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I've been working with JavaScript for a few days now and have got to a point where I want to overload operators for my defined objects.
After a stint on google searching for this it seems you can't officially do this, yet there are a few people out there claiming some long-winded way of performing this action.
Basically I've made a Vector2 class and want to be able to do the following:
var x = new Vector2(10,10);
var y = new Vector2(10,10);
x += y; //This does not result in x being a vector with 20,20 as its x & y values.
Instead I'm having to do this:
var x = new Vector2(10,10);
var y = new Vector2(10,10);
x = x.add(y); //This results in x being a vector with 20,20 as its x & y values.
Is there an approach I can take to overload operators in my Vector2 class? As this just looks plain ugly.
As you've found, JavaScript doesn't support operator overloading. The closest you can come is to implement toString (which will get called when the instance needs to be coerced to being a string) and valueOf (which will get called to coerce it to a number, for instance when using + for addition, or in many cases when using it for concatenation because + tries to do addition before concatenation), which is pretty limited. Neither lets you create a Vector2 object as a result. Similarly, Proxy (added in ES2015) lets you intercept various object operations (including property access), but again won't let you control the result of += on Vector instances.
For people coming to this question who want a string or number as a result (instead of a Vector2), though, here are examples of valueOf and toString. These examples do not demonstrate operator overloading, just taking advantage of JavaScript's built-in handling converting to primitives:
valueOf
This example doubles the value of an object's val property in response to being coerced to a primitive, for instance via +:
function Thing(val) {
this.val = val;
}
Thing.prototype.valueOf = function() {
// Here I'm just doubling it; you'd actually do your longAdd thing
return this.val * 2;
};
var a = new Thing(1);
var b = new Thing(2);
console.log(a + b); // 6 (1 * 2 + 2 * 2)
Or with ES2015's class:
class Thing {
constructor(val) {
this.val = val;
}
valueOf() {
return this.val * 2;
}
}
const a = new Thing(1);
const b = new Thing(2);
console.log(a + b); // 6 (1 * 2 + 2 * 2)
Or just with objects, no constructors:
var thingPrototype = {
valueOf: function() {
return this.val * 2;
}
};
var a = Object.create(thingPrototype);
a.val = 1;
var b = Object.create(thingPrototype);
b.val = 2;
console.log(a + b); // 6 (1 * 2 + 2 * 2)
toString
This example converts the value of an object's val property to upper case in response to being coerced to a primitive, for instance via +:
function Thing(val) {
this.val = val;
}
Thing.prototype.toString = function() {
return this.val.toUpperCase();
};
var a = new Thing("a");
var b = new Thing("b");
console.log(a + b); // AB
Or with ES2015's class:
class Thing {
constructor(val) {
this.val = val;
}
toString() {
return this.val.toUpperCase();
}
}
const a = new Thing("a");
const b = new Thing("b");
console.log(a + b); // AB
Or just with objects, no constructors:
var thingPrototype = {
toString: function() {
return this.val.toUpperCase();
}
};
var a = Object.create(thingPrototype);
a.val = "a";
var b = Object.create(thingPrototype);
b.val = "b";
console.log(a + b); // AB
As T.J. said, you cannot overload operators in JavaScript. However you can take advantage of the valueOf function to write a hack which looks better than using functions like add every time, but imposes the constraints on the vector that the x and y are between 0 and MAX_VALUE. Here is the code:
var MAX_VALUE = 1000000;
var Vector = function(a, b) {
var self = this;
//initialize the vector based on parameters
if (typeof(b) == "undefined") {
//if the b value is not passed in, assume a is the hash of a vector
self.y = a % MAX_VALUE;
self.x = (a - self.y) / MAX_VALUE;
} else {
//if b value is passed in, assume the x and the y coordinates are the constructors
self.x = a;
self.y = b;
}
//return a hash of the vector
this.valueOf = function() {
return self.x * MAX_VALUE + self.y;
};
};
var V = function(a, b) {
return new Vector(a, b);
};
Then you can write equations like this:
var a = V(1, 2); //a -> [1, 2]
var b = V(2, 4); //b -> [2, 4]
var c = V((2 * a + b) / 2); //c -> [2, 4]
It's possible to do vector math with two numbers packed into one. Let me first show an example before I explain how it works:
let a = vec_pack([2,4]);
let b = vec_pack([1,2]);
let c = a+b; // Vector addition
let d = c-b; // Vector subtraction
let e = d*2; // Scalar multiplication
let f = e/2; // Scalar division
console.log(vec_unpack(c)); // [3, 6]
console.log(vec_unpack(d)); // [2, 4]
console.log(vec_unpack(e)); // [4, 8]
console.log(vec_unpack(f)); // [2, 4]
if(a === f) console.log("Equality works");
if(a > b) console.log("Y value takes priority");
I am using the fact that if you bit shift two numbers X times and then add or subtract them before shifting them back, you will get the same result as if you hadn't shifted them to begin with. Similarly scalar multiplication and division works symmetrically for shifted values.
A JavaScript number has 52 bits of integer precision (64 bit floats), so I will pack one number into he higher available 26 bits, and one into the lower. The code is made a bit more messy because I wanted to support signed numbers.
function vec_pack(vec){
return vec[1] * 67108864 + (vec[0] < 0 ? 33554432 | vec[0] : vec[0]);
}
function vec_unpack(number){
switch(((number & 33554432) !== 0) * 1 + (number < 0) * 2){
case(0):
return [(number % 33554432),Math.trunc(number / 67108864)];
break;
case(1):
return [(number % 33554432)-33554432,Math.trunc(number / 67108864)+1];
break;
case(2):
return [(((number+33554432) % 33554432) + 33554432) % 33554432,Math.round(number / 67108864)];
break;
case(3):
return [(number % 33554432),Math.trunc(number / 67108864)];
break;
}
}
The only downside I can see with this is that the x and y has to be in the range +-33 million, since they have to fit within 26 bits each.
Actually, there is one variant of JavaScript that does support operator overloading. ExtendScript, the scripting language used by Adobe applications such as Photoshop and Illustrator, does have operator overloading. In it, you can write:
Vector2.prototype["+"] = function( b )
{
return new Vector2( this.x + b.x, this.y + b.y );
}
var a = new Vector2(1,1);
var b = new Vector2(2,2);
var c = a + b;
This is described in more detail in the "Adobe Extendscript JavaScript tools guide" (current link here). The syntax was apparently based on a (now long abandoned) draft of the ECMAScript standard.
FYI paper.js solves this issue by creating PaperScript, a self-contained, scoped javascript with operator overloading of vectors, which it then processing back into javascript.
But the paperscript files need to be specifically specified and processed as such.
We can use React-like Hooks to evaluate arrow function with different values from valueOf method on each iteration.
const a = Vector2(1, 2) // [1, 2]
const b = Vector2(2, 4) // [2, 4]
const c = Vector2(() => (2 * a + b) / 2) // [2, 4]
// There arrow function will iterate twice
// 1 iteration: method valueOf return X component
// 2 iteration: method valueOf return Y component
const Vector2 = (function() {
let index = -1
return function(x, y) {
if (typeof x === 'function') {
const calc = x
index = 0, x = calc()
index = 1, y = calc()
index = -1
}
return Object.assign([x, y], {
valueOf() {
return index == -1 ? this.toString() : this[index]
},
toString() {
return `[${this[0]}, ${this[1]}]`
},
len() {
return Math.sqrt(this[0] ** 2 + this[1] ** 2)
}
})
}
})()
const a = Vector2(1, 2)
const b = Vector2(2, 4)
console.log('a = ' + a) // a = [1, 2]
console.log(`b = ${b}`) // b = [2, 4]
const c = Vector2(() => (2 * a + b) / 2) // [2, 4]
a[0] = 12
const d = Vector2(() => (2 * a + b) / 2) // [13, 4]
const normalized = Vector2(() => d / d.len()) // [0.955..., 0.294...]
console.log(c, d, normalized)
Library #js-basics/vector uses the same idea for Vector3.
I wrote a library that exploits a bunch of evil hacks to do it in raw JS. It allows expressions like these.
Complex numbers:
>> Complex()({r: 2, i: 0} / {r: 1, i: 1} + {r: -3, i: 2}))
<- {r: -2, i: 1}
Automatic differentiation:
Let f(x) = x^3 - 5x:
>> var f = x => Dual()(x * x * x - {x:5, dx:0} * x);
Now map it over some values:
>> [-2,-1,0,1,2].map(a=>({x:a,dx:1})).map(f).map(a=>a.dx)
<- [ 7, -2, -5, -2, 7 ]
i.e. f'(x) = 3x^2 - 5.
Polynomials:
>> Poly()([1,-2,3,-4]*[5,-6]).map((c,p)=>''+c+'x^'+p).join(' + ')
<- "5x^0 + -16x^1 + 27x^2 + -38x^3 + 24x^4"
For your particular problem, you would define a Vector2 function (or maybe something shorter) using the library, then write x = Vector2()(x + y);
https://gist.github.com/pyrocto/5a068100abd5ff6dfbe69a73bbc510d7
Whilst not an exact answer to the question, it is possible to implement some of the python __magic__ methods using ES6 Symbols
A [Symbol.toPrimitive]() method doesn't let you imply a call Vector.add(), but will let you use syntax such as Decimal() + int.
class AnswerToLifeAndUniverseAndEverything {
[Symbol.toPrimitive](hint) {
if (hint === 'string') {
return 'Like, 42, man';
} else if (hint === 'number') {
return 42;
} else {
// when pushed, most classes (except Date)
// default to returning a number primitive
return 42;
}
}
}
https://www.keithcirkel.co.uk/metaprogramming-in-es6-symbols/
Interesting is also experimental library operator-overloading-js . It does overloading in a defined context (callback function) only.
I've been working with JavaScript for a few days now and have got to a point where I want to overload operators for my defined objects.
After a stint on google searching for this it seems you can't officially do this, yet there are a few people out there claiming some long-winded way of performing this action.
Basically I've made a Vector2 class and want to be able to do the following:
var x = new Vector2(10,10);
var y = new Vector2(10,10);
x += y; //This does not result in x being a vector with 20,20 as its x & y values.
Instead I'm having to do this:
var x = new Vector2(10,10);
var y = new Vector2(10,10);
x = x.add(y); //This results in x being a vector with 20,20 as its x & y values.
Is there an approach I can take to overload operators in my Vector2 class? As this just looks plain ugly.
As you've found, JavaScript doesn't support operator overloading. The closest you can come is to implement toString (which will get called when the instance needs to be coerced to being a string) and valueOf (which will get called to coerce it to a number, for instance when using + for addition, or in many cases when using it for concatenation because + tries to do addition before concatenation), which is pretty limited. Neither lets you create a Vector2 object as a result. Similarly, Proxy (added in ES2015) lets you intercept various object operations (including property access), but again won't let you control the result of += on Vector instances.
For people coming to this question who want a string or number as a result (instead of a Vector2), though, here are examples of valueOf and toString. These examples do not demonstrate operator overloading, just taking advantage of JavaScript's built-in handling converting to primitives:
valueOf
This example doubles the value of an object's val property in response to being coerced to a primitive, for instance via +:
function Thing(val) {
this.val = val;
}
Thing.prototype.valueOf = function() {
// Here I'm just doubling it; you'd actually do your longAdd thing
return this.val * 2;
};
var a = new Thing(1);
var b = new Thing(2);
console.log(a + b); // 6 (1 * 2 + 2 * 2)
Or with ES2015's class:
class Thing {
constructor(val) {
this.val = val;
}
valueOf() {
return this.val * 2;
}
}
const a = new Thing(1);
const b = new Thing(2);
console.log(a + b); // 6 (1 * 2 + 2 * 2)
Or just with objects, no constructors:
var thingPrototype = {
valueOf: function() {
return this.val * 2;
}
};
var a = Object.create(thingPrototype);
a.val = 1;
var b = Object.create(thingPrototype);
b.val = 2;
console.log(a + b); // 6 (1 * 2 + 2 * 2)
toString
This example converts the value of an object's val property to upper case in response to being coerced to a primitive, for instance via +:
function Thing(val) {
this.val = val;
}
Thing.prototype.toString = function() {
return this.val.toUpperCase();
};
var a = new Thing("a");
var b = new Thing("b");
console.log(a + b); // AB
Or with ES2015's class:
class Thing {
constructor(val) {
this.val = val;
}
toString() {
return this.val.toUpperCase();
}
}
const a = new Thing("a");
const b = new Thing("b");
console.log(a + b); // AB
Or just with objects, no constructors:
var thingPrototype = {
toString: function() {
return this.val.toUpperCase();
}
};
var a = Object.create(thingPrototype);
a.val = "a";
var b = Object.create(thingPrototype);
b.val = "b";
console.log(a + b); // AB
As T.J. said, you cannot overload operators in JavaScript. However you can take advantage of the valueOf function to write a hack which looks better than using functions like add every time, but imposes the constraints on the vector that the x and y are between 0 and MAX_VALUE. Here is the code:
var MAX_VALUE = 1000000;
var Vector = function(a, b) {
var self = this;
//initialize the vector based on parameters
if (typeof(b) == "undefined") {
//if the b value is not passed in, assume a is the hash of a vector
self.y = a % MAX_VALUE;
self.x = (a - self.y) / MAX_VALUE;
} else {
//if b value is passed in, assume the x and the y coordinates are the constructors
self.x = a;
self.y = b;
}
//return a hash of the vector
this.valueOf = function() {
return self.x * MAX_VALUE + self.y;
};
};
var V = function(a, b) {
return new Vector(a, b);
};
Then you can write equations like this:
var a = V(1, 2); //a -> [1, 2]
var b = V(2, 4); //b -> [2, 4]
var c = V((2 * a + b) / 2); //c -> [2, 4]
It's possible to do vector math with two numbers packed into one. Let me first show an example before I explain how it works:
let a = vec_pack([2,4]);
let b = vec_pack([1,2]);
let c = a+b; // Vector addition
let d = c-b; // Vector subtraction
let e = d*2; // Scalar multiplication
let f = e/2; // Scalar division
console.log(vec_unpack(c)); // [3, 6]
console.log(vec_unpack(d)); // [2, 4]
console.log(vec_unpack(e)); // [4, 8]
console.log(vec_unpack(f)); // [2, 4]
if(a === f) console.log("Equality works");
if(a > b) console.log("Y value takes priority");
I am using the fact that if you bit shift two numbers X times and then add or subtract them before shifting them back, you will get the same result as if you hadn't shifted them to begin with. Similarly scalar multiplication and division works symmetrically for shifted values.
A JavaScript number has 52 bits of integer precision (64 bit floats), so I will pack one number into he higher available 26 bits, and one into the lower. The code is made a bit more messy because I wanted to support signed numbers.
function vec_pack(vec){
return vec[1] * 67108864 + (vec[0] < 0 ? 33554432 | vec[0] : vec[0]);
}
function vec_unpack(number){
switch(((number & 33554432) !== 0) * 1 + (number < 0) * 2){
case(0):
return [(number % 33554432),Math.trunc(number / 67108864)];
break;
case(1):
return [(number % 33554432)-33554432,Math.trunc(number / 67108864)+1];
break;
case(2):
return [(((number+33554432) % 33554432) + 33554432) % 33554432,Math.round(number / 67108864)];
break;
case(3):
return [(number % 33554432),Math.trunc(number / 67108864)];
break;
}
}
The only downside I can see with this is that the x and y has to be in the range +-33 million, since they have to fit within 26 bits each.
Actually, there is one variant of JavaScript that does support operator overloading. ExtendScript, the scripting language used by Adobe applications such as Photoshop and Illustrator, does have operator overloading. In it, you can write:
Vector2.prototype["+"] = function( b )
{
return new Vector2( this.x + b.x, this.y + b.y );
}
var a = new Vector2(1,1);
var b = new Vector2(2,2);
var c = a + b;
This is described in more detail in the "Adobe Extendscript JavaScript tools guide" (current link here). The syntax was apparently based on a (now long abandoned) draft of the ECMAScript standard.
FYI paper.js solves this issue by creating PaperScript, a self-contained, scoped javascript with operator overloading of vectors, which it then processing back into javascript.
But the paperscript files need to be specifically specified and processed as such.
We can use React-like Hooks to evaluate arrow function with different values from valueOf method on each iteration.
const a = Vector2(1, 2) // [1, 2]
const b = Vector2(2, 4) // [2, 4]
const c = Vector2(() => (2 * a + b) / 2) // [2, 4]
// There arrow function will iterate twice
// 1 iteration: method valueOf return X component
// 2 iteration: method valueOf return Y component
const Vector2 = (function() {
let index = -1
return function(x, y) {
if (typeof x === 'function') {
const calc = x
index = 0, x = calc()
index = 1, y = calc()
index = -1
}
return Object.assign([x, y], {
valueOf() {
return index == -1 ? this.toString() : this[index]
},
toString() {
return `[${this[0]}, ${this[1]}]`
},
len() {
return Math.sqrt(this[0] ** 2 + this[1] ** 2)
}
})
}
})()
const a = Vector2(1, 2)
const b = Vector2(2, 4)
console.log('a = ' + a) // a = [1, 2]
console.log(`b = ${b}`) // b = [2, 4]
const c = Vector2(() => (2 * a + b) / 2) // [2, 4]
a[0] = 12
const d = Vector2(() => (2 * a + b) / 2) // [13, 4]
const normalized = Vector2(() => d / d.len()) // [0.955..., 0.294...]
console.log(c, d, normalized)
Library #js-basics/vector uses the same idea for Vector3.
I wrote a library that exploits a bunch of evil hacks to do it in raw JS. It allows expressions like these.
Complex numbers:
>> Complex()({r: 2, i: 0} / {r: 1, i: 1} + {r: -3, i: 2}))
<- {r: -2, i: 1}
Automatic differentiation:
Let f(x) = x^3 - 5x:
>> var f = x => Dual()(x * x * x - {x:5, dx:0} * x);
Now map it over some values:
>> [-2,-1,0,1,2].map(a=>({x:a,dx:1})).map(f).map(a=>a.dx)
<- [ 7, -2, -5, -2, 7 ]
i.e. f'(x) = 3x^2 - 5.
Polynomials:
>> Poly()([1,-2,3,-4]*[5,-6]).map((c,p)=>''+c+'x^'+p).join(' + ')
<- "5x^0 + -16x^1 + 27x^2 + -38x^3 + 24x^4"
For your particular problem, you would define a Vector2 function (or maybe something shorter) using the library, then write x = Vector2()(x + y);
https://gist.github.com/pyrocto/5a068100abd5ff6dfbe69a73bbc510d7
Whilst not an exact answer to the question, it is possible to implement some of the python __magic__ methods using ES6 Symbols
A [Symbol.toPrimitive]() method doesn't let you imply a call Vector.add(), but will let you use syntax such as Decimal() + int.
class AnswerToLifeAndUniverseAndEverything {
[Symbol.toPrimitive](hint) {
if (hint === 'string') {
return 'Like, 42, man';
} else if (hint === 'number') {
return 42;
} else {
// when pushed, most classes (except Date)
// default to returning a number primitive
return 42;
}
}
}
https://www.keithcirkel.co.uk/metaprogramming-in-es6-symbols/
Interesting is also experimental library operator-overloading-js . It does overloading in a defined context (callback function) only.
I need to have two variables, x and y, and an equation involving both that always equals one.
This is a simple example. This example may be easy to define in terms of y, like y = 1/x, but I have another equation I need to use, and it is too hard to define in terms of y.
var x, y;
x*y = 1;
x = Math.random()*20;
console.log(y);
I would get an error message for this, like
Uncaught ReferenceError: Invalid left-hand side in assignment (line 2)
a variable could be defined as x*y, like var z= x*y, but apparently not a constant. Maybe there is some way around this, like defining two variables, one as the constant and the other as the equation and finding some way to relate them? Maybe javascript's looseness will allow for some new technique?
Thanks ahead of time! :)
You can't do this directly. The value of x depends on the value of y. You must describe their dependency.
You can do something like:
var x_y = (function () {
var x = 1, y = 1;
return {
set_x: function (new_x) {
x = new_x;
y = 1 / new_x;
},
set_y: function (new_y) {
y = new_y;
x = 1 / new_y;
},
get_x: function () {
return x;
},
get_y: function () {
return y;
}
};
}());
x_y.set_x(Math.random()*20);
console.log(x_y.get_y());
So essentially we're saying x = 1 / y; and y = 1 / x; and we couple the values: if you change one, the other changes as well.
So, I'm being a bit creative in searching through persistent graphical objects in HTML5 canvas by using PouchDB and MapRepduce. (I'm trying to tell if the user's clicked on that object with simple bounding box logic) That part isn't all that important; it might be silly, but I just want to do it, because I'm a dork like that.
That said, I want to pass a pair of custom values to the reducer function of my PouchDB query. I'm unsure how to do that, exactly.
Here's kinda what I'm doing right now:
var x = evt.clientX, y = evt.clientY
var map = function (doc) {
emit('bbox',
{
x0: doc.x,
x1: doc.x + doc.w,
y0: doc.y,
y1: doc.y + doc.h
}
)
}
var reduce = function (keys, values, rereduce) {
return values.forEach(function (bbox) {
if (x >= bbox.x0 && x < bbox.x1 && y >= bbox.y0 && y < bbox.y1) {
return true
}
})
}
var result = db.px.query({map: map, reduce: reduce}, function (err, rsp) {
cb(rsp)
})
It doesn't work right now because the reduce function can't access the x and y values since, for some reason, they are inaccessible from the scope in which the functions are run. So, I need to pass them to Pouch/Couch through that query method, I think. I'm kinda stuck here.
Shouldn't it be sufficient to have a "createReduce" function that makes the x and y parameters more accessible?
var createReduce = function(x,y) { return function(keys, values, rereduce) {...} }
It seemed I was trying to do the impossible, and I really didn't need the persistence for this particular application. Furthermore, more complex graphics-oriented spatial queries will require a more specialized data persistence and manipulation framework. I'll be working on such a thing in the future.
That said, here's some helpful filter-based bbox code to help out any intrepid coders out there who might be walking down my own path in the future.
var db = {
// 2d, canvas-related data store and methods
px: {
store: [],
add: function (obj) {
db.px.store.push(obj)
},
pick: function (x, y) {
return db.px.store.filter(function (obj) {
return x >= obj.x
&& x < obj.x + obj.w * gfx.px.ratio
&& y >= obj.y
&& y < obj.y + obj.h * gfx.px.ratio
})
}
}
}
This works over graphical objects formatted like so:
{
x: 0, y: 0, w: 0, h: 0
}
I hope that's helpful for anyone who tries to do what I'm doing in the future.
Also, the gfx.px.ratio variable is for hi-DPI (retina) display compatibility.
I've been working with JavaScript for a few days now and have got to a point where I want to overload operators for my defined objects.
After a stint on google searching for this it seems you can't officially do this, yet there are a few people out there claiming some long-winded way of performing this action.
Basically I've made a Vector2 class and want to be able to do the following:
var x = new Vector2(10,10);
var y = new Vector2(10,10);
x += y; //This does not result in x being a vector with 20,20 as its x & y values.
Instead I'm having to do this:
var x = new Vector2(10,10);
var y = new Vector2(10,10);
x = x.add(y); //This results in x being a vector with 20,20 as its x & y values.
Is there an approach I can take to overload operators in my Vector2 class? As this just looks plain ugly.
As you've found, JavaScript doesn't support operator overloading. The closest you can come is to implement toString (which will get called when the instance needs to be coerced to being a string) and valueOf (which will get called to coerce it to a number, for instance when using + for addition, or in many cases when using it for concatenation because + tries to do addition before concatenation), which is pretty limited. Neither lets you create a Vector2 object as a result. Similarly, Proxy (added in ES2015) lets you intercept various object operations (including property access), but again won't let you control the result of += on Vector instances.
For people coming to this question who want a string or number as a result (instead of a Vector2), though, here are examples of valueOf and toString. These examples do not demonstrate operator overloading, just taking advantage of JavaScript's built-in handling converting to primitives:
valueOf
This example doubles the value of an object's val property in response to being coerced to a primitive, for instance via +:
function Thing(val) {
this.val = val;
}
Thing.prototype.valueOf = function() {
// Here I'm just doubling it; you'd actually do your longAdd thing
return this.val * 2;
};
var a = new Thing(1);
var b = new Thing(2);
console.log(a + b); // 6 (1 * 2 + 2 * 2)
Or with ES2015's class:
class Thing {
constructor(val) {
this.val = val;
}
valueOf() {
return this.val * 2;
}
}
const a = new Thing(1);
const b = new Thing(2);
console.log(a + b); // 6 (1 * 2 + 2 * 2)
Or just with objects, no constructors:
var thingPrototype = {
valueOf: function() {
return this.val * 2;
}
};
var a = Object.create(thingPrototype);
a.val = 1;
var b = Object.create(thingPrototype);
b.val = 2;
console.log(a + b); // 6 (1 * 2 + 2 * 2)
toString
This example converts the value of an object's val property to upper case in response to being coerced to a primitive, for instance via +:
function Thing(val) {
this.val = val;
}
Thing.prototype.toString = function() {
return this.val.toUpperCase();
};
var a = new Thing("a");
var b = new Thing("b");
console.log(a + b); // AB
Or with ES2015's class:
class Thing {
constructor(val) {
this.val = val;
}
toString() {
return this.val.toUpperCase();
}
}
const a = new Thing("a");
const b = new Thing("b");
console.log(a + b); // AB
Or just with objects, no constructors:
var thingPrototype = {
toString: function() {
return this.val.toUpperCase();
}
};
var a = Object.create(thingPrototype);
a.val = "a";
var b = Object.create(thingPrototype);
b.val = "b";
console.log(a + b); // AB
As T.J. said, you cannot overload operators in JavaScript. However you can take advantage of the valueOf function to write a hack which looks better than using functions like add every time, but imposes the constraints on the vector that the x and y are between 0 and MAX_VALUE. Here is the code:
var MAX_VALUE = 1000000;
var Vector = function(a, b) {
var self = this;
//initialize the vector based on parameters
if (typeof(b) == "undefined") {
//if the b value is not passed in, assume a is the hash of a vector
self.y = a % MAX_VALUE;
self.x = (a - self.y) / MAX_VALUE;
} else {
//if b value is passed in, assume the x and the y coordinates are the constructors
self.x = a;
self.y = b;
}
//return a hash of the vector
this.valueOf = function() {
return self.x * MAX_VALUE + self.y;
};
};
var V = function(a, b) {
return new Vector(a, b);
};
Then you can write equations like this:
var a = V(1, 2); //a -> [1, 2]
var b = V(2, 4); //b -> [2, 4]
var c = V((2 * a + b) / 2); //c -> [2, 4]
It's possible to do vector math with two numbers packed into one. Let me first show an example before I explain how it works:
let a = vec_pack([2,4]);
let b = vec_pack([1,2]);
let c = a+b; // Vector addition
let d = c-b; // Vector subtraction
let e = d*2; // Scalar multiplication
let f = e/2; // Scalar division
console.log(vec_unpack(c)); // [3, 6]
console.log(vec_unpack(d)); // [2, 4]
console.log(vec_unpack(e)); // [4, 8]
console.log(vec_unpack(f)); // [2, 4]
if(a === f) console.log("Equality works");
if(a > b) console.log("Y value takes priority");
I am using the fact that if you bit shift two numbers X times and then add or subtract them before shifting them back, you will get the same result as if you hadn't shifted them to begin with. Similarly scalar multiplication and division works symmetrically for shifted values.
A JavaScript number has 52 bits of integer precision (64 bit floats), so I will pack one number into he higher available 26 bits, and one into the lower. The code is made a bit more messy because I wanted to support signed numbers.
function vec_pack(vec){
return vec[1] * 67108864 + (vec[0] < 0 ? 33554432 | vec[0] : vec[0]);
}
function vec_unpack(number){
switch(((number & 33554432) !== 0) * 1 + (number < 0) * 2){
case(0):
return [(number % 33554432),Math.trunc(number / 67108864)];
break;
case(1):
return [(number % 33554432)-33554432,Math.trunc(number / 67108864)+1];
break;
case(2):
return [(((number+33554432) % 33554432) + 33554432) % 33554432,Math.round(number / 67108864)];
break;
case(3):
return [(number % 33554432),Math.trunc(number / 67108864)];
break;
}
}
The only downside I can see with this is that the x and y has to be in the range +-33 million, since they have to fit within 26 bits each.
Actually, there is one variant of JavaScript that does support operator overloading. ExtendScript, the scripting language used by Adobe applications such as Photoshop and Illustrator, does have operator overloading. In it, you can write:
Vector2.prototype["+"] = function( b )
{
return new Vector2( this.x + b.x, this.y + b.y );
}
var a = new Vector2(1,1);
var b = new Vector2(2,2);
var c = a + b;
This is described in more detail in the "Adobe Extendscript JavaScript tools guide" (current link here). The syntax was apparently based on a (now long abandoned) draft of the ECMAScript standard.
FYI paper.js solves this issue by creating PaperScript, a self-contained, scoped javascript with operator overloading of vectors, which it then processing back into javascript.
But the paperscript files need to be specifically specified and processed as such.
We can use React-like Hooks to evaluate arrow function with different values from valueOf method on each iteration.
const a = Vector2(1, 2) // [1, 2]
const b = Vector2(2, 4) // [2, 4]
const c = Vector2(() => (2 * a + b) / 2) // [2, 4]
// There arrow function will iterate twice
// 1 iteration: method valueOf return X component
// 2 iteration: method valueOf return Y component
const Vector2 = (function() {
let index = -1
return function(x, y) {
if (typeof x === 'function') {
const calc = x
index = 0, x = calc()
index = 1, y = calc()
index = -1
}
return Object.assign([x, y], {
valueOf() {
return index == -1 ? this.toString() : this[index]
},
toString() {
return `[${this[0]}, ${this[1]}]`
},
len() {
return Math.sqrt(this[0] ** 2 + this[1] ** 2)
}
})
}
})()
const a = Vector2(1, 2)
const b = Vector2(2, 4)
console.log('a = ' + a) // a = [1, 2]
console.log(`b = ${b}`) // b = [2, 4]
const c = Vector2(() => (2 * a + b) / 2) // [2, 4]
a[0] = 12
const d = Vector2(() => (2 * a + b) / 2) // [13, 4]
const normalized = Vector2(() => d / d.len()) // [0.955..., 0.294...]
console.log(c, d, normalized)
Library #js-basics/vector uses the same idea for Vector3.
I wrote a library that exploits a bunch of evil hacks to do it in raw JS. It allows expressions like these.
Complex numbers:
>> Complex()({r: 2, i: 0} / {r: 1, i: 1} + {r: -3, i: 2}))
<- {r: -2, i: 1}
Automatic differentiation:
Let f(x) = x^3 - 5x:
>> var f = x => Dual()(x * x * x - {x:5, dx:0} * x);
Now map it over some values:
>> [-2,-1,0,1,2].map(a=>({x:a,dx:1})).map(f).map(a=>a.dx)
<- [ 7, -2, -5, -2, 7 ]
i.e. f'(x) = 3x^2 - 5.
Polynomials:
>> Poly()([1,-2,3,-4]*[5,-6]).map((c,p)=>''+c+'x^'+p).join(' + ')
<- "5x^0 + -16x^1 + 27x^2 + -38x^3 + 24x^4"
For your particular problem, you would define a Vector2 function (or maybe something shorter) using the library, then write x = Vector2()(x + y);
https://gist.github.com/pyrocto/5a068100abd5ff6dfbe69a73bbc510d7
Whilst not an exact answer to the question, it is possible to implement some of the python __magic__ methods using ES6 Symbols
A [Symbol.toPrimitive]() method doesn't let you imply a call Vector.add(), but will let you use syntax such as Decimal() + int.
class AnswerToLifeAndUniverseAndEverything {
[Symbol.toPrimitive](hint) {
if (hint === 'string') {
return 'Like, 42, man';
} else if (hint === 'number') {
return 42;
} else {
// when pushed, most classes (except Date)
// default to returning a number primitive
return 42;
}
}
}
https://www.keithcirkel.co.uk/metaprogramming-in-es6-symbols/
Interesting is also experimental library operator-overloading-js . It does overloading in a defined context (callback function) only.