Mar
30

Conversion from uint8 to int8 (x << 24 >> 24)

vjeux Javascript 2013-03-30

Daniel Baulig, a co-worker at Facebook, told me a little trick related to jDataView function to convert from a uint8 to a int8 in Javascript.

Here's the version I had:

function getInt8() {
  var b = this.getUint8();
  if (b > Math.pow(2, 7) - 1) {
    return b - Math.pow(2, 8);
  }
  return b;
}

Compare it to his version:

< <function getInt8() {
  return this.getUint8() << 24 >> 24;
}

I was really confused because it seems like it's doing a no-op. Here's the full explanation of why the two versions are working.

How it works?

The following table (borrowed from Wikipedia) shows how various 8 bits values are in represented with bits and how they are interpreted in unsigned and signed (using two-complement rule).

Bits uint8 int8
0000 0000 0 0
0000 0001 1 1
0000 0010 2 2
0111 1110 126 126
0111 1111 127 127
1000 0000 128 −128
1000 0001 129 −127
1000 0010 130 −126
1111 1110 254 −2
1111 1111 255 −1

Javascript doesn't natively have a 8 bit integer type, it only has a 32 bits one. When you put a 8 bit integer into a 32 bits one, Javascript is going to fill the remaining bits on the left with zeros as the following table shows.

Bits int32
0000 0000 ... 0000 0000 0
0000 0000 ... 0000 0001 1
0000 0000 ... 0000 0010 2
0000 0000 ... 0111 1110 126
0000 0000 ... 0111 1111 127
0000 0000 ... 1000 0000 128
0000 0000 ... 1000 0001 129
0000 0000 ... 1000 0010 130
0000 0000 ... 1111 1110 254
0000 0000 ... 1111 1111 255

Unfortunately, this doesn't properly handle negative numbers. Because we use two-complement, we've got to fill all the bits with 1 for negative numbers in order to have the same number in a signed 32 bits representation.

Bits int32
0000 0000 ... 0000 0000 0
0000 0000 ... 0000 0001 1
0000 0000 ... 0000 0010 2
0000 0000 ... 0111 1110 126
0000 0000 ... 0111 1111 127
1111 1111 ... 1000 0000 −128
1111 1111 ... 1000 0001 −127
1111 1111 ... 1000 0010 −126
1111 1111 ... 1111 1110 −2
1111 1111 ... 1111 1111 −1

So basically, we've got to fill the 24 remaining bits on the left with the same first bit we have: 0 for positive numbers and 1 for negative numbers.

This is when the trick comes into place. In javascript, there's a binary operator: >> Sign-propagating right shift that moves all the bits to the right and fills the missing bits with the first bit.

So all we have to do is to put our 8 good digits to the far left using << and then use the previous trick to fill the bits with the proper ones 🙂

x x < < 24 (x << 24) >> 24
0000 0000 ... 0000 0000 0000 0000 ... 0000 0000 0000 0000 ... 0000 0000
0000 0000 ... 0000 0001 0000 0001 ... 0000 0000 0000 0000 ... 0000 0001
0000 0000 ... 0000 0010 0000 0010 ... 0000 0000 0000 0000 ... 0000 0010
0000 0000 ... 0111 1110 0111 1110 ... 0000 0000 0000 0000 ... 0111 1110
0000 0000 ... 0111 1111 0111 1111 ... 0000 0000 0000 0000 ... 0111 1111
0000 0000 ... 1000 0000 1000 0000 ... 0000 0000 1111 1111 ... 1000 0000
0000 0000 ... 1000 0001 1000 0001 ... 0000 0000 1111 1111 ... 1000 0001
0000 0000 ... 1000 0010 1000 0010 ... 0000 0000 1111 1111 ... 1000 0010
0000 0000 ... 1111 1110 1111 1110 ... 0000 0000 1111 1111 ... 1111 1110
0000 0000 ... 1111 1111 1111 1111 ... 0000 0000 1111 1111 ... 1111 1111
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