Numbers and Math

BigInt Arithmetic

BigInt is Dart's arbitrary-precision integer. Build values with BigInt.parse(text) for decimal text or BigInt.from(int) to widen an ordinary int. The usual operators +, -, *, ~/ stay exact on BigInt operands no matter how large, so they handle magnitudes the 64-bit int cannot represent. BigInt.toString() is the full decimal expansion.

Program

Play the program to parse a 21-digit BigInt, double it, integer-divide it, and count its decimal digits.

bigint.dart
Replay: real traced execution (multi-file project)
void main() {
  var big = BigInt.parse('100000000000000000000');
  var two = BigInt.from(2);
  var doubled = big * two;
  var halved = big ~/ two;
  var digits = big.toString().length;
  print('$doubled $halved digits=$digits');
}

  1. big ← 100000000000000000000 (BigInt)

    1void main() {2  var big = BigInt.parse('100000000000000000000');3  var two = BigInt.from(2);
    values this step100000000000000000000 (BigInt)big

  2. two ← 2 (BigInt)

    2var big = BigInt.parse('100000000000000000000');3var two = BigInt.from(2);4var doubled = big * two;
    values this step2 (BigInt)two

  3. doubled ← 200000000000000000000 (BigInt)

    3var two = BigInt.from(2);4var doubled = big * two;5var halved = big ~/ two;
    values this step200000000000000000000 (BigInt)doubled

  4. halved ← 50000000000000000000 (BigInt)

    4var doubled = big * two;5var halved = big ~/ two;6var digits = big.toString().length;
    values this step50000000000000000000 (BigInt)halved

  5. digits ← 21 (int)

    5var halved = big ~/ two;6var digits = big.toString().length;7print('$doubled $halved digits=$digits');
    values this step21 (int)digits100000000000000000000big

  6. print('$doubled $halved digits=$digits');

    6  var digits = big.toString().length;7  print('$doubled $halved digits=$digits');8}
    output200000000000000000000 50000000000000000000 digits=21
    values this step200000000000000000000doubled50000000000000000000halved21digits

Follow the Values

  1. big starts as 100000000000000000000.
  2. two is 2.
  3. doubled becomes 200000000000000000000.
  4. halved becomes 50000000000000000000.
  5. The decimal text has 21 digits, so the program prints digits=21. | name | value | | --- | --- | | big | 100000000000000000000 | | doubled | 200000000000000000000 | | halved | 50000000000000000000 | | digits | 21 |
BigInt.parse `BigInt.parse(decimal)` reads arbitrary-precision integers from text. There is no overflow on the parsed value.
BigInt.from `BigInt.from(int)` widens an ordinary `int` to a `BigInt` so it can mix with other `BigInt` operands.
exact arithmetic `+`, `*`, `~/` on `BigInt` operands stay exact regardless of magnitude; the result is another `BigInt`.

Exercise: bigint.dart

Reproduce the doubled value and digits=21, then identify which printed value is half of big.