/// print(BigInt.tryParse('0xffffffffffffffff')); // 18446744073709551615
///
/// // From binary (base 2) value.
/// print(BigInt.tryParse('1100', radix: 2)); // 12
/// print(BigInt.tryParse('00011111', radix: 2)); // 31
/// print(BigInt.tryParse('011111100101', radix: 2)); // 2021
/// // From octal (base 8) value.
/// print(BigInt.tryParse('14', radix: 8)); // 12
/// print(BigInt.tryParse('37', radix: 8)); // 31
/// print(BigInt.tryParse('3745', radix: 8)); // 2021
/// // From hexadecimal (base 16) value.
/// print(BigInt.tryParse('c', radix: 16)); // 12
/// print(BigInt.tryParse('1f', radix: 16)); // 31
/// print(BigInt.tryParse('7e5', radix: 16)); // 2021
/// // From base 35 value.
/// print(BigInt.tryParse('y1', radix: 35)); // 1191 == 34 * 35 + 1
/// print(BigInt.tryParse('z1', radix: 35)); // null
/// // From base 36 value.
/// print(BigInt.tryParse('y1', radix: 36)); // 1225 == 34 * 36 + 1
/// print(BigInt.tryParse('z1', radix: 36)); // 1261 == 35 * 36 + 1
/// ```
external static BigInt? tryParse(String source, {int? radix});
/// Creates a big integer from the provided [value] number.
///
/// Examples:
/// ```dart
/// var bigInteger = BigInt.from(1); // 1
/// bigInteger = BigInt.from(0.9999); // 0
/// bigInteger = BigInt.from(-10.99); // -10
/// ```
external factory BigInt.from(num value);
/// Returns the absolute value of this integer.
///
/// For any integer `x`, the result is the same as `x < 0 ? -x : x`.
BigInt abs();
/// Return the negative value of this integer.
///
/// The result of negating an integer always has the opposite sign, except
/// for zero, which is its own negation.
BigInt operator -();
/// Adds [other] to this big integer.
///
/// The result is again a big integer.
BigInt operator +(BigInt other);
/// Subtracts [other] from this big integer.
///
/// The result is again a big integer.
BigInt operator -(BigInt other);
/// Multiplies [other] by this big integer.
///
/// The result is again a big integer.
BigInt operator *(BigInt other);
/// Double division operator.
///
/// Matching the similar operator on [int],
/// this operation first performs [toDouble] on both this big integer
/// and [other], then does [double.operator/] on those values and
/// returns the result.
///
/// **Note:** The initial [toDouble] conversion may lose precision.
///
/// Example:
/// ```dart
/// print(BigInt.from(1) / BigInt.from(2)); // 0.5
/// print(BigInt.from(1.99999) / BigInt.from(2)); // 0.5
/// ```
double operator /(BigInt other);
/// Truncating integer division operator.
///
/// Performs a truncating integer division, where the remainder is discarded.
///
/// The remainder can be computed using the [remainder] method.
///
/// Examples:
/// ```dart
/// var seven = BigInt.from(7);
/// var three = BigInt.from(3);
/// seven ~/ three; // => 2
/// (-seven) ~/ three; // => -2
/// seven ~/ -three; // => -2
/// seven.remainder(three); // => 1
/// (-seven).remainder(three); // => -1
/// seven.remainder(-three); // => 1
/// ```
BigInt operator ~/(BigInt other);
/// Euclidean modulo operator.
///
/// Returns the remainder of the Euclidean division. The Euclidean division of
/// two integers `a` and `b` yields two integers `q` and `r` such that
/// `a == b * q + r` and `0 <= r < b.abs()`.
///
/// The sign of the returned value `r` is always positive.
///
/// See [remainder] for the remainder of the truncating division.
///
/// Example:
/// ```dart
/// print(BigInt.from(5) % BigInt.from(3)); // 2
/// print(BigInt.from(-5) % BigInt.from(3)); // 1
/// print(BigInt.from(5) % BigInt.from(-3)); // 2
/// print(BigInt.from(-5) % BigInt.from(-3)); // 1
/// ```
BigInt operator %(BigInt other);
/// Returns the remainder of the truncating division of `this` by [other].
///
/// The result `r` of this operation satisfies:
/// `this == (this ~/ other) * other + r`.
/// As a consequence the remainder `r` has the same sign as the divider `this`.
///
/// Example:
/// ```dart
/// print(BigInt.from(5).remainder(BigInt.from(3))); // 2
/// print(BigInt.from(-5).remainder(BigInt.from(3))); // -2
/// print(BigInt.from(5).remainder(BigInt.from(-3))); // 2
/// print(BigInt.from(-5).remainder(BigInt.from(-3))); // -2
/// ```
BigInt remainder(BigInt other);
/// Shift the bits of this integer to the left by [shiftAmount].
///
/// Shifting to the left makes the number larger, effectively multiplying
/// the number by `pow(2, shiftIndex)`.
///
/// There is no limit on the size of the result. It may be relevant to
/// limit intermediate values by using the "and" operator with a suitable
/// mask.
///
/// It is an error if [shiftAmount] is negative.
BigInt operator <<(int shiftAmount);
/// Shift the bits of this integer to the right by [shiftAmount].
///
/// Shifting to the right makes the number smaller and drops the least
/// significant bits, effectively doing an integer division by
///`pow(2, shiftIndex)`.
///
/// It is an error if [shiftAmount] is negative.
BigInt operator >>(int shiftAmount);
/// Bit-wise and operator.
///
/// Treating both `this` and [other] as sufficiently large two's component
/// integers, the result is a number with only the bits set that are set in
/// both `this` and [other]
///
/// Of both operands are negative, the result is negative, otherwise
/// the result is non-negative.
BigInt operator &(BigInt other);
/// Bit-wise or operator.
///
/// Treating both `this` and [other] as sufficiently large two's component
/// integers, the result is a number with the bits set that are set in either
/// of `this` and [other]
///
/// If both operands are non-negative, the result is non-negative,
/// otherwise the result is negative.
BigInt operator |(BigInt other);
/// Bit-wise exclusive-or operator.
///
/// Treating both `this` and [other] as sufficiently large two's component
/// integers, the result is a number with the bits set that are set in one,
/// but not both, of `this` and [other]
///
/// If the operands have the same sign, the result is non-negative,
/// otherwise the result is negative.
BigInt operator ^(BigInt other);
/// The bit-wise negate operator.
///
/// Treating `this` as a sufficiently large two's component integer,
/// the result is a number with the opposite bits set.
///
/// This maps any integer `x` to `-x - 1`.
BigInt operator ~();
/// Whether this big integer is numerically smaller than [other].
bool operator <(BigInt other);
/// Whether [other] is numerically greater than this big integer.
bool operator <=(BigInt other);
/// Whether this big integer is numerically greater than [other].
bool operator >(BigInt other);
/// Whether [other] is numerically smaller than this big integer.
bool operator >=(BigInt other);
/// Compares this to `other`.
///
/// Returns a negative number if `this` is less than `other`, zero if they are
/// equal, and a positive number if `this` is greater than `other`.
///
/// Example:
/// ```dart
/// print(BigInt.from(1).compareTo(BigInt.from(2))); // => -1
/// print(BigInt.from(2).compareTo(BigInt.from(1))); // => 1
/// print(BigInt.from(1).compareTo(BigInt.from(1))); // => 0
/// ```
int compareTo(BigInt other);
/// Returns the minimum number of bits required to store this big integer.
///
/// The number of bits excludes the sign bit, which gives the natural length
/// for non-negative (unsigned) values. Negative values are complemented to
/// return the bit position of the first bit that differs from the sign bit.
///
/// To find the number of bits needed to store the value as a signed value,
/// add one, i.e. use `x.bitLength + 1`.
///
/// ```dart
/// x.bitLength == (-x-1).bitLength;
///
/// BigInt.from(3).bitLength == 2; // 00000011
/// BigInt.from(2).bitLength == 2; // 00000010
/// BigInt.from(1).bitLength == 1; // 00000001
/// BigInt.from(0).bitLength == 0; // 00000000
/// BigInt.from(-1).bitLength == 0; // 11111111
/// BigInt.from(-2).bitLength == 1; // 11111110
/// BigInt.from(-3).bitLength == 2; // 11111101
/// BigInt.from(-4).bitLength == 2; // 11111100
/// ```
int get bitLength;
/// Returns the sign of this big integer.
///
/// Returns 0 for zero, -1 for values less than zero and
/// +1 for values greater than zero.
int get sign;
/// Whether this big integer is even.
bool get isEven;
/// Whether this big integer is odd.
bool get isOdd;
/// Whether this number is negative.
bool get isNegative;
/// Returns `this` to the power of [exponent].
///
/// Returns [one] if the [exponent] equals 0.
///
/// The [exponent] must otherwise be positive.
///
/// The result is always equal to the mathematical result of this to the power
/// [exponent], only limited by the available memory.
///
/// Example:
/// ```dart
/// var value = BigInt.from(1000);
/// print(value.pow(0)); // 1
/// print(value.pow(1)); // 1000
/// print(value.pow(2)); // 1000000
/// print(value.pow(3)); // 1000000000
/// print(value.pow(4)); // 1000000000000
/// print(value.pow(5)); // 1000000000000000
/// print(value.pow(6)); // 1000000000000000000
/// print(value.pow(7)); // 1000000000000000000000
/// print(value.pow(8)); // 1000000000000000000000000
/// ```
BigInt pow(int exponent);
/// Returns this integer to the power of [exponent] modulo [modulus].
///
/// The [exponent] must be non-negative and [modulus] must be
/// positive.
BigInt modPow(BigInt exponent, BigInt modulus);
/// Returns the modular multiplicative inverse of this big integer
/// modulo [modulus].
///
/// The [modulus] must be positive.
///
/// It is an error if no modular inverse exists.
// Returns 1/this % modulus, with modulus > 0.
BigInt modInverse(BigInt modulus);
/// Returns the greatest common divisor of this big integer and [other].
///
/// If either number is non-zero, the result is the numerically greatest
/// integer dividing both `this` and `other`.
///
/// The greatest common divisor is independent of the order,
/// so `x.gcd(y)` is always the same as `y.gcd(x)`.
///
/// For any integer `x`, `x.gcd(x)` is `x.abs()`.
///
/// If both `this` and `other` is zero, the result is also zero.
///
/// Example:
/// ```dart
/// print(BigInt.from(4).gcd(BigInt.from(2))); // 2
/// print(BigInt.from(8).gcd(BigInt.from(4))); // 4
/// print(BigInt.from(10).gcd(BigInt.from(12))); // 2
/// print(BigInt.from(10).gcd(BigInt.from(10))); // 10
/// print(BigInt.from(-2).gcd(BigInt.from(-3))); // 1
/// ```
BigInt gcd(BigInt other);
/// Returns the least significant [width] bits of this big integer as a
/// non-negative number (i.e. unsigned representation). The returned value has
/// zeros in all bit positions higher than [width].
///
/// ```dart
/// BigInt.from(-1).toUnsigned(5) == 31 // 11111111 -> 00011111
/// ```
///
/// This operation can be used to simulate arithmetic from low level languages.
/// For example, to increment an 8 bit quantity:
///
/// ```dart
/// q = (q + 1).toUnsigned(8);
/// ```
///
/// `q` will count from `0` up to `255` and then wrap around to `0`.
///
/// If the input fits in [width] bits without truncation, the result is the
/// same as the input. The minimum width needed to avoid truncation of `x` is
/// given by `x.bitLength`, i.e.
///
/// ```dart
/// x == x.toUnsigned(x.bitLength);
/// ```
BigInt toUnsigned(int width);
/// Returns the least significant [width] bits of this integer, extending the
/// highest retained bit to the sign. This is the same as truncating the value
/// to fit in [width] bits using an signed 2-s complement representation. The
/// returned value has the same bit value in all positions higher than [width].
///
/// ```dart
/// var big15 = BigInt.from(15);
/// var big16 = BigInt.from(16);
/// var big239 = BigInt.from(239);
/// // V--sign bit-V
/// big16.toSigned(5) == -big16; // 00010000 -> 11110000
/// big239.toSigned(5) == big15; // 11101111 -> 00001111
/// // ^ ^
/// ```
///
/// This operation can be used to simulate arithmetic from low level languages.
/// For example, to increment an 8 bit signed quantity:
///
/// ```dart
/// q = (q + 1).toSigned(8);
/// ```
///
/// `q` will count from `0` up to `127`, wrap to `-128` and count back up to
/// `127`.
///
/// If the input value fits in [width] bits without truncation, the result is
/// the same as the input. The minimum width needed to avoid truncation of `x`
/// is `x.bitLength + 1`, i.e.
///
/// ```dart
/// x == x.toSigned(x.bitLength + 1);
/// ```
BigInt toSigned(int width);
/// Whether this big integer can be represented as an `int` without losing
/// precision.
///
/// **Warning:** this function may give a different result on
/// dart2js, dev compiler, and the VM, due to the differences in
/// integer precision.
///
/// Example:
/// ```dart
/// var bigNumber = BigInt.parse('100000000000000000000000');
/// print(bigNumber.isValidInt); // false
///
/// var value = BigInt.parse('0xFF'); // 255
/// print(value.isValidInt); // true
/// ```
bool get isValidInt;
/// Returns this [BigInt] as an [int].
///
/// If the number does not fit, clamps to the max (or min)
/// integer.
///
/// **Warning:** the clamping behaves differently between the web and
/// native platforms due to the differences in integer precision.
///
/// Example:
/// ```dart
/// var bigNumber = BigInt.parse('100000000000000000000000');
/// print(bigNumber.isValidInt); // false
/// print(bigNumber.toInt()); // 9223372036854775807
/// ```
int toInt();
/// Returns this [BigInt] as a [double].
///
/// If the number is not representable as a [double], an
/// approximation is returned. For numerically large integers, the
/// approximation may be infinite.
///
/// Example:
/// ```dart
/// var bigNumber = BigInt.parse('100000000000000000000000');
/// print(bigNumber.toDouble()); // 1e+23
/// ```
double toDouble();
/// Returns a String-representation of this integer.
///
/// The returned string is parsable by [parse].
/// For any `BigInt` `i`, it is guaranteed that
/// `i == BigInt.parse(i.toString())`.
///
/// Example:
/// ```dart
/// var bigNumber = BigInt.parse('100000000000000000000000');
/// print(bigNumber.toString()); // "100000000000000000000000"
/// ```
String toString();
/// Converts [this] to a string representation in the given [radix].
///
/// In the string representation, lower-case letters are used for digits above
/// '9', with 'a' being 10 an 'z' being 35.
///
/// The [radix] argument must be an integer in the range 2 to 36.
///
/// Example:
/// ```dart
/// // Binary (base 2).
/// print(BigInt.from(12).toRadixString(2)); // 1100
/// print(BigInt.from(31).toRadixString(2)); // 11111
/// print(BigInt.from(2021).toRadixString(2)); // 11111100101
/// print(BigInt.from(-12).toRadixString(2)); // -1100
/// // Octal (base 8).
/// print(BigInt.from(12).toRadixString(8)); // 14
/// print(BigInt.from(31).toRadixString(8)); // 37
/// print(BigInt.from(2021).toRadixString(8)); // 3745
/// // Hexadecimal (base 16).
/// print(BigInt.from(12).toRadixString(16)); // c
/// print(BigInt.from(31).toRadixString(16)); // 1f
/// print(BigInt.from(2021).toRadixString(16)); // 7e5
/// // Base 36.
/// print(BigInt.from(35 * 36 + 1).toRadixString(36)); // z1
/// ```
String toRadixString(int radix);
}