break_eternity.js

A Javascript numerical library to represent numbers as large as 10^^1e308 and as small as 10^-10^^1e308. Sequel to break_infinity.js, designed for incremental games.

Usage no npm install needed!

<script type="module">
  import breakEternityJs from 'https://cdn.skypack.dev/break_eternity.js';
</script>

README

break_eternity.js

A Javascript numerical library to represent numbers as large as 10^^1e308 and as 'small' as 10^-(10^^1e308). This is a sequel to break_infinity.js, my other library which maxes out at 1e1e308 ( https://github.com/Patashu/break_infinity.js ) and its C# port ( https://github.com/Razenpok/BreakInfinity.cs ). Despite handling a wider range of numbers, execution time is comparable (within 2x/0.5x as fast as break_infinity.js in testing) and it has the same interface, so it can be used as a drop-in replacement for break_infinity.js and decimal.js.

Now with arbitrary real height and base handling in your favourite hyper 4 operators (tetrate, iterated exponentiation, iterated logarithm, super logarithm, super square root) and even in pentate (if you want to do that for some reason)! Using the linear approximation. (Analytical approximation is too hard for me atm.)

The internal representation is as follows: Decimal.fromComponents(sign, layer, mag) === sign*10^10^10^ ... (layer times) mag. So a layer 0 number is just sign*mag, a layer 1 number is sign*10^mag, a layer 2 number is sign*10^10^mag, and so on. If layer > 0 and mag < 0, then the number's exponent is negative, e.g. sign*10^-10^10^10^ ... mag.

  • sign is -1, 0 or 1.
  • layer is a non-negative integer.
  • mag is a Number, normalized as follows: if it is above 9e15, log10(mag) it and increment layer. If it is below log10(9e15) (about 15.954) and layer > 0, Math.pow(10, mag) it and decrement layer. At layer 0, sign is extracted from negative mags. Zeroes (this.sign === 0 || (this.mag === 0 && this.layer === 0)) become 0, 0, 0 in all fields.

Create a Decimal with new Decimal(String or Number or Decimal) or with Decimal.fromComponents(sign, layer, mag). Use operations

IMPORTANT NOTE TO PEOPLE CONVERTING FROM break_infinity.js: log/log2/log10/ln now return Decimal not Number! You'll also need to reconsider your string parsing/displaying functions and consider moving e/exponent calls to absLog10. Support for very small numbers has finally been added, so things like tickspeed multiplier being 1e-400 will be fine now!

Functions you can call include abs, neg, round, floor, ceil, trunc, add, sub, mul, div, recip, cmp, cmpabs, max, min, maxabs, minabs, log, log10, ln, pow, root, factorial, gamma, exp, sqrt, tetrate, iteratedexp, iteratedlog, layeradd10, layeradd, slog, ssqrt, lambertw, pentate and more! Javascript operators like + and * do not work - you need to call the equivalent functions instead.

Accepted input formats to new Decimal or Decimal.fromString:

M === M
eX === 10^X
MeX === M*10^X
eXeY === 10^(XeY)
MeXeY === M*10^(XeY)
eeX === 10^10^X
eeXeY === 10^10^(XeY)
eeeX === 10^10^10^X
eeeXeY === 10^10^10^(XeY)
eeee... (N es) X === 10^10^10^ ... (N 10^s) X
(e^N)X === 10^10^10^ ... (N 10^s) X
N PT X === 10^10^10^ ... (N 10^s) X
N PT (X) === 10^10^10^ ... (N 10^s) X
NpX === 10^10^10^ ... (N 10^s) X
X^Y === X^Y
X^^N === X^X^X^ ... (N X^s) 1
X^^N;Y === X^X^X^ ... (N X^s) Y
X^^^N === X^^X^^X^^ ... (N X^^s) 1
X^^^N;Y === X^^X^^X^^ ... (N X^^s) Y

Use

The library exports a single function object, Decimal, the constructor of Decimal instances.

It accepts a value of type number, string or Decimal.

    x = new Decimal(123.4567)
    y = new Decimal('123456.7e-3')
    z = new Decimal(x)
    x.equals(y) && y.equals(z) && x.equals(z)        // true

The methods that return a Decimal can be chained.

    x.dividedBy(y).plus(z).times(9).floor()
    x.times('1.23456780123456789e+9').plus(9876.5432321).dividedBy('4444562598.111772').ceil()

A list of functions is provided earlier in this readme, or you can use autocomplete or read through the js file to see for yourself.

If you want to just mess around with the library to try it, download break_eternity.js, add tags to the beginning and end respectively, rename it break_eternity.html, open it in chrome, right click -> inspect, go to the Javascript Console, and type in and execute whatever commands you want. Enjoy!

Special thanks:

obligatory SEO: number library, big number, big num, bignumber, bignum, big integer, biginteger, bigint, incremental games, idle games, large numbers, huge numbers

Want to go even further? Check out Naruyoko's OmegaNum.js: https://github.com/Naruyoko/OmegaNum.js