@thi.ng/math - npm Package Compare versions

Comparing version 1.1.1 to 1.2.0

angle.d.ts

@@ -0,7 +1,42 @@
+/**
+ * Returns vector of `[sin(theta)*n, cos(theta)*n]`.
+ *
+ * @param theta
+ * @param n
+ */
 export declare const sincos: (theta: number, n?: number) => number[];
+/**
+ * Returns vector of `[cos(theta)*n, sin(theta)*n]`.
+ *
+ * @param theta
+ * @param n
+ */
 export declare const cossin: (theta: number, n?: number) => number[];
+/**
+ * Projects `theta` into [0 .. 2π] interval.
+ *
+ * @param theta
+ */
 export declare const absTheta: (theta: number) => number;
-export declare const absInnerAngle: (x: number) => number;
+export declare const absInnerAngle: (theta: number) => number;
+/**
+ * Returns smallest absolute angle difference between `a` and `b`.
+ * Result will be in [0 .. π] interval.
+ *
+ * @param a
+ * @param b
+ */
 export declare const angleDist: (a: number, b: number) => number;
+/**
+ * Like `Math.atan2`, but always returns angle in [0 .. TAU) interval.
+ *
+ * @param y
+ * @param x
+ */
 export declare const atan2Abs: (y: number, x: number) => number;
+/**
+ * Returns quadrant ID (0-3) of given angle (in radians).
+ *
+ * @param theta
+ */
 export declare const quadrant: (theta: number) => number;
@@ -11,10 +46,58 @@ /**
  *
- * @param x angle in radians
+ * @param theta angle in radians
  */
-export declare const deg: (x: number) => number;
+export declare const deg: (theta: number) => number;
 /**
  * Converts angle to radians.
  *
- * @param x angle in degrees
+ * @param theta angle in degrees
  */
-export declare const rad: (x: number) => number;
+export declare const rad: (theta: number) => number;
+/**
+ * Cosecant. Approaches `±Infinity` for `theta` near multiples of π.
+ *
+ * @param theta angle in radians
+ */
+export declare const csc: (theta: number) => number;
+/**
+ * Secant. Approaches `±Infinity` for `theta` near π/2 ± nπ
+ *
+ * @param theta angle in radians
+ */
+export declare const sec: (theta: number) => number;
+/**
+ * Cotangent. Approaches `±Infinity` for `theta` near multiples of π.
+ *
+ * @param theta angle in radians
+ */
+export declare const cot: (theta: number) => number;
+/**
+ * Law of Cosines. Takes length of two sides of a triangle and the inner
+ * angle (in radians) between them. Returns length of third side.
+ *
+ * @param a
+ * @param b
+ * @param gamma
+ */
+export declare const loc: (a: number, b: number, gamma: number) => number;
+/**
+ * Approximates cos(xπ) for x in [-1,1]
+ *
+ * @param x
+ */
+export declare const normCos: (x: number) => number;
+/**
+ * Fast cosine approximation using `normCos()` (polynomial). Max. error
+ * ~0.00059693
+ *
+ * In [0 .. 2π] interval, approx. 18-20% faster than `Math.cos` on V8.
+ *
+ * @param theta in radians
+ */
+export declare const fastCos: (theta: number) => number;
+/**
+ * @see fastCos
+ *
+ * @param theta in radians
+ */
+export declare const fastSin: (theta: number) => number;

angle.js

@@ -1,2 +0,8 @@
-import { DEG2RAD, HALF_PI, PI, RAD2DEG, TAU } from "./api";
+import { DEG2RAD, HALF_PI, INV_HALF_PI, PI, RAD2DEG, TAU } from "./api";
+/**
+ * Returns vector of `[sin(theta)*n, cos(theta)*n]`.
+ *
+ * @param theta
+ * @param n
+ */
 export const sincos = (theta, n = 1) => [
@@ -6,2 +12,8 @@ Math.sin(theta) * n,
 ];
+/**
+ * Returns vector of `[cos(theta)*n, sin(theta)*n]`.
+ *
+ * @param theta
+ * @param n
+ */
 export const cossin = (theta, n = 1) => [
@@ -11,18 +23,109 @@ Math.cos(theta) * n,
 ];
+/**
+ * Projects `theta` into [0 .. 2π] interval.
+ *
+ * @param theta
+ */
 export const absTheta = (theta) => ((theta %= TAU), theta < 0 ? TAU + theta : theta);
-export const absInnerAngle = (x) => ((x = Math.abs(x)), x > PI ? TAU - x : x);
+export const absInnerAngle = (theta) => ((theta = Math.abs(theta)), theta > PI ? TAU - theta : theta);
+/**
+ * Returns smallest absolute angle difference between `a` and `b`.
+ * Result will be in [0 .. π] interval.
+ *
+ * @param a
+ * @param b
+ */
 export const angleDist = (a, b) => absInnerAngle(absTheta((b % TAU) - (a % TAU)));
+/**
+ * Like `Math.atan2`, but always returns angle in [0 .. TAU) interval.
+ *
+ * @param y
+ * @param x
+ */
 export const atan2Abs = (y, x) => absTheta(Math.atan2(y, x));
-export const quadrant = (theta) => (absTheta(theta) / HALF_PI) | 0;
 /**
+ * Returns quadrant ID (0-3) of given angle (in radians).
+ *
+ * @param theta
+ */
+export const quadrant = (theta) => (absTheta(theta) * INV_HALF_PI) | 0;
+/**
  * Converts angle to degrees.
  *
- * @param x angle in radians
+ * @param theta angle in radians
  */
-export const deg = (x) => x * RAD2DEG;
+export const deg = (theta) => theta * RAD2DEG;
 /**
  * Converts angle to radians.
  *
- * @param x angle in degrees
+ * @param theta angle in degrees
  */
-export const rad = (x) => x * DEG2RAD;
+export const rad = (theta) => theta * DEG2RAD;
+/**
+ * Cosecant. Approaches `±Infinity` for `theta` near multiples of π.
+ *
+ * @param theta angle in radians
+ */
+export const csc = (theta) => 1 / Math.sin(theta);
+/**
+ * Secant. Approaches `±Infinity` for `theta` near π/2 ± nπ
+ *
+ * @param theta angle in radians
+ */
+export const sec = (theta) => 1 / Math.cos(theta);
+/**
+ * Cotangent. Approaches `±Infinity` for `theta` near multiples of π.
+ *
+ * @param theta angle in radians
+ */
+export const cot = (theta) => 1 / Math.tan(theta);
+/**
+ * Law of Cosines. Takes length of two sides of a triangle and the inner
+ * angle (in radians) between them. Returns length of third side.
+ *
+ * @param a
+ * @param b
+ * @param gamma
+ */
+export const loc = (a, b, gamma) => Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(gamma));
+/**
+ * Approximates cos(xπ) for x in [-1,1]
+ *
+ * @param x
+ */
+export const normCos = (x) => {
+    const x2 = x * x;
+    return 1.0 + x2 * (-4 + 2 * x2);
+};
+const __fastCos = (x) => {
+    const x2 = x * x;
+    return 0.99940307 + x2 * (-0.49558072 + 0.03679168 * x2);
+};
+/**
+ * Fast cosine approximation using `normCos()` (polynomial). Max. error
+ * ~0.00059693
+ *
+ * In [0 .. 2π] interval, approx. 18-20% faster than `Math.cos` on V8.
+ *
+ * @param theta in radians
+ */
+export const fastCos = (theta) => {
+    theta %= TAU;
+    theta < 0 && (theta = -theta);
+    switch ((theta * INV_HALF_PI) | 0) {
+        case 0:
+            return __fastCos(theta);
+        case 1:
+            return -__fastCos(PI - theta);
+        case 2:
+            return -__fastCos(theta - PI);
+        default:
+            return __fastCos(TAU - theta);
+    }
+};
+/**
+ * @see fastCos
+ *
+ * @param theta in radians
+ */
+export const fastSin = (theta) => fastCos(HALF_PI - theta);

api.d.ts

@@ -7,2 +7,5 @@ export declare const PI: number;
 export declare const SIXTH_PI: number;
+export declare const INV_PI: number;
+export declare const INV_TAU: number;
+export declare const INV_HALF_PI: number;
 export declare const DEG2RAD: number;
@@ -13,2 +16,4 @@ export declare const RAD2DEG: number;
 export declare const SQRT3: number;
+export declare const SQRT2_2: number;
+export declare const SQRT2_3: number;
 export declare const THIRD: number;
@@ -15,0 +20,0 @@ export declare const TWO_THIRD: number;

api.js

@@ -7,2 +7,5 @@ export const PI = Math.PI;
 export const SIXTH_PI = PI / 6;
+export const INV_PI = 1 / PI;
+export const INV_TAU = 1 / TAU;
+export const INV_HALF_PI = 1 / HALF_PI;
 export const DEG2RAD = PI / 180;
@@ -13,2 +16,4 @@ export const RAD2DEG = 180 / PI;
 export const SQRT3 = Math.sqrt(3);
+export const SQRT2_2 = SQRT2 / 2;
+export const SQRT2_3 = SQRT3 / 2;
 export const THIRD = 1 / 3;
@@ -15,0 +20,0 @@ export const TWO_THIRD = 2 / 3;

CHANGELOG.md

@@ -6,2 +6,15 @@ # Change Log
 
+# [1.2.0](https://github.com/thi-ng/umbrella/compare/@thi.ng/math@[e-mail]/math@1.2.0) (2019-03-18)
+
+
+### Features
+
+* **math:** add consts ([28e9898](https://github.com/thi-ng/umbrella/commit/28e9898))
+* **math:** add cos/sin approximations, loc(), add docstrings ([78ed751](https://github.com/thi-ng/umbrella/commit/78ed751))
+* **math:** more trigonometry ([b5e1c02](https://github.com/thi-ng/umbrella/commit/b5e1c02))
+
+
+
+
+
 ## [1.1.1](https://github.com/thi-ng/umbrella/compare/@thi.ng/math@[e-mail]/math@1.1.1) (2019-03-01)
@@ -8,0 +21,0 @@

lib/index.js

@@ -11,2 +11,5 @@ 'use strict';
 const SIXTH_PI = PI / 6;
+const INV_PI = 1 / PI;
+const INV_TAU = 1 / TAU;
+const INV_HALF_PI = 1 / HALF_PI;
 const DEG2RAD = PI / 180;
@@ -17,2 +20,4 @@ const RAD2DEG = 180 / PI;
 const SQRT3 = Math.sqrt(3);
+const SQRT2_2 = SQRT2 / 2;
+const SQRT2_3 = SQRT3 / 2;
 const THIRD = 1 / 3;
@@ -35,8 +40,35 @@ const TWO_THIRD = 2 / 3;
 const absTheta = (theta) => ((theta %= TAU), theta < 0 ? TAU + theta : theta);
-const absInnerAngle = (x) => ((x = Math.abs(x)), x > PI ? TAU - x : x);
+const absInnerAngle = (theta) => ((theta = Math.abs(theta)), theta > PI ? TAU - theta : theta);
 const angleDist = (a, b) => absInnerAngle(absTheta((b % TAU) - (a % TAU)));
 const atan2Abs = (y, x) => absTheta(Math.atan2(y, x));
-const quadrant = (theta) => (absTheta(theta) / HALF_PI) | 0;
-const deg = (x) => x * RAD2DEG;
-const rad = (x) => x * DEG2RAD;
+const quadrant = (theta) => (absTheta(theta) * INV_HALF_PI) | 0;
+const deg = (theta) => theta * RAD2DEG;
+const rad = (theta) => theta * DEG2RAD;
+const csc = (theta) => 1 / Math.sin(theta);
+const sec = (theta) => 1 / Math.cos(theta);
+const cot = (theta) => 1 / Math.tan(theta);
+const loc = (a, b, gamma) => Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(gamma));
+const normCos = (x) => {
+    const x2 = x * x;
+    return 1.0 + x2 * (-4 + 2 * x2);
+};
+const __fastCos = (x) => {
+    const x2 = x * x;
+    return 0.99940307 + x2 * (-0.49558072 + 0.03679168 * x2);
+};
+const fastCos = (theta) => {
+    theta %= TAU;
+    theta < 0 && (theta = -theta);
+    switch ((theta * INV_HALF_PI) | 0) {
+        case 0:
+            return __fastCos(theta);
+        case 1:
+            return -__fastCos(PI - theta);
+        case 2:
+            return -__fastCos(theta - PI);
+        default:
+            return __fastCos(TAU - theta);
+    }
+};
+const fastSin = (theta) => fastCos(HALF_PI - theta);
 
@@ -256,2 +288,5 @@ const abs = Math.abs;
 exports.SIXTH_PI = SIXTH_PI;
+exports.INV_PI = INV_PI;
+exports.INV_TAU = INV_TAU;
+exports.INV_HALF_PI = INV_HALF_PI;
 exports.DEG2RAD = DEG2RAD;
@@ -262,2 +297,4 @@ exports.RAD2DEG = RAD2DEG;
 exports.SQRT3 = SQRT3;
+exports.SQRT2_2 = SQRT2_2;
+exports.SQRT2_3 = SQRT2_3;
 exports.THIRD = THIRD;
@@ -278,2 +315,9 @@ exports.TWO_THIRD = TWO_THIRD;
 exports.rad = rad;
+exports.csc = csc;
+exports.sec = sec;
+exports.cot = cot;
+exports.loc = loc;
+exports.normCos = normCos;
+exports.fastCos = fastCos;
+exports.fastSin = fastSin;
 exports.eqDelta = eqDelta;
@@ -280,0 +324,0 @@ exports.eqDeltaFixed = eqDeltaFixed;

lib/index.umd.js

@@ -13,2 +13,5 @@ (function (global, factory) {
     const SIXTH_PI = PI / 6;
+    const INV_PI = 1 / PI;
+    const INV_TAU = 1 / TAU;
+    const INV_HALF_PI = 1 / HALF_PI;
     const DEG2RAD = PI / 180;
@@ -19,2 +22,4 @@ const RAD2DEG = 180 / PI;
     const SQRT3 = Math.sqrt(3);
+    const SQRT2_2 = SQRT2 / 2;
+    const SQRT2_3 = SQRT3 / 2;
     const THIRD = 1 / 3;
@@ -37,8 +42,35 @@ const TWO_THIRD = 2 / 3;
     const absTheta = (theta) => ((theta %= TAU), theta < 0 ? TAU + theta : theta);
-    const absInnerAngle = (x) => ((x = Math.abs(x)), x > PI ? TAU - x : x);
+    const absInnerAngle = (theta) => ((theta = Math.abs(theta)), theta > PI ? TAU - theta : theta);
     const angleDist = (a, b) => absInnerAngle(absTheta((b % TAU) - (a % TAU)));
     const atan2Abs = (y, x) => absTheta(Math.atan2(y, x));
-    const quadrant = (theta) => (absTheta(theta) / HALF_PI) | 0;
-    const deg = (x) => x * RAD2DEG;
-    const rad = (x) => x * DEG2RAD;
+    const quadrant = (theta) => (absTheta(theta) * INV_HALF_PI) | 0;
+    const deg = (theta) => theta * RAD2DEG;
+    const rad = (theta) => theta * DEG2RAD;
+    const csc = (theta) => 1 / Math.sin(theta);
+    const sec = (theta) => 1 / Math.cos(theta);
+    const cot = (theta) => 1 / Math.tan(theta);
+    const loc = (a, b, gamma) => Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(gamma));
+    const normCos = (x) => {
+        const x2 = x * x;
+        return 1.0 + x2 * (-4 + 2 * x2);
+    };
+    const __fastCos = (x) => {
+        const x2 = x * x;
+        return 0.99940307 + x2 * (-0.49558072 + 0.03679168 * x2);
+    };
+    const fastCos = (theta) => {
+        theta %= TAU;
+        theta < 0 && (theta = -theta);
+        switch ((theta * INV_HALF_PI) | 0) {
+            case 0:
+                return __fastCos(theta);
+            case 1:
+                return -__fastCos(PI - theta);
+            case 2:
+                return -__fastCos(theta - PI);
+            default:
+                return __fastCos(TAU - theta);
+        }
+    };
+    const fastSin = (theta) => fastCos(HALF_PI - theta);
 
@@ -258,2 +290,5 @@ const abs = Math.abs;
     exports.SIXTH_PI = SIXTH_PI;
+    exports.INV_PI = INV_PI;
+    exports.INV_TAU = INV_TAU;
+    exports.INV_HALF_PI = INV_HALF_PI;
     exports.DEG2RAD = DEG2RAD;
@@ -264,2 +299,4 @@ exports.RAD2DEG = RAD2DEG;
     exports.SQRT3 = SQRT3;
+    exports.SQRT2_2 = SQRT2_2;
+    exports.SQRT2_3 = SQRT2_3;
     exports.THIRD = THIRD;
@@ -280,2 +317,9 @@ exports.TWO_THIRD = TWO_THIRD;
     exports.rad = rad;
+    exports.csc = csc;
+    exports.sec = sec;
+    exports.cot = cot;
+    exports.loc = loc;
+    exports.normCos = normCos;
+    exports.fastCos = fastCos;
+    exports.fastSin = fastSin;
     exports.eqDelta = eqDelta;
@@ -282,0 +326,0 @@ exports.eqDeltaFixed = eqDeltaFixed;

package.json

 {
     "name": "@thi.ng/math",
-    "version": "1.1.1",
+    "version": "1.2.0",
     "description": "Assorted common math functions & utilities",
@@ -47,3 +47,3 @@ "module": "./index.js",
     "sideEffects": false,
-    "gitHead": "e43f57c7554fd78380bba58d37ae62ca01221eeb"
+    "gitHead": "b032167da28b83e93d3cbc54a47b053092ad7c4f"
 }

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Improved metrics

Total package byte prevSize

105912

increased by11.61%

Number of package files

35

increased by2.94%

Lines of code

1764

increased by19.19%

No dependency changes