JavaScript floating point curiosity

Question

I tried doing some floating point comparison and here is what I found:

130 === 130.000000000000014210854715 // true
130 === 130.000000000000014210854716 // false
9 === 9.0000000000000008881784197001 // true
9 === 9.0000000000000008881784197002 // false
0.1 === 0.100000000000000012490009027033 // true
0.1 === 0.100000000000000012490009027034 // false

I tried running those on Firefox and Chrome with the same results. Okay, I KNOW that floating point comparison is a bad practice and has unexpected behavior. But I just curious about those numbers, why or how does those sequence of fractional digits calculated?

If you wish you could even expand those sequence further (kind of binary searching for the next sequence).

score 4 · Accepted Answer · edited Jan 05 '20 at 11:04

4

The fractional portion exceeds the precision of JavaScript's Number type.

JavaScript can only handle the 130.0000000000000 portion of your number, so it becomes 130 (those 0s have no significance).

Every Number in JavaScript is really a 64-bit IEEE-754 float, so the number 130.000000000000014210854715 will look like in binary...

0,10000000110,10000010000000000000000000000000000000000000000000000

Where the groups are sign (+ or -), exponent and significand/mantissa.

You can see that the number 130 is the same...

0,10000000110,10000010000000000000000000000000000000000000000000000

You'd need a 128 bit Number for JavaScript to be able to tell these two numbers apart, ot use a float128 implementation for JavaScript or bignum.

edited Jan 05 '20 at 11:04

Community

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answered Jul 05 '12 at 07:17

alex

479,566
201
878
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then what about 130.000000000000014210854716 in binary? – Captain kurO Jul 05 '12 at 07:33
@CaptainkurO It has the last bit of the mantissa turned on: `0000010000000000000000000000000000000000000000000001` – alex Jul 05 '12 at 07:34

JavaScript floating point curiosity

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