smikhalevski/algomatic

🔢 Various algorithms and math utilities.

Algomatic

Various algorithms and utilities.

• High performance and low memory consumption: in-out arguments and no heap allocations;
• Lightweight and tree-shakable;
• Thoroughly tested.

Algomatic is used in Paint Bucket, an extremely fast color manipulation library, check out its performance.

🔢 API documentation is available here.

npm install --save-prod algomatic

• Arrays
  binarySearch sort^🚀 copyOver range swap asc desc

• Interpolation
  lerp cspline csplineMonot

• Bitwise
  int byte uint left right and or xor

• Numbers
  unNaN clamp clamp1 closest cycle snap flip

• Math
  logx deg rad sq sign trunc

• Checks
  isBetween isEpsClose isNumeric

• Functions
  callOrGet

• Easing
  easeExp easeLog easeInQuad easeOutQuad easeInOutQuad easeInCubic easeOutCubic easeInOutCubic easeInQuart easeOutQuart easeInOutQuart easeInQuint easeOutQuint easeInOutQuint

Arrays

Utilities copyOver range swap asc desc

binarySearch

Searches the specified array for the specified value using the binary search algorithm. The array must be sorted into ascending order according to the natural ordering of its elements prior to making this call. If it is not sorted, the results are undefined.

Returns the index of the searched value, if it is contained in the array; otherwise, -(insertion point) - 1. The insertion point is defined as the point at which the searched value would be inserted into the array: the index of the first element greater than the searched value, or array length if all elements in the array are less than the specified key. Note that this guarantees that the return value will be ≥ 0 if and only if the searched value is found.

binarySearch([10, 20, 30, 40], 20); // → 1

binarySearch([10, 20, 30, 40], 25); // → -3

sort

Sorts the array in-place using an optional comparator and invokes a callback after a pair of elements was swapped.

sort(
    arr, // Mutable array that would be sorted
    (i, j) => {
      // Called when i and j elements of arr were swapped
      // Use this to sort multiple arrays in parallel
    },
    (a, b) => 0, // Comparator works the same way as in Array.sort
);

sort uses a non-recursive Quicksort algorithm. In contrast to Array.sort, sort doesn't convert array elements to strings before comparison and uses comparison operators directly. So numeric arrays are sorted in natural order with sort(arr). You can provide an element comparator to change the sorting order.

sort is order of magnitude faster than Array.sort on both small and big arrays. The plot below uses a log scale and shows the dependency of number of operations per second from the input array length.

Interpolation

lerp

Creates a linear interpolator:

const f = lerp(xs, ys);
const y = f(x);

Here xs is the array of X coordinates of pivot points in ascending order, and ys is the array of corresponding Y coordinates of pivot points.

cspline

Creates a cubic spline interpolator for given pivot points:

const f = cspline(xs, ys);
const y = f(x);

More control over spline caching and computation:

// Pre-allocate an array of spline components that can be later reused
// to avoid excessive memory allocations
const splines = new Float32Array(xs.length * 3);

createCSplines(xs, ys, xs.length, splines); // → splines
// or
// const splines = createCSplines(xs, ys, xs.length); // → Float32Array

const y = interpolateCSpline(xs, ys, x, xs.length, splines);

csplineMonot

Creates a monotone cubic interpolator for given pivot points:

const f = csplineMonot(xs, ys);
const y = f(x);

Or using more fine-grained approach:

const y = interpolateCSplineMonot(xs, ys, x, xs.length, createCSplinesMonot(xs, ys, xs.length));

The plot below shows that cspline interpolation overshoots pivot points while csplineMonot provides monotonous results.

Bitwise

Utilities int byte uint

Bitwise operations left, right, and, or and xor for unsigned integers that exceed 32-bit range:

left(0xAB, 8); // Same as 0xAB << 8
// → 0xAB_00 

left(0xAB_CD_EF_AB_CD, 24)
// → 0xAB_CD_EF_AB_CD_00_00_00

right(0xAB_CD, 8); // Same as 0xAB_CD >> 8
// → 0xAB