Develop Reference

is there a difference between these two snippets of code and if yes what is it?

function addBinary(a,b) {
let sum= a+b
if (sum<0){
sum=0xffffffff+sum+1
}
return parseInt(sum).toString(2)
}
and especially the logic of how 0xffffffff has been used to achieve same result
function decimalToBinary(decimal){
return (decimal >>> 0).toString(2);
}
function addBinary(a,b) {
return decimalToBinary(a+b);
}

The >>> operator always interprets the given number as an unsigned 32 bit number. When the second operand is 0, nothing changes to that and the result is unsigned.
So for instance, -1 in binary is 0xffffffff in signed 32-bit, where the most significant bit (at the left) is the sign bit. But because exceptionally the >>> does not interpret that as a sign bit, it actually is seen as a positive number, i.e. 0xffffffff. Compared to the original -1 that is 0x100000000 more! This is always the difference for negative inputs. For -2 you'll get 0xfffffffe, for -3 you'll get 0xfffffffd, ...etc.
The first function emulates this. If sum is negative, we must do something, as the other function (using >>>) will never return a negative number.
The idea is to add that 0x100000000 difference. In fact, the author of this function was prudent, and evidently didn't want to work with numbers that exceed the 32 bit range, so 0x100000000 was off the board (it uses 33 bits). But one can split the job into parts. We can add one less (0xffffffff) to the sum, and then add the remaining 1. This is just a theoretical game though. In JavaScript there is no problem in adding 0x100000000, so they could just as well have done that. In other languages however, those that use 32 bit numbers, it would be necessary to first add 0xffffffff and only then 1.

Why does 100 >> 100 and 100 >>> 100 return 6 in Javascript? [duplicate]

This question already has answers here:
Javascript's Shift right with zero-fill operator (>>>) yielding unexpected result
(2 answers)
Closed 1 year ago.
From the documentation:
The right shift operator (>>) shifts the first operand the specified number of bits to the right. Excess bits shifted off to the right are discarded. Copies of the leftmost bit are shifted in from the left. Since the new leftmost bit has the same value as the previous leftmost bit, the sign bit (the leftmost bit) does not change. Hence the name "sign-propagating".
From what I understand, since 100 is 0b1100100, shifting it 100 times to the right should yield 0b0. However, when I run 100 >> 100 in Javascript (using chrome), it returns 6. Why is this the case? I am guessing it has something to do with JS's internal representation of numbers but would like to know more clearly.
Edit: The answer is still 6, even when using the unsigned >>> operator. Sign/unsigned does not seem to matter.
Unsigned operation documentation:
The unsigned right shift operator (>>>) (zero-fill right shift) shifts the first operand the specified number of bits to the right. Excess bits shifted off to the right are discarded. Zero bits are shifted in from the left. The sign bit becomes 0, so the result is always non-negative. Unlike the other bitwise operators, zero-fill right shift returns an unsigned 32-bit integer.

The value to the right is taken mod 32. (i.e. Only the last five bits are used.) If you calculate 100>>32, you get 100, which is the same thing you get when you compute 100>>0. After that, 100>>33 is 50, and the cycle repeats.

I need an explanation (and possible workaround) for ((2^32-1) << 0) resulting -1 in Javascript

EDIT: Explanation at the end.
I was trying to implement a 64bit integer class using a Uint32Array and have bitwise operations performed under the hood on two uint32 members. I quickly found out that, as to my understanding of the specification, bitwise operations return a signed 32bit integer. Initially I was hoping that the Uint32Array would just take care of the sign bit, but it doesn't.
I tried coding around the sign issue, but I am stuck at something I simply can't make sense of at all.
var a = (Math.pow(2, 32)-1); //set a to uint32 max value
So far, so good.
a.toString(2);// gives "11111111111111111111111111111111", as expected
However:
(a << 0); // gives "-1"
(a >> 1); // gives "-1"
(a << 0) == (a >> 1); // evaluates to true
Even if JS bitwise operations turn numbers into signed 32bit integers, 32 set bits shifted to the right by 1 should never be -1. Or should they? Should a non-zero number shifted by 0 bits equal itself shifted 1 bit? Is this a bug? Am I running into undefined behaviour?
Usually the answer to similar questions has to do with the signed 32bit conversion but I can't see how that should cause this behaviour.
EDIT2, explanation: The cause of my confusion was a fundamental misunderstanding of how negative numbers are represented in binary. While the first bit is in fact the sign bit, 1 indicating a negative, 0 a positive number, the remaining bits aren't just used to store the abs(), as I assumed.
Signed 4bit example:
0111 equals +7. 1111 does not equal -7, it equals -1. How do we end up with negative one? Because the two's complement of 1111 is 0001. To get a number's two's complement, flip all bits and add one:
1111 -> 0000 -> 0001.
Now that I know that, making sense of 11..11 << 0 being -1 is easy. It's perfectly similar to my 4bit example. 11..11 >> 1 being -1 is also completely expected now. The signed right shift >> is 1 filling, so 11..11 >> 1 is still 11..11 which is still -1.
I will leave this as is for now, because I'm certainly not the only one misunderstanding binary signed integer representation. Thanks for everyone's time.

Even if JS bitwise operations turn numbers into signed 32bit integers, 32 set bits shifted to the right by 1 should never be -1. Or should they? Should a non-zero number shifted by 0 bits equal itself shifted 1 bit? Is this a bug? Am I running into undefined behaviour?
That's normal, expected and defined. And yes, they should.
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Right_shift is what you use, and its description is this:
The right shift operator (>>) shifts the first operand the specified number of bits to the right. Excess bits shifted off to the right are discarded. Copies of the leftmost bit are shifted in from the left. Since the new leftmost bit has the same value as the previous leftmost bit, the sign bit (the leftmost bit) does not change. Hence the name "sign-propagating".
So if you have 32 bits of 1, after applying right shift by 1 you will have 32 bits of 1.
The fact that it's 32 bits wide is in the specs, https://tc39.es/ecma262/
6.1.6.1.10 Number::signedRightShift ( x, y )
[...]
4. Return the result of performing a sign-extending right shift of lnum by shiftCount bits. The most significant bit is propagated. The result is a signed 32-bit integer.
(Similarly, << produces 32-bit signed integer)

In JavaScript, can bit shifting be used to isolate 1 or more bits in a byte?

In JavaScript code where the 8 bits of a byte represent 8 Boolean "decisions" (aka: flags), there is a need to isolate each given bit for conversion to a Boolean variable. Consider my solution using String parsing:
var bitParser = function (_nTestByte, _nBitOrdinal) {
var bits = ("00000000" + _nTestByte.toString(2)).slice(-8); // convert to binary and zero-pad
return bits[_nBitOrdinal] === "1";
};
console.log(bitParser(0b10100101, 2)); // ECMAScript 6+ prefix, returns true
It works, and shows the desired result. However I have a hypothesis stating that a bit shifting technique would be a faster option than String manipulation. I tend to believe that but desire to prove it.
The problem is, I have yet to produce such a function that works correctly, let alone something I can test. I have created the following logic plan that I believe is accurate:
/*
LOGIC PLAN
----------
0) Remember: all bitwise operators return 32 bits even though we are using 8
1) Left shift until the desired bit is the left-most (highest) position;
2) Right shift (zero filling) 31 bits to eliminate all right bits
*/
The implementation of the login plan follows. Because of the 32 bit nature of bitwise operators, its my belief that the entire left 3 bytes (24 bits) must be shifted off first before we even reach the byte being worked on. Then, assuming a scenario where the 3rd bit from the left (String ordinal 2) is the desired bit, I am shifting off 2 more bits (ordinals 0 & 1), for a total of 26 bits of left shifting.
This should produce a binary number with the desired bit all the way left followed by 31 undesired zero bytes. Right shifting those 31 bits away produces a binary with 31 (now) leading zero bits which evaluates to whatever the value of the desired bit is. But of course, I would not be writing this question if THAT were true, now would I? :-)
// hardcoded, assuming the second "1" (ordinal 2) is the bit to be examined
console.log((0b10100101 << 26) >> 31); // instead of 1, returns -1
I feel like I am really close, but missing something or pushing JavaScript too hard (lol).

In JavaScript code where the 8 bits of a byte represent 8 Boolean "decisions" (aka: flags), there is a need to isolate each given bit for conversion to a Boolean variable...
If that's the actual goal, bitshifting is neither necessary nor useful: Just use a bitwise & with the desired bit, which will give you either 0 or a number with that bit set. 0 is falsy, the number with a bit set is truthy. You can either use that as-is, or force it to boolean via !!flag or Boolean(flag):
Here's your bitParser function using bitmasking:
var bitParser = function (_nTestByte, _nBitOrdinal) {
return !!(_nTestByte & Math.pow(2, _nBitOrdinal));
};
console.log(bitParser(0b10100101, 2)); // true
console.log(bitParser(0b10100101, 1)); // false
Rather than doing the Math.pow every time, of course, we'd probably be better off with a lookup table:
var bits = [
0b00000001,
0b00000010,
0b00000100,
0b00001000,
0b00010000,
0b00100000,
0b01000000,
0b10000000
];
var bitParser = function (_nTestByte, _nBitOrdinal) {
return !!(_nTestByte & bits[_nBitOrdinal]);
};
console.log(bitParser(0b10100101, 2)); // true
console.log(bitParser(0b10100101, 1)); // false

From your question I took
console.log((0b10100101 << 26) >> 31); //instead of 1, returns -1.
And to answer your question why it returned -1 instead of 1
You need to do unsigned right shift >>> instead of signed one >>
console.log((0b10100101 << 26 ) >>>31);

Yes it can, and what you're doing is almost correct.
Integers are represented as a 32bit binary number, with the leftmost bit representing the sign (it's 1 if the number is negative and 0 if the number is positive). Lets look at some of the numbers' representations:
//last 31 digits keeps increasing as the number decreases
// ...
-2 => 0b11111111111111111111111111111110
-1 => 0b11111111111111111111111111111111
0 => 0b00000000000000000000000000000000
1 => 0b00000000000000000000000000000001
2 => 0b00000000000000000000000000000010
// ...
// last 31 digits keep increasing as the number increases
Now, what you're having (0b10100101 << 26) should give you 10010100000000000000000000000000, which you'd expect to be a big negative number (because the left-most bit is 1). Then right afterwards, you have >> 31 which you're expecting to strip off all 31 bits and leave you with the left-most bit.
That should work, but it's not what's happening. And why is that? It's because the people who came up with ECMAScript thought it would make more sense if 4 >> 1 returns 2 and -4 >> 1 returns -2.
4 >> 1 // returns 2 which is 0b00000000000000000000000000000010
0b0000000000000000000000000000000100 >> 1 // returns 2, same
-4 >> 1 // returns -2, which is 0b11111111111111111111111111111110
But -4 is 0b11111111111111111111111111111100, and for your purposes right shifting it by 1 should yield 0b01111111111111111111111111111110 (big positive number, since left-post bit is 0), and that's not -2!
To overcome that, you can use the other right shift operator which doesn't care about about the sign: >>>. -4 >>> 1 is 2147483646 which is what we want.
So console.log((0b10100101 << 26) >>> 31); gives you 1, which is what you want. You can also keep using >> and regarding any negative outcome to be a result of 1 being the chosen bit.

The most simple way to achieve your actual need is to use simple conditions rather than trying to isolate bits.
var bitParser = function (_nTestByte, _nBitOrdinal) {
return (_nTestByte & _nBitOrdinal);
};
console.log(bitParser(6, 2) ? true : false); // true
console.log(bitParser(6, 1) ? true : false); // false
I adapted the console.log() expression in a way that may seem complicated.
It's only to really show the logical result at this step, while I didn't choose to use !! inside of the function, so returning a truly/falsy value rather than true|false.
Actually this way keeps all the most simple possible, because the expected use else where in the code is if (bitParser(...)), which automatically casts the result to boolean.
BTW, this works whatever is the _nTestByte size (may be more than 1 byte).

2.9999999999999999 >> .5?

I heard that you could right-shift a number by .5 instead of using Math.floor(). I decided to check its limits to make sure that it was a suitable replacement, so I checked the following values and got the following results in Google Chrome:
2.5 >> .5 == 2;
2.9999 >> .5 == 2;
2.999999999999999 >> .5 == 2; // 15 9s
2.9999999999999999 >> .5 == 3; // 16 9s
After some fiddling, I found out that the highest possible value of two which, when right-shifted by .5, would yield 2 is 2.9999999999999997779553950749686919152736663818359374999999¯ (with the 9 repeating) in Chrome and Firefox. The number is 2.9999999999999997779¯ in IE.
My question is: what is the significance of the number .0000000000000007779553950749686919152736663818359374? It's a very strange number and it really piqued my curiosity.
I've been trying to find an answer or at least some kind of pattern, but I think my problem lies in the fact that I really don't understand the bitwise operation. I understand the idea in principle, but shifting a bit sequence by .5 doesn't make any sense at all to me. Any help is appreciated.
For the record, the weird digit sequence changes with 2^x. The highest possible values of the following numbers that still truncate properly:
for 0: 0.9999999999999999444888487687421729788184165954589843749¯
for 1: 1.9999999999999999888977697537484345957636833190917968749¯
for 2-3: x+.99999999999999977795539507496869191527366638183593749¯
for 4-7: x+.9999999999999995559107901499373838305473327636718749¯
for 8-15: x+.999999999999999111821580299874767661094665527343749¯
...and so forth

Actually, you're simply ending up doing a floor() on the first operand, without any floating point operations going on. Since the left shift and right shift bitwise operations only make sense with integer operands, the JavaScript engine is converting the two operands to integers first:
2.999999 >> 0.5
Becomes:
Math.floor(2.999999) >> Math.floor(0.5)
Which in turn is:
2 >> 0
Shifting by 0 bits means "don't do a shift" and therefore you end up with the first operand, simply truncated to an integer.
The SpiderMonkey source code has:
switch (op) {
case JSOP_LSH:
case JSOP_RSH:
if (!js_DoubleToECMAInt32(cx, d, &i)) // Same as Math.floor()
return JS_FALSE;
if (!js_DoubleToECMAInt32(cx, d2, &j)) // Same as Math.floor()
return JS_FALSE;
j &= 31;
d = (op == JSOP_LSH) ? i << j : i >> j;
break;
Your seeing a "rounding up" with certain numbers is due to the fact the JavaScript engine can't handle decimal digits beyond a certain precision and therefore your number ends up getting rounded up to the next integer. Try this in your browser:
alert(2.999999999999999);
You'll get 2.999999999999999. Now try adding one more 9:
alert(2.9999999999999999);
You'll get a 3.

This is possibly the single worst idea I have ever seen. Its only possible purpose for existing is for winning an obfusticated code contest. There's no significance to the long numbers you posted -- they're an artifact of the underlying floating-point implementation, filtered through god-knows how many intermediate layers. Bit-shifting by a fractional number of bytes is insane and I'm surprised it doesn't raise an exception -- but that's Javascript, always willing to redefine "insane".
If I were you, I'd avoid ever using this "feature". Its only value is as a possible root cause for an unusual error condition. Use Math.floor() and take pity on the next programmer who will maintain the code.
Confirming a couple suspicions I had when reading the question:
Right-shifting any fractional number x by any fractional number y will simply truncate x, giving the same result as Math.floor() while thoroughly confusing the reader.
2.999999999999999777955395074968691915... is simply the largest number that can be differentiated from "3". Try evaluating it by itself -- if you add anything to it, it will evaluate to 3. This is an artifact of the browser and local system's floating-point implementation.

If you wanna go deeper, read "What Every Computer Scientist Should Know About Floating-Point Arithmetic": https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

Try this javascript out:
alert(parseFloat("2.9999999999999997779553950749686919152736663818359374999999"));
Then try this:
alert(parseFloat("2.9999999999999997779553950749686919152736663818359375"));
What you are seeing is simple floating point inaccuracy. For more information about that, see this for example: http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems.
The basic issue is that the closest that a floating point value can get to representing the second number is greater than or equal to 3, whereas the closes that the a float can get to the first number is strictly less than three.
As for why right shifting by 0.5 does anything sane at all, it seems that 0.5 is just itself getting converted to an int (0) beforehand. Then the original float (2.999...) is getting converted to an int by truncation, as usual.

I don't think your right shift is relevant. You are simply beyond the resolution of a double precision floating point constant.
In Chrome:
var x = 2.999999999999999777955395074968691915273666381835937499999;
var y = 2.9999999999999997779553950749686919152736663818359375;
document.write("x=" + x);
document.write(" y=" + y);
Prints out: x = 2.9999999999999996 y=3

The shift right operator only operates on integers (both sides). So, shifting right by .5 bits should be exactly equivalent to shifting right by 0 bits. And, the left hand side is converted to an integer before the shift operation, which does the same thing as Math.floor().

I suspect that converting 2.9999999999999997779553950749686919152736663818359374999999
to it's binary representation would be enlightening. It's probably only 1 bit different
from true 3.
Good guess, but no cigar.
As the double precision FP number has 53 bits, the last FP number before 3 is actually
(exact): 2.999999999999999555910790149937383830547332763671875
But why it is
2.9999999999999997779553950749686919152736663818359375
(and this is exact, not 49999... !)
which is higher than the last displayable unit ? Rounding. The conversion routine (String to number) simply is correctly programmed to round the input the the next floating point number.
2.999999999999999555910790149937383830547332763671875
.......(values between, increasing) -> round down
2.9999999999999997779553950749686919152736663818359375
....... (values between, increasing) -> round up to 3
3
The conversion input must use full precision. If the number is exactly the half between
those two fp numbers (which is 2.9999999999999997779553950749686919152736663818359375)
the rounding depends on the setted flags. The default rounding is round to even, meaning that the number will be rounded to the next even number.
Now
3 = 11. (binary)
2.999... = 10.11111111111...... (binary)
All bits are set, the number is always odd. That means that the exact half number will be rounded up, so you are getting the strange .....49999 period because it must be smaller than the exact half to be distinguishable from 3.

I suspect that converting 2.9999999999999997779553950749686919152736663818359374999999 to its binary representation would be enlightening. It's probably only 1 bit different from true 3.

And to add to John's answer, the odds of this being more performant than Math.floor are vanishingly small.
I don't know if JavaScript uses floating-point numbers or some kind of infinite-precision library, but either way, you're going to get rounding errors on an operation like this -- even if it's pretty well defined.

It should be noted that the number ".0000000000000007779553950749686919152736663818359374" is quite possibly the Epsilon, defined as "the smallest number E such that (1+E) > 1."