Lambda math

Pseudo lambda expressions for JS arbitrary-precision arithmetic operations.

Install

npm install --save lambda-math

Example

Consider adding the floating point number 300 / 293 many times. 72 times in fact. Now, we don't want to simply multiply a number by 72. We want to add it 72 times. This way, we can clearly see the problem with floating point number rounding which exists in standard JavaScript.

The simple JavaScript way of doing such a sum:

let result = 0;

for (let i = 0; i < 72; i += 1) {
  result += 300 / 293;
}

console.log(result); // 73.72013651877126

Or, a more functional (fancy) JS approach:

console.log(
  Array
    .from(Array(72).keys())
    .map(() => { return 300 / 293; })
    .reduce((a, b) => { return a + b; })
); // 73.72013651877126

You may have noticed that both approaches produce exactly the same output: 73.72013651877126. If you go and use some cool mathematical environment to actually perform this arithmetic, you will see that the output is something like: 73.7201365187713310580204778156996587.... Comparing the JS output and mathematical output, we can see that the last 2 digits are wrong in the JS version:

JS:   73.72...77126
Math: 73.72...77133

Can we do any better? Using lambda-math library, we can write:

const { div, add, λ, Σ } = require('lambda-math');

λ( div, [300, 293] )
 ( add, [λ[0], λ[0]], [Σ, λ[0]], 70 );

console.log(λ[1].number); // 73.72013651877133
console.log(λ[1].string); // '73.72013651877133105776'

As you can see, the pseudo lambda approach doesn't have the problem with rounding floating point numbers. Also, some (mathematicians) can argue that the syntax lambda-math introduces is more elegant, shorter, and cleaner overall (compared to pure JavaScript way of doing things).

Internals

Besides adding pseudo syntactic sugar, lambda-math uses bignumber.js under the hood for actual arbitrary-precision decimal arithmetic.

Library API

The library lambda-math exports the symbols λ, Ω, and Σ, along with a number of mathematical functions. At the moment there are just 4 arithmetic functions available. Addition, subtraction, multiplication, and division:

c = add(a, b) // same as: a + b
c = sub(a, b) // same as: a - b
c = mul(a, b) // same as: a * b
c = div(a, b) // same as: a / b

These 4 functions accept either JavaScript number, string, or a BigNumber as parameters (can mix either way).

While you can use these functions directly, what you want to do is use them via the λ function. The λ function expects several parameters. The first parameter is the math function to be applied. It can be one of the above 4 functions. The 2nd, 3rd, etc. params must be arrays containing the numbers that will be passed to each subsequent call of the math function.

Optionally, you can pass to λ a simple JavaScript number as the last param. It will indicate how many times the last math function needs to be called with the last set of params. You should think of this as a for loop.

Additionally, besides numbers, any of the parameter arrays can contain the symbol Σ. You can use the symbol Σ to tell lambda-math to substitute the result of the last operation as a param to a math function call. You should think of this as a variable.

The function Ω can be used to easily index any of the results produced by the λ function. This is helpful when the number of invocation of λ is dynamic and you don't want to keep track of the index of last result.

Some examples follow below to better demonstrate these concepts.

Example 1

λ(add, [1, 2]);
console.log(λ[0].number); // 3

// The same as:
let c = add(1, 2);
console.log(c.toNumber()); // 3

Example 2

λ(add, [3, 4], [5, 6]);
console.log(λ[0].number); // 11

// Is the same as:
let c = add(3, 4);
c = add(5, 6);
console.log(c.toNumber()); // 11

Example 3

λ(add, [3, 4], [Σ, 6]);
console.log(λ[0].number); // 13

// Is the same as:
let c = add(3, 4);
c = add(c, 6);
console.log(c.toNumber()); // 13

Example 4

λ(add, [3, 4], 10);
console.log(λ[0].number); // 7

// Is the same as:
let c;
for (let i = 0; i < 10; i += 1) {
  c = add(3, 4);
}
console.log(c.toNumber()); // 7

Example 5

λ(add, [3, 4], [Σ, 1], 10);
console.log(λ[0].number); // 17

// Is the same as:
let c = add(3, 4);
for (let i = 0; i < 10; i += 1) {
  c = add(c, 1);
}
console.log(c.toNumber()); // 17

Example 6

Besides using λ as a function, you can also access the results of each invocation of the function via the array index, starting from 0. So first invocation of λ will store the result as λ[0], second invocation as λ[1], and so on. For convenience, λ[i].number will contain the JavaScript number result value, λ[i].string will contain the JavaScript string result value, and λ[i] will contain the BigNumber result value.

λ(add, [1, 2]);
λ(add, [3, 4]);
λ(add, [5, 6]);

console.log(λ[0].number); // 3
console.log(λ[1].number); // 7
console.log(λ[2].number); // 11

console.log(λ[0].string); // '3'
console.log(λ[1].string); // '7'
console.log(λ[2].string); // '11'

Example 7

You can also chain any number of calls to λ, and this will not have any affect on your program:

λ(add, [1, 2])
 (add, [3, 4])
 (add, [5, 6]);

console.log(λ[0].number); // 3
console.log(λ[1].number); // 7
console.log(λ[2].number); // 11

This is possible due to the fact that an invocation of λ returns an instance of itself ;)

Example 8

If you want to quickly reference some of the latest λ results, but don't want to store the invocation number in a variable, lambda-math provides the Ω function. This function has two goals.

Firstly, if you call it without any parameter, it will return the number of times λ has been called up to this point. I.e. the number of results available. For example:

λ(add, [1, 2])
 (add, [3, 4])
 (add, [5, 6])
 (add, [7, 8]);

console.log(Ω()); // 4

Secondly, if you pass an integer, you will get the Nth result from the start or from the end, depending on the sign of the integer passed. For example:

λ( add, [1, 2] )
 ( add, [3, 4] )
 ( add, [5, 6] )
 ( add, [7, 8] )
 ( add, [9, 10] );

console.log(Ω(1).number); // 19
console.log(Ω(2).number); // 15
console.log(Ω(3).number); // 11
console.log(Ω(4).number); //  7
console.log(Ω(5).number); //  3

And if you pass negative integers:

λ( add, [1, 2] )
 ( add, [3, 4] )
 ( add, [5, 6] )
 ( add, [7, 8] )
 ( add, [9, 10] );

console.log(Ω(-1).number); //  3
console.log(Ω(-2).number); //  7
console.log(Ω(-3).number); // 11
console.log(Ω(-4).number); // 15
console.log(Ω(-5).number); // 19

Please note, passing 0 as a parameter to Ω function is undefined behavior, and the library will throw an error.

Example 9

Last, but not least, λ.reset() is available to clear all lambda-math state, and reset the results stack to zero.

λ(add, [1, 2])
 (add, [3, 4])
 (add, [5, 6]);

console.log(λ[0].number); // 3
console.log(λ[1].number); // 7
console.log(λ[2].number); // 11
console.log(λ[3]); // undefined
console.log(λ[4]); // undefined
console.log(λ[5]); // undefined

λ.reset();

λ(add, [10, 20])
 (add, [30, 40])
 (add, [50, 60]);

console.log(λ[0].number); // 30
console.log(λ[1].number); // 70
console.log(λ[2].number); // 110
console.log(λ[3]); // undefined
console.log(λ[4]); // undefined
console.log(λ[5]); // undefined

Running tests

Clone this repo, do npm install, followed by npm run test.

Lint the source code

You can use ESLint to check for potential problems in source code by running npm run lint.

License

MIT License. See LICENSE for more details.