I'm building a javascript-based web-app;
With a particular data input, a function returns a value of 10/3 = 3.333333333333333 (this is the amound of decimals shown by a colsole.log call); After about 200 lines of code, I have 2 variables (A and B) that contains that value, and I need to check if it is the same value;
The fact is, how is it possible to have an output like this?
console.log(A); //3.333333333333333
console.log(B); //3.333333333333333
console.log(A == B) //false
console.log(A-B == 0) //true??
I can imagine A == B is false due to how numbers are saved in the memory, but I wish it was a true; and what is really unexplainable to me is how comes the last line output is true?
console.log (or even toString) won't show you the full number down to the bit-by-bit difference. The floating point numbers used in JavaScript (and many other languages) are IEEE-754 double-precision floating point, and they're not perfectly precise, small discrepancies appear and can multiply.
Now, if you literally created A and B like this:
var A = 10 / 3;
var B = 10 / 3;
...then both comparisons would be true (proof). So apparently you're getting A one way, and B another, and the fact is that they are ever-so-slightly-different. (I'm quite surprised to hear A == B says false but A - B == 0 says true, though.)
You'll need to round them to the number of digits you think is appropriate, and compare the rounded result.
Related
I think my logic is wrong but I can't understand where I am making a mistake. I am trying to find the great common divisor, and code will determine what to do if a is bigger than b or b is bigger than a.
I tried many loops, if, while but in the end I deleted all to clear my sight. I made flowchart however it is not coming along with my code.
var a = 64;
var b = 12;
var newA;
while(a > b && newA != 0){
newA = a - b;
if(newA === 0){
outputObj.innerHTML = outputObj.innerHTML + "GCD is " + b;
}
}
while(a < b && newA != 0){
newA = b - a;
}
if(newA === 0){
outputObj.innerHTML = outputObj.innerHTML + "GCD is " + a;
}
}
If a is 64 and b is 12 the GCD is 4, if a is 35 and b is 42 the GCD is 7
You have a few different problems here. This looks like homework, so I'll try to point you in the right direction for a couple of the problems rather than e.g. telling you exactly what your code should say.
In your loops, you never update the value of either a or b.
Pretending that that's fixed, your code will either subtract a from b several times or subtract b from a lots of times. Doing that computes the remainder on dividing one number by the other, not the greatest common divisor.
I'm betting that you've been given a description of an algorithm for computing the greatest common divisor. Read through it again, comparing what it does against what your code does.
Here's a powerful method for finding problems in this sort of code: try to run it in your head, pretending that you're the computer. Go through, step by step, doing what the computer will do. With your code above, it might begin like this:
OK, I've got variables called a and b, whose values are 64 and 12. And a variable called newA, whose value hasn't been specified yet.
Now I need to check whether a is bigger than b -- yup, it is -- and then whether newA is zero.
Wait, I haven't given newA a value at this point. (You've found a bug here. Let's pretend it's fixed and move on.)
Now I set newA to be a-b, which is 52.
Now I check whether newA is zero, which it isn't so I don't need to do the stuff inside the if block there.
OK, so we've done one iteration of the while loop. Back to the start of the loop.
Now I need to check whether a is bigger than b -- yup, it is -- and then whether newA is zero.
Wait a minute, I'm checking the exact same thing as last time: nothing's changed. How's this loop going to end? (You've found another bug here.)
And so on.
I've got two numbers that I want to compare. The numbers in the following example are the result of 26^26 computed in two different systems. One of which is my javascript code.
However, when comparing the two numbers I end up with something like this:
AssertionError [ERR_ASSERTION]: 4.0329146112660565e+26 == 4.0329146112661e+26
They're obviously not equal, but theoretically they should.
What's the proper way to perform equality on big numbers in javascript (even if it's an approximation)?
If what you're trying to do is determine if two numbers are practically equivalent you'll have to come up with your margin of error. One way to do this is to compute the difference between the numbers and then determine if that difference is significant or not.
So, taking your numbers from before, we could evaluate the difference between these numbers through subtraction. Since we don't really care about the sign of this difference, I'll go ahead and get the absolute value of the difference.
Math.abs(4.0329146112660565e+26 - 4.0329146112661e+26) === 4329327034368
(Sidenote: Now is not the time to explain why, but the == operator in JavaScript has confusing and error-prone behavior, use === when you want to compare values.)
That difference is a HUGE number, but related to how big our numbers are in the first place, it's rather insignificant. Intuitively, I'm tempted to divide the difference by the smallest of our original numbers like so:
4329327034368 / 4.0329146112660565e+26 === 1.0734983136696987e-14
That looks like a pretty small number. Repeat that same operation with a bunch of values and you should be able to determine what you want your margin of error to be. Then, all you'll have to do is perform the same operations with arbitrary numbers and see if that "difference ratio" is small enough for you.
function similar(a, b) {
let diff = Math.abs(a - b);
let smallest = Math.min(Math.abs(a), Math.abs(b));
let ratio = diff / smallest;
return ratio < MARGIN_OF_ERROR;
}
Now I just came up with that way of determining the importance of the difference between two numbers. It might not be a very smart way to compute it, it might be appropriate to some situations and not to others. But the general idea is that you'll have to make a function that determines if two values are close enough with your own definition of "close".
Be aware though, JavaScript is one of the worst languages you can be doing math in. Integers become imprecise when they go beyond Number.MAX_SAFE_INT (which seems to be 9007199254740991 according to Chrome, not sure if it varies between browsers or if that's a standardized constant).
Update: If your target engine is es2020 or above, you can use the new BigInt javascript primitive, for numbers higher than Number.MAX_SAFE_INTEGER
BigInt(4.0329146112660565e+26) === BigInt(4.0329146112661e+26)
//false
See more information in MDN
var a = 4.0329146112660565e+26;
var b = 4.0329146112661e+26;
a = Math.round(a/10e+20)*10e+20
b = Math.round(b/10e+20)*10e+20
a == b;
I would suggest to use one of big numbers library:
big.js (https://www.npmjs.com/package/big.js)
Example:
var x = new Big('4.0329146112660565e+26');
var y = new Big('4.0329146112661e+26');
// Should print false
console.log('Comparision result' + x.eq(y));
big-numbers (https://www.npmjs.com/package/big-numbers)
Example:
var x = bn.of('4.0329146112660565e+26');
var y = bn.of('4.0329146112661e+26');
// Should print false
console.log('Comparision result' + x.equals(y));
Writing some test cases for my Javascript program that deals with binary and right now I'm just using stringify to check if the value and expected values are equal:
JSON.stringify(val) === JSON.stringify(expected)
This works fine except for when I have floating point values. This is what happens:
Given Value: [10,20,30,32.400001525878906,{"test":3,"asdf":23}]
Expected Value: [10,20,30,32.4,{"test":3,"asdf":23}]
Test Failed!
So I guess I can't use stringify anymore to check if my two objects/arrays are equal. What's a good way to check if two potentially deeply nested objects/arrays are equal while also taking in to account floating point values? That is, two floating point values should be considered equal if they are 99.99% the same or whatever.
You'll need to test each element in the array in order, and you'll need to do it recursively for objects. This is typically known as a deep comparison or deep equality. You should be able to do this using a recursive function that checks the type(s) of the comparands.
When comparing floating point values, you'll want to use a tolerance. You do this by taking the absolute value of subtracting the two numbers from each other, and then comparing that to either a fixed tolerance value of your choosing, or a small number known as an epsilon.
In JavaScript, the machine epsilon is available as Number.EPSILON, and is defined to be the difference between 1 and the smallest number that is greater than 1 and can be represented as a Number. Similar constants are available in most languages and are typically used for tolerance-based comparisons.
Tolerance-based comparison turns floating point comparisons from simple equality into a subtract and compare. If you'd normally write
if (a === b) { ... }
you'd write that using the absolute value and a tolerance to eliminate floating point weirdness:
var tolerance = Number.EPSILON;
if (Math.abs(a - b) < tolerance) { ... }
If the difference between a and b is smaller than tolerance, you treat them as equal.
For a more nuanced (but possibly overkill for your case) approach, see The Floating Point Guide's section on comparison. The implementation presented there is in Java, but is likely portable to JavaScript without much effort.
I need to convert a string returned from prompt into an equation, however the parseFloat returns as only the first number, and symbols in an equation, and stops at the variable. The variable will always = x. The program is designed to convert an algebraic expression say 15*x(5^4-56)*17/x=15 into an expression, and calculate the value of x. If someone could show me how to do this, it would help dramatically. I am currently using multiple prompts, having the user put in the equation before x, then the equation after x, then it inserts a variable in between the two, and calculates it's value.
Edit:
I have no variables predefined, and it must work in equations where x > 1000, or x != //an integer.
Thanks in advance!
Seems to be a complex problem...
This is a solution for a simple relaxed version of your problem. Hope you can use some components of this.
Constraints:
answer for x should be integers between 0 and 1000
the left hand side of the expression should be proper javascript syntax
var input = prompt("enter the equation"); //eg: x*x+x+1=241
var parts = input.split('=');
//solving equation starts
var x = 0;
var temp = eval(parts[0]);
while (temp != parts[1] && x<1000){
x++;
temp = eval(parts[0]);
}
var ans = (x<1000)?"answer is "+x:"this program cannot solve this";
//solving equation finishes
alert(ans);
You can replace the "solving equation" part with some numerical methods used in computer science to solve equations (more details here) . You will have to parse the left side of equation and map them to proper javascript expressions (as a string to execute with eval()) if you want to allow users to use your syntax.
Javascript can evaluate strings using the eval function, but the variable as to be defined before hand, and the equation has to be formatted in way that javascript can understand:
var x = 15
var string = "15*x*17/x"
eval(string)
Your example: "15*x(5^4-56)*17/x=15" would not run however, because it would evaluate x(5^4-56) as a javascript expression, which is invalid.
Using all the info, and other mehtods I found about this, I have put together a communinty answer. Anyone is invited to change and/or add their methods to this.
In order to do this with the least work possible for the user and coder, you would implement the following code.
var input = prompt("enter the equation"); //eg: x*x+x+1=241
var parts = input.split('=');
//solving equation starts
var x = 0; //Or the lowest possible value of "x"
var temp = eval(parts[0]);
while (temp != parts[1] && x<1000){ // && x < The highest number to evaluate
x++; //Add the increment (determines the maximum amount of digits) eg x+0.1 for tenths max, x+2 for only even integers etc.
temp = eval(parts[0]);
}
var ans = (x<1000)?"answer is "+x:"this program cannot solve this"; //make sure x< is the same as line 7.
//solving equation finishes
alert(ans);
But, this runs very slowly if you allow tenths, or a range larger than 2000.`
A faster way of running this would be to define arrays allowing any variable (instead of just x) and a different eveulation process such as here. (do the right click view html and click on the first js source to see code) but, this is 2k lines. Both are usable, but the second is more efficient, and can solve multivariate equations.
Division by 0 gives this special value:
3/0 output:Infinity
You can’t play positive and negative infinity against each other:
Infinity - Infinity output:NaN (Why?)
It also turns out that “beyond infinity” is still infinity:
Infinity + Infinity output:Infinity(this is accepted)
5 * Infinity
Infinity(this is also accepted)
so why infinity-infinity evalutes to NaN?It should be infinity isn't it?Also i wanted to know why cant object be converted to primitive values?Sorry for posting two question at a time ,as this is the last question i can post.See here:
var obj = {
valueOf: function () {
console.log("valueOf");
return {}; // not a primitive
},
toString: function () {
console.log("toString");
return {}; // not a primitive
}
}
Number(obj) //TypeError: Cannot convert object to primitive values
That's how ∞ works in mathematics. Infinity itself is not a number, it is a concept. The general idea is that
∞ + x = ∞ ∀ x
∞ is, obviously, infinitely big. If you subtract an infinitely big thing from another infinitely big thing, you can't define what you have left. If the first infinity is bigger, you'll get a negative result, but if it's smaller then the result will be positive (basic rule of subtraction), but since both are infinitely big you have no way of knowing which is bigger (unless more information is given, such as the context leading to these infinities*). Therefore, as far as the computer is concerned, ∞ - ∞ is mathematically undefined, or Not a Number.
* Example: Let x = the sum of all positive integers, and y = the sum of each positive integer doubled. In this case, we can say that y > x, even though both are infinity.
Because it's an indeterminate form, so it's not infinity. NaN reflects this the best way possible.
http://en.wikipedia.org/wiki/Indeterminate_form
Related question:
https://math.stackexchange.com/questions/60766/what-is-the-result-of-infinity-minus-infinity
var A = 1/0
var B = 2 * A
var c = B - A
Note that even though B = 2 * A, still A = B (2 * infinity is still infinity, so they are both infinity), so what do you expect C to be? infinity or 0?
Infinity is not really a number, mathematically speaking. Though IsNaN(1/0) = false.