3 ms·

Float128 emulation in Javascript, fastest way how to make 0.1 + 0.2 == 0.3

5 points by munrocket 7y ago

ktpsns 7y ago
The fastest way are probably rational numbers, as they are natively available in many functional languages or Perl6. That is, 0.1 is represented as the integer tupls (1,10) instead of a floating point number.
- munrocket 7y ago
  How many FLOP do you need to add two rationals? We don't have int type in javascript, only bigInt but it not supported in some browsers and probably not fast enough. UPD: I added Fraction.js to benchmark https://munrocket.github.io/double.js/docs/benchmark.html https://munrocket.github.io/double.js/docs/benchmark.html but it slower and overflows for some reason, .round(31) not helps.
  - ktpsns 7y ago
    Adding two rationals boils down to adding 2x two integers. Integer arithmetic is in general less complex then floating point arithmetic. But of course that's not true if your hardware supports single instruction double floating point arithmetic (which any relevant 64bit architecture does).
    - munrocket 7y ago
      The problems begins when calculations is long and int64/int32 not enough to store full fraction precision. Lol seems that I find a bug in Fraction.js in rounding https://runkit.com/munrocket/fraction-js-test https://runkit.com/munrocket/fraction-js-test, but it used in popular Math.js library.
- lizmat 7y ago
  Please note that Perl 6 has been renamed to Raku (https://raku.org https://raku.org using the #rakulang tag on social media). So in Perl `say "same" if .1 + .2 == .3` will not say anything, as that condition is not true. In Raku, `say "same" if .1 + .2 == .3` will display "same".
Someone 7y ago
This doesn’t solve the general problem that binary floating point cannot exactly represent decimal fractions. The first example new Double('0.3').sub(new Double('0.1')).toNumber() does the equivalent of float f = (float)(0.3 - 0.1); which happens to produce a ‘float32’ that prints as “0.2”, but for ‘float64’ vs ‘float128’. I expect that adding a sufficient number of zeroes, as in double f = (float128)0.00003 - (float128)0.00001); (actual number of zeroes is too low here, to prevent wrapping on phone screens) will surface the problem again.
- munrocket 7y ago
  Nope, check this demo https://runkit.com/munrocket/double.js-hn-example https://runkit.com/munrocket/double.js-hn-example

5 points by munrocket 7y ago

The fastest way are probably rational numbers, as they are natively available in many functional languages or Perl6. That is, 0.1 is represented as the integer tupls (1,10) instead of a floating point number.

munrocket 7y ago
How many FLOP do you need to add two rationals? We don't have int type in javascript, only bigInt but it not supported in some browsers and probably not fast enough. UPD: I added Fraction.js to benchmark https://munrocket.github.io/double.js/docs/benchmark.html https://munrocket.github.io/double.js/docs/benchmark.html but it slower and overflows for some reason, .round(31) not helps.
- ktpsns 7y ago
  Adding two rationals boils down to adding 2x two integers. Integer arithmetic is in general less complex then floating point arithmetic. But of course that's not true if your hardware supports single instruction double floating point arithmetic (which any relevant 64bit architecture does).
  - munrocket 7y ago
    The problems begins when calculations is long and int64/int32 not enough to store full fraction precision. Lol seems that I find a bug in Fraction.js in rounding https://runkit.com/munrocket/fraction-js-test https://runkit.com/munrocket/fraction-js-test, but it used in popular Math.js library.
lizmat 7y ago
Please note that Perl 6 has been renamed to Raku (https://raku.org https://raku.org using the #rakulang tag on social media). So in Perl `say "same" if .1 + .2 == .3` will not say anything, as that condition is not true. In Raku, `say "same" if .1 + .2 == .3` will display "same".

Someone 7y ago

This doesn’t solve the general problem that binary floating point cannot exactly represent decimal fractions. The first example new Double('0.3').sub(new Double('0.1')).toNumber() does the equivalent of float f = (float)(0.3 - 0.1); which happens to produce a ‘float32’ that prints as “0.2”, but for ‘float64’ vs ‘float128’. I expect that adding a sufficient number of zeroes, as in double f = (float128)0.00003 - (float128)0.00001); (actual number of zeroes is too low here, to prevent wrapping on phone screens) will surface the problem again.

munrocket 7y ago
Nope, check this demo https://runkit.com/munrocket/double.js-hn-example https://runkit.com/munrocket/double.js-hn-example