lambda-math

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, so that we can clearly see the problem with floating point rounding which exists in standard JavaScript. So, 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

Compare the above to 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

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 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 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.

Some examples 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

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, and λ[i] will contain the BigNumber result value.

Example 6

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

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

Example 7

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 ;)

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

Example 8

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.

License

See LICENSE for more details.