add atan()

Author: victorpoughon

README.md

@@ -250,6 +250,7 @@ function complement(A: Union | Interval): Union;
 |           Tangent | `nsf.tan(A)`   |
 |            Arccos | `nsf.acos(A)`  |
 |            Arcsin | `nsf.asin(A)`  |
+|            Arctan | `nsf.atan(A)`  |
 
 </div>
 

src/index.ts

@@ -4,4 +4,4 @@ export { overlap, disjoint, intersection, complement } from "./compare.ts";
 export { Union, union, single, bounded, EMPTY, FULL } from "./union.ts";
 export { add, sub, mul, div, neg } from "./arithmetic.ts";
 export { abs, min, max, exp, log, pow, powInt, sqrt, sqinv, powIntInv } from "./math.ts";
-export { cos, sin, tan, acos, asin } from "./trigonometry.ts";
+export { cos, sin, tan, acos, asin, atan } from "./trigonometry.ts";

src/trigonometry.ts

@@ -139,3 +139,23 @@ export function iasin(X: Interval): Union {
 
 export const uasin = makeUnaryOpUnion(iasin);
 export const asin = makeUnaryOpEither(uasin);
+
+// ARCTAN
+
+function leftAtan(x: number): number {
+    if (x === 0) return 0;
+    return prev(Math.atan(x));
+}
+
+function rightAtan(x: number): number {
+    if (x === 0) return 0;
+    return next(Math.atan(x));
+}
+
+export function iatan(X: Interval): Union {
+    typeCheckIsInterval(X);
+    return new Union([new Interval(leftAtan(X.lo), rightAtan(X.hi))]);
+}
+
+export const uatan = makeUnaryOpUnion(iatan);
+export const atan = makeUnaryOpEither(uatan);

tests/trigonometry.test.ts

@@ -259,6 +259,7 @@ describe("acos", () => {
 
     assert.deepStrictEqual(nsf.acos(nsf.single(-1.2, -1.1)), nsf.EMPTY);
     assert.deepStrictEqual(nsf.acos(nsf.single(1.1, 1.2)), nsf.EMPTY);
+    assert.deepStrictEqual(nsf.acos(nsf.EMPTY), nsf.EMPTY);
 });
 
 describe("asin", () => {
@@ -304,4 +305,47 @@ describe("asin", () => {
 
     assert.deepStrictEqual(nsf.asin(nsf.single(-1.2, -1.1)), nsf.EMPTY);
     assert.deepStrictEqual(nsf.asin(nsf.single(1.1, 1.2)), nsf.EMPTY);
+    assert.deepStrictEqual(nsf.asin(nsf.EMPTY), nsf.EMPTY);
+});
+
+describe("atan", () => {
+    assert.deepStrictEqual(nsf.atan(nsf.single(0)), nsf.single(0));
+
+    assert.deepStrictEqual(
+        nsf.atan(nsf.single(-0.1)),
+        nsf.single(prev(Math.atan(-0.1)), next(Math.atan(-0.1)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.atan(nsf.single(0.2)),
+        nsf.single(prev(Math.atan(0.2)), next(Math.atan(0.2)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.atan(nsf.single(0.2, 0.5)),
+        nsf.single(prev(Math.atan(0.2)), next(Math.atan(0.5)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.atan(nsf.single(-0.2, 0.5)),
+        nsf.single(prev(Math.atan(-0.2)), next(Math.atan(0.5)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.atan(nsf.single(-1.1, 1.1)),
+        nsf.single(prev(Math.atan(-1.1)), next(Math.atan(1.1)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.atan(nsf.single(-1.1, -0.5)),
+        nsf.single(prev(Math.atan(-1.1)), next(Math.atan(-0.5)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.atan(nsf.single(0.5, 1.5)),
+        nsf.single(prev(Math.atan(0.5)), next(Math.atan(1.5)))
+    );
+
+    assert.deepStrictEqual(nsf.atan(nsf.FULL), nsf.single(prev(-Math.PI / 2), next(Math.PI / 2)));
+    assert.deepStrictEqual(nsf.atan(nsf.EMPTY), nsf.EMPTY);
 });