I am trying to understand Javascript logical operators and came across 2 statements with seeminlgy similar functionality and trying to understand the difference. So, What's the difference between these 2 lines of code in Javascript?
For a number x,
x >>>= 0;
x &= 0x7fffffff;
If I understand it correctly, they both should give unsigned 32 bit output. However, for same negative value of x (i.e. most significant bit always 1 in both case), I get different outputs, what am I missing?
Thanks
To truncate a number to 32 bits, the simplest and most common method is to use the "|" bit-wise operator:
x |= 0;
JavaScript always considers the result of any 32-bit computation to be negative if the highest bit (bit 31) is set. Don't let that bother you. And don't clear bit 31 in an attempt to make it positive; that incorrectly alters the value.
To convert a negative 32-bit number as a positive value (a value in the range 0 to 4294967295), you can do this:
x = x < 0? x + 0x100000000 : x;
By adding a 33-bit value, automatic sign-extension of bit 31 is inhibited. However, the result is now outside the signed 32-bit range.
Another (tidier) solution is to use the unsigned right-shift operator with a zero shift count:
x >>>= 0;
Technically, all JavaScript numbers are 64-bit floating-point values, but in reality, as long as you keep numbers within the signed 32-bit range, you make it possible for JavaScript runtimes to optimize your code using 32-bit integer operations.
Be aware that when you convert a negative 32-bit value to a positive value using either of above methods, you have essentially produced a 33-bit value, which may defeat any 32-bit optimizations your JavaScript engine uses.
Related
I Have a hash function like this.
class Hash {
static rotate (x, b) {
return (x << b) ^ (x >> (32-b));
}
static pcg (a) {
let b = a;
for (let i = 0; i < 3; i++) {
a = Hash.rotate((a^0xcafebabe) + (b^0xfaceb00c), 23);
b = Hash.rotate((a^0xdeadbeef) + (b^0x8badf00d), 5);
}
return a^b;
}
}
// source Adam Smith: https://groups.google.com/forum/#!msg/proceduralcontent/AuvxuA1xqmE/T8t88r2rfUcJ
I use it like this.
console.log(Hash.pcg(116)); // Output: -191955715
As long as I send an integer in, I get an integer out. Now here comes the problem. If I have a floating number as input, rounding will happen. The number Hash.pcg(1.1) and Hash.pcg(1.2) will yield the same. I want different inputs to yield different results. A possible solution could be to multiply the input so the decimal is not rounded down, but is there a more elegant and flexible solution to this?
Is there a way to convert a floating point number to a unique integer? Each floating point number would result in a different integer number.
Performance is important.
This isn't quite an answer, but I was running out of room to make it a comment. :)
You'll hit a problem with integers outside of the 32-bit range as well as with non-integer values.
JavaScript handles all numbers as 64-bit floating point. This gives you exact integers over the range -9007199254740991 to 9007199254740991 (±(2^53 - 1)), but the bit-wise operators used in your hash algorithm (^, <<, >>) only work in a 32-bit range.
Since there are far more non-integer numbers possible than integers, no one-to-one mapping is possible with ordinary numbers. You could work something out with BigInts, but that will likely lead to comparatively much slower performance.
If you're willing to deal with the performance hit, your can use JavaScript buffer functions to get at the actual bits of a floating point number. (I'd say more now about how to do that, but I've got to run!)
Edit... back from dinner...
You can convert JavaScript's standard number type, which is 64-bit floating point, to a BigInt like this:
let dv = new DataView(new ArrayBuffer(8));
dv.setFloat64(0, Math.PI);
console.log(dv.getFloat64(0), dv.getBigInt64(0), dv.getBigInt64(0).toString(16).toUpperCase())
The output from this is:
3.141592653589793 4614256656552045848n "400921FB54442D18"
The first item shows that the number was properly stored as byte array, the second shows the BigInt created from the same bits, and the last is the same BigInt over again, but in hex to better show the floating point data format.
Once you've converted a number like this to a BigInt (which is not the same numeric value, but it is the same string of bits) every possible value of number will be uniquely represented.
The same bit-wise operators you used in your algorithm above will work with BigInts, but without the 32-bit limitation. I'm guessing that for best results you'd want to change the 32 in your code to 64, and use 16-digit (instead of 8-digit) hex constants as hash keys.
A colleague of mine stumbled upon a method to floor float numbers using a bitwise or:
var a = 13.6 | 0; //a == 13
We were talking about it and wondering a few things.
How does it work? Our theory was that using such an operator casts the number to an integer, thus removing the fractional part
Does it have any advantages over doing Math.floor? Maybe it's a bit faster? (pun not intended)
Does it have any disadvantages? Maybe it doesn't work in some cases? Clarity is an obvious one, since we had to figure it out, and well, I'm writting this question.
Thanks.
How does it work? Our theory was that using such an operator casts the
number to an integer, thus removing the fractional part
All bitwise operations except unsigned right shift, >>>, work on signed 32-bit integers. So using bitwise operations will convert a float to an integer.
Does it have any advantages over doing Math.floor? Maybe it's a bit
faster? (pun not intended)
http://jsperf.com/or-vs-floor/2 seems slightly faster
Does it have any disadvantages? Maybe it doesn't work in some cases?
Clarity is an obvious one, since we had to figure it out, and well,
I'm writting this question.
Will not pass jsLint.
32-bit signed integers only
Odd Comparative behavior: Math.floor(NaN) === NaN, while (NaN | 0) === 0
This is truncation as opposed to flooring. Howard's answer is sort of correct; But I would add that Math.floor does exactly what it is supposed to with respect to negative numbers. Mathematically, that is what a floor is.
In the case you described above, the programmer was more interested in truncation or chopping the decimal completely off. Although, the syntax they used sort of obscures the fact that they are converting the float to an int.
In ECMAScript 6, the equivalent of |0 is Math.trunc, kind of I should say:
Returns the integral part of a number by removing any fractional digits. It just truncate the dot and the digits behind it, no matter whether the argument is a positive number or a negative number.
Math.trunc(13.37) // 13
Math.trunc(42.84) // 42
Math.trunc(0.123) // 0
Math.trunc(-0.123) // -0
Math.trunc("-1.123")// -1
Math.trunc(NaN) // NaN
Math.trunc("foo") // NaN
Math.trunc() // NaN
Javascript represents Number as Double Precision 64-bit Floating numbers.
Math.floor works with this in mind.
Bitwise operations work in 32bit signed integers. 32bit signed integers use first bit as negative signifier and the other 31 bits are the number. Because of this, the min and max number allowed 32bit signed numbers are -2,147,483,648 and 2147483647 (0x7FFFFFFFF), respectively.
So when you're doing | 0, you're essentially doing is & 0xFFFFFFFF. This means, any number that is represented as 0x80000000 (2147483648) or greater will return as a negative number.
For example:
// Safe
(2147483647.5918 & 0xFFFFFFFF) === 2147483647
(2147483647 & 0xFFFFFFFF) === 2147483647
(200.59082098 & 0xFFFFFFFF) === 200
(0X7FFFFFFF & 0xFFFFFFFF) === 0X7FFFFFFF
// Unsafe
(2147483648 & 0xFFFFFFFF) === -2147483648
(-2147483649 & 0xFFFFFFFF) === 2147483647
(0x80000000 & 0xFFFFFFFF) === -2147483648
(3000000000.5 & 0xFFFFFFFF) === -1294967296
Also. Bitwise operations don't "floor". They truncate, which is the same as saying, they round closest to 0. Once you go around to negative numbers, Math.floor rounds down while bitwise start rounding up.
As I said before, Math.floor is safer because it operates with 64bit floating numbers. Bitwise is faster, yes, but limited to 32bit signed scope.
To summarize:
Bitwise works the same if you work from 0 to 2147483647.
Bitwise is 1 number off if you work from -2147483647 to 0.
Bitwise is completely different for numbers less than -2147483648 and greater than 2147483647.
If you really want to tweak performance and use both:
function floor(n) {
if (n >= 0 && n < 0x80000000) {
return n & 0xFFFFFFFF;
}
if (n > -0x80000000 && n < 0) {
const bitFloored = n & 0xFFFFFFFF;
if (bitFloored === n) return n;
return bitFloored - 1;
}
return Math.floor(n);
}
Just to add Math.trunc works like bitwise operations. So you can do this:
function trunc(n) {
if (n > -0x80000000 && n < 0x80000000) {
return n & 0xFFFFFFFF;
}
return Math.trunc(n);
}
Your first point is correct. The number is cast to an integer and thus any decimal digits are removed. Please note, that Math.floor rounds to the next integer towards minus infinity and thus gives a different result when applied to negative numbers.
The specs say that it is converted to an integer:
Let lnum be ToInt32(lval).
Performance: this has been tested at jsperf before.
note: dead link to spec removed
var myNegInt = -1 * Math.pow(2, 32);
var myFloat = 0.010203040506070809;
var my64BitFloat = myNegInt - myFloat;
var trunc1 = my64BitFloat | 0;
var trunc2 = ~~my64BitFloat;
var trunc3 = my64BitFloat ^ 0;
var trunc4 = my64BitFloat - my64BitFloat % 1;
var trunc5 = parseInt(my64BitFloat);
var trunc6 = Math.floor(my64BitFloat);
console.info(my64BitFloat);
console.info(trunc1);
console.info(trunc2);
console.info(trunc3);
console.info(trunc4);
console.info(trunc5);
console.info(trunc6);
IMO: The question "How does it work?", "Does it have any advantages over doing Math.floor?", "Does it have any disadvantages?" pale in comparison to "Is it at all logical to use it for this purpose?"
I think, before you try to get clever with your code, you may want to run these. My advice; just move along, there is nothing to see here. Using bitwise to save a few operations and having that matter to you at all, usually means your code architecture needs work. As far as why it may work sometimes, well a stopped clock is accurate twice a day, that does not make it useful. These operators have their uses, but not in this context.
I am facing weird issued.
parseFloat(11111111111111111) converts it to 11111111111111112.
I noticed that it works fine till length is 16 but rounds off higher when input length is > 16.
I want to retain the original value passed in parseFloat after it is executed.
Any help?
Integers (numbers without a period or exponent notation) are considered accurate up to 15 digits.
More information here
Numbers in javascript are represented using 64 bit floating point values (so called doubles in other languages).
doubles can hold at most 15/16 significant digits (depends on number magnitute). Since range of double is 1.7E+/-308 some numbers can only be aproximated by double, in your case 11111111111111111 cannot be represented exactly but is aproximated by 11111111111111112 value. If this sounds strange then remember that 0.3 cannot be represented exactly as double too.
double can hold exact integers values in range +/-2^53, when you are operating in this range - you may expect exact values.
Javascript has a constant, Number.MAX_SAFE_INTEGER which is the highest integer that can be exactly represented.
Safe in this context refers to the ability to represent integers exactly and to correctly compare them. For example, Number.MAX_SAFE_INTEGER + 1 === Number.MAX_SAFE_INTEGER + 2 will evaluate to true, which is mathematically incorrect.
The value is 9007199254740991 (2^53 - 1) which makes a maximum of 15 digits safe.
JavaScript now has BigInt
BigInt is a built-in object that provides a way to represent whole numbers larger than 253 - 1, which is the largest number JavaScript can reliably represent with the Number primitive.
BigInt can be used for arbitrarily large integers.
As you can see in the following blog post, JavaScript only supports 53 bit integers.
if you type in the console
var x = 11111111111111111
and then type
x
you'll get
11111111111111112
This has nothing to do with the parseFloat method.
There's also a related question here about working with big numbers in JavaScript.
Try using the unary + operator.
Like this + ("1111111111111111") + 1 = 1111111111111112
I am trying to perform some bitshift operations and dealing with binary numbers in JavaScript.
Here's what I'm trying to do. A user inputs a value and I do the following with it:
// Square Input and mod with 65536 to keep it below that value
var squaredInput = (inputVal * inputVal) % 65536;
// Figure out how many bits is the squared input number
var bits = Math.floor(Math.log(squaredInput) / Math.log(2)) + 1;
// Convert that number to a 16-bit number using bitshift.
var squaredShifted = squaredInput >>> (16 - bits);
As long as the number is larger than 46, it works. Once it is less than 46, it does not work.
I know the problem is the in bitshift. Now coming from a C background, I know this would be done differently, since all numbers will be stored in 32-bit format (given it is an int). Does JavaScript do the same (since it vars are not typed)?
If so, is it possible to store a 16-bit number? If not, can I treat it as 32-bits and do the required calculations to assume it is 16-bits?
Note: I am trying to extract the middle 4-bits of the 16-bit value in squaredInput.
Another note: When printing out the var, it just prints out the value without the padding so I couldn't figure it out. Tried using parseInt and toString.
Thanks
Are you looking for this?
function get16bitnumber( inputVal ){
return ("0000000000000000"+(inputVal * inputVal).toString(2)).substr(-16);
}
This function returns last 16 bits of (inputVal*inputVal) value.By having binary string you could work with any range of bits.
Don't use bitshifting in JS if you don't absolutely have to. The specs mention at least four number formats
IEEE 754
Int32
UInt32
UInt16
It's really confusing to know which is used when.
For example, ~ applies a bitwise inversion while converting to Int32. UInt16 seems to be used only in String.fromCharCode. Using bitshift operators converts the operands to either UInt32 or to Int32.
In your case, the right shift operator >>> forces conversion to UInt32.
When you type
a >>> b
this is what you get:
ToUInt32(a) >>> (ToUInt32(b) & 0x1f)
A colleague of mine stumbled upon a method to floor float numbers using a bitwise or:
var a = 13.6 | 0; //a == 13
We were talking about it and wondering a few things.
How does it work? Our theory was that using such an operator casts the number to an integer, thus removing the fractional part
Does it have any advantages over doing Math.floor? Maybe it's a bit faster? (pun not intended)
Does it have any disadvantages? Maybe it doesn't work in some cases? Clarity is an obvious one, since we had to figure it out, and well, I'm writting this question.
Thanks.
How does it work? Our theory was that using such an operator casts the
number to an integer, thus removing the fractional part
All bitwise operations except unsigned right shift, >>>, work on signed 32-bit integers. So using bitwise operations will convert a float to an integer.
Does it have any advantages over doing Math.floor? Maybe it's a bit
faster? (pun not intended)
http://jsperf.com/or-vs-floor/2 seems slightly faster
Does it have any disadvantages? Maybe it doesn't work in some cases?
Clarity is an obvious one, since we had to figure it out, and well,
I'm writting this question.
Will not pass jsLint.
32-bit signed integers only
Odd Comparative behavior: Math.floor(NaN) === NaN, while (NaN | 0) === 0
This is truncation as opposed to flooring. Howard's answer is sort of correct; But I would add that Math.floor does exactly what it is supposed to with respect to negative numbers. Mathematically, that is what a floor is.
In the case you described above, the programmer was more interested in truncation or chopping the decimal completely off. Although, the syntax they used sort of obscures the fact that they are converting the float to an int.
In ECMAScript 6, the equivalent of |0 is Math.trunc, kind of I should say:
Returns the integral part of a number by removing any fractional digits. It just truncate the dot and the digits behind it, no matter whether the argument is a positive number or a negative number.
Math.trunc(13.37) // 13
Math.trunc(42.84) // 42
Math.trunc(0.123) // 0
Math.trunc(-0.123) // -0
Math.trunc("-1.123")// -1
Math.trunc(NaN) // NaN
Math.trunc("foo") // NaN
Math.trunc() // NaN
Javascript represents Number as Double Precision 64-bit Floating numbers.
Math.floor works with this in mind.
Bitwise operations work in 32bit signed integers. 32bit signed integers use first bit as negative signifier and the other 31 bits are the number. Because of this, the min and max number allowed 32bit signed numbers are -2,147,483,648 and 2147483647 (0x7FFFFFFFF), respectively.
So when you're doing | 0, you're essentially doing is & 0xFFFFFFFF. This means, any number that is represented as 0x80000000 (2147483648) or greater will return as a negative number.
For example:
// Safe
(2147483647.5918 & 0xFFFFFFFF) === 2147483647
(2147483647 & 0xFFFFFFFF) === 2147483647
(200.59082098 & 0xFFFFFFFF) === 200
(0X7FFFFFFF & 0xFFFFFFFF) === 0X7FFFFFFF
// Unsafe
(2147483648 & 0xFFFFFFFF) === -2147483648
(-2147483649 & 0xFFFFFFFF) === 2147483647
(0x80000000 & 0xFFFFFFFF) === -2147483648
(3000000000.5 & 0xFFFFFFFF) === -1294967296
Also. Bitwise operations don't "floor". They truncate, which is the same as saying, they round closest to 0. Once you go around to negative numbers, Math.floor rounds down while bitwise start rounding up.
As I said before, Math.floor is safer because it operates with 64bit floating numbers. Bitwise is faster, yes, but limited to 32bit signed scope.
To summarize:
Bitwise works the same if you work from 0 to 2147483647.
Bitwise is 1 number off if you work from -2147483647 to 0.
Bitwise is completely different for numbers less than -2147483648 and greater than 2147483647.
If you really want to tweak performance and use both:
function floor(n) {
if (n >= 0 && n < 0x80000000) {
return n & 0xFFFFFFFF;
}
if (n > -0x80000000 && n < 0) {
const bitFloored = n & 0xFFFFFFFF;
if (bitFloored === n) return n;
return bitFloored - 1;
}
return Math.floor(n);
}
Just to add Math.trunc works like bitwise operations. So you can do this:
function trunc(n) {
if (n > -0x80000000 && n < 0x80000000) {
return n & 0xFFFFFFFF;
}
return Math.trunc(n);
}
Your first point is correct. The number is cast to an integer and thus any decimal digits are removed. Please note, that Math.floor rounds to the next integer towards minus infinity and thus gives a different result when applied to negative numbers.
The specs say that it is converted to an integer:
Let lnum be ToInt32(lval).
Performance: this has been tested at jsperf before.
note: dead link to spec removed
var myNegInt = -1 * Math.pow(2, 32);
var myFloat = 0.010203040506070809;
var my64BitFloat = myNegInt - myFloat;
var trunc1 = my64BitFloat | 0;
var trunc2 = ~~my64BitFloat;
var trunc3 = my64BitFloat ^ 0;
var trunc4 = my64BitFloat - my64BitFloat % 1;
var trunc5 = parseInt(my64BitFloat);
var trunc6 = Math.floor(my64BitFloat);
console.info(my64BitFloat);
console.info(trunc1);
console.info(trunc2);
console.info(trunc3);
console.info(trunc4);
console.info(trunc5);
console.info(trunc6);
IMO: The question "How does it work?", "Does it have any advantages over doing Math.floor?", "Does it have any disadvantages?" pale in comparison to "Is it at all logical to use it for this purpose?"
I think, before you try to get clever with your code, you may want to run these. My advice; just move along, there is nothing to see here. Using bitwise to save a few operations and having that matter to you at all, usually means your code architecture needs work. As far as why it may work sometimes, well a stopped clock is accurate twice a day, that does not make it useful. These operators have their uses, but not in this context.