pcjs/blog/2014/10/26/README.md
2015-01-27 15:46:22 -08:00

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JavaScript Negativity
---
Coming from the C programming language, it's easy to be "negative" about how JavaScript deals with 32-bit integers.
As a newcomer, you quickly learn that JavaScript supports only one numeric data type -- 64-bit floats -- and you groan.
Then you learn that all the "bitwise" operators (**~**, **|**, **&**, **^**, **<<**, **>>** and
**>>>**) treat their operands as 32-bit integer values and produce 32-bit integer results, and you breathe
a sigh of relief.
But then you start noticing oddities. In C, you can take any 32-bit value, such as -1526726656 (which is equivalent
to 0xA5000000), mask it with 0x80808080, and get 0x80000000. However, in JavaScript, you actually get -0x80000000,
which, sadly, is not equal to 0x80000000.
To verify, type the following into any JavaScript REPL (eg, Node):
> n = -1526726656
-1526726656
> n &= 0x80808080
-2147483648
> n == 0x80000000
false
> n == -0x80000000
true
So the notion that bitwise operators yield 32-bit results isn't exactly right; the sign (bit 31) of every 32-bit
result is always extended into the entire 52 "significand" bits of the underlying 64-bit float. And it's
impossible to simply "mask away" those additional sign bits, thanks to the fundamental restriction of JavaScript bitwise
operators: they operate *only* on the low 32 bits.
The easiest way to remove the high-order sign bits from a negative 32-bit value is to add the 33-bit value 0x100000000:
> n = (n < 0? n + 0x100000000 : n)
2147483648
> n.toString(16)
'80000000'
This works because JavaScript is perfectly capable of representing 0x80000000, or any other 32-bit value, as a positive
number, albeit in floating point. And be careful, because as soon as you perform *any* bitwise operation on a value
with bit 31 set, even an operation as innocuous-looking as:
> n |= 0
-2147483648
> n.toString(16)
'-80000000'
Viola: instant negative number!
This might tempt you to think that the right way to write negative 32-bit constants in hex is to simply precede
them with a minus sign. But that would be wrong. For example, if you wrote the constant 0x80000080 as "-0x80000080",
JavaScript would treat that as negation of 2147483776, resulting in a value whose low 32 bits are 0x7FFFFF80, not
0x80000080.
The safest way to write a 32-bit constant like 0x80000080 is "0x80000080|0", which will produce -2147483520. If you
write all your negative 32-bit constants that way, then you won't have to resort to 33-bit addition and potential
floating point operations.
To continue the fun, try setting bit 0 of 0x80000000, which should give you 0x80000001:
> n |= 1
-2147483647
> n.toString(16)
'-7fffffff'
WTF? Have all the low 32 bits flipped instead?
Actually, no, this time, I'm pulling your leg. The low 32 bits of the internal value are exactly what you would
expect: 0x80000001 (the internal representation is more like 0xFFFFF80000001). But as the
[MDN Docs](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/toString)
explain, for a negative number, toString() returns the positive representation of the number, preceded by a - sign,
*not* the "two's complement" of the number.
*[@jeffpar](http://twitter.com/jeffpar)*
*October 26, 2014*