Why are big numbers from a Number limited to 2^26 - 1 ?

[ryanxcharles]

Why are big numbers from a Number limited to 2^26 - 1 ?

[dcousens]

This is because the internal word size is limited to 2^26 and as can be seen, it is stored directly, not splitting the number across multiple words.

This is clearly intended behaviour, I guess it might be up for discussion as to whether it is developer friendly though.

[indutny]

@ryanxcharles I think I could support numbers up to 2^52 - 1, but... is it really required? :)

[ryanxcharles]

In order to make bn.js backwards-compatible with our old big number implementation in bitcore, we've had to work around this by converting Numbers into Strings before creating a new bn, which we do by using a different constructor. IMO the developer-friendly version would accept any integer as input, or at least throw an error when you have surpassed the internal word size.

[indutny]

Ok... I think one more branch won't hurt.

[indutny]

Fixed and published in 0.13.3, thanks! (I don't see any significant difference in benchmarks)

[ryanxcharles]

Awesome, thanks.

[Yaffle]

it is possible to extend this solution to support any numbers

[indutny]

Yes, but... why? :) There is a precision loss after that boundary.

[Yaffle]

I think, division by power of 2 and multiplication should be exact in case it is IEEE 754 binary, although, i am not an expert.
Anyway, just to complete number to bn conversion:

if (number < 0x4000000 *  0x4000000) {
  // ...
} else {
  number = Math.floor(number); 
  this.words = [];
  while (number !== 0) {
    var q = Math.floor(number / 0x4000000);
    var digit = number - 0x4000000 * q;
    this.words.push(digit);
    number = q;
  }
  this.length = this.words.length;
}

[indutny]

This will work, but the supplied number is not an integer anymore. See Number.MAX_SAFE_INTEGER for details.

[indutny]

@Yaffle also I do object increasing the number of branches in .init().

[Yaffle]

@indutny , ok

actually, i was thinking about performance for small integers...
in dart and some other languages build-in integers allows to efficiently work with small numbers and switch to bigint, as described in https://www.dartlang.org/articles/numeric-computation/#integers

What do you think, when will this be possible in javascript?
i tried to use "Number.prototype.add" to implement something similar: (1).add(2).add(9007199254740991), but performance is not good in Chrome.

[indutny]

@Yaffle I do exploit the integer representation in the JavaScript compilers heavily. There are usually two classes of numbers: SMIs (small 32bit integers) and Heap numbers (64bit floating point number). The bn.js mostly operates on 26bit SMIs, converting them to heap numbers only to perform multiplication. 26bit * 26bit multiplication results in 52bit numbers, which is exactly how much you could store in a IEE754 FP number without a precision loss.

[Yaffle]

@indutny ,

var a = bn(1);
var b = bn(3);
var c = a.add(b);

can this code perform as fast, as with integers ?

var a = 1;
var b = 3;
var c = a + b;

in javascript there are no "value objects":
http://wiki.ecmascript.org/doku.php?id=strawman:value_objects
in javascript there are no built-in "bignum".
But there is "Number.prototype", which cannot give comparable performance do not know why...

[indutny]

it certainly can't perform as fast. The whole point of this module is big integer arithmetics, not small ones.