add asin, acos

Author: victorpoughon

README.md

@@ -248,6 +248,8 @@ function complement(A: Union | Interval): Union;
 |            Cosine | `nsf.cos(A)`   |
 |              Sine | `nsf.sin(A)`   |
 |           Tangent | `nsf.tan(A)`   |
+|            Arccos | `nsf.acos(A)`  |
+|            Arcsin | `nsf.asin(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 } from "./trigonometry.ts";
+export { cos, sin, tan, acos, asin } from "./trigonometry.ts";

src/trigonometry.ts

@@ -1,6 +1,13 @@
 import { prev, next } from "./nextafter.ts";
 import { Interval, typeCheckIsInterval } from "./interval.ts";
-import { Union, typeCheckIsUnion, makeUnaryOpUnion, makeUnaryOpEither, bounded } from "./union.ts";
+import {
+    Union,
+    typeCheckIsUnion,
+    makeUnaryOpUnion,
+    makeUnaryOpEither,
+    bounded,
+    EMPTY,
+} from "./union.ts";
 import { udiv, usub } from "./arithmetic.ts";
 
 const pi = Math.PI;
@@ -105,3 +112,30 @@ export function utan(U: Union): Union {
 }
 
 export const tan = makeUnaryOpEither(utan);
+
+// ARCCOS
+
+export function iacos(X: Interval): Union {
+    typeCheckIsInterval(X);
+
+    if (X.lo > 1 || X.hi < -1) return EMPTY;
+    const lower = X.hi >= 1 ? 0 : prev(Math.acos(X.hi));
+    const upper = next(Math.acos(Math.max(-1, X.lo)));
+    return new Union([new Interval(lower, upper)]);
+}
+
+export const uacos = makeUnaryOpUnion(iacos);
+export const acos = makeUnaryOpEither(uacos);
+
+// ARCSIN
+
+export function iasin(X: Interval): Union {
+    typeCheckIsInterval(X);
+
+    if (X.lo > 1 || X.hi < -1) return EMPTY;
+    const [l, h] = [Math.max(-1, X.lo), Math.min(1, X.hi)];
+    return new Union([new Interval(prev(Math.asin(l)), next(Math.asin(h)))]);
+}
+
+export const uasin = makeUnaryOpUnion(iasin);
+export const asin = makeUnaryOpEither(uasin);

tests/trigonometry.test.ts

@@ -221,3 +221,87 @@ describe("tan", () => {
         checkTan(nsf.bounded(Math.PI / 6));
     });
 });
+
+describe("acos", () => {
+    assert.deepStrictEqual(
+        nsf.acos(nsf.single(0)),
+        nsf.single(prev(Math.acos(0)), next(Math.acos(0)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.acos(nsf.single(-0.1)),
+        nsf.single(prev(Math.acos(-0.1)), next(Math.acos(-0.1)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.acos(nsf.single(0.2)),
+        nsf.single(prev(Math.acos(0.2)), next(Math.acos(0.2)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.acos(nsf.single(0.2, 0.5)),
+        nsf.single(prev(Math.acos(0.5)), next(Math.acos(0.2)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.acos(nsf.single(-0.2, 0.5)),
+        nsf.single(prev(Math.acos(0.5)), next(Math.acos(-0.2)))
+    );
+
+    assert.deepStrictEqual(nsf.acos(nsf.single(-1.1, 1.1)), nsf.single(0, next(Math.acos(-1))));
+
+    assert.deepStrictEqual(
+        nsf.acos(nsf.single(-1.1, -0.5)),
+        nsf.single(prev(Math.acos(-0.5)), next(Math.acos(-1)))
+    );
+
+    assert.deepStrictEqual(nsf.acos(nsf.single(0.5, 1.5)), nsf.single(0, next(Math.acos(0.5))));
+
+    assert.deepStrictEqual(nsf.acos(nsf.single(-1.2, -1.1)), nsf.EMPTY);
+    assert.deepStrictEqual(nsf.acos(nsf.single(1.1, 1.2)), nsf.EMPTY);
+});
+
+describe("asin", () => {
+    assert.deepStrictEqual(
+        nsf.asin(nsf.single(0)),
+        nsf.single(prev(Math.asin(0)), next(Math.asin(0)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.asin(nsf.single(-0.1)),
+        nsf.single(prev(Math.asin(-0.1)), next(Math.asin(-0.1)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.asin(nsf.single(0.2)),
+        nsf.single(prev(Math.asin(0.2)), next(Math.asin(0.2)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.asin(nsf.single(0.2, 0.5)),
+        nsf.single(prev(Math.asin(0.2)), next(Math.asin(0.5)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.asin(nsf.single(-0.2, 0.5)),
+        nsf.single(prev(Math.asin(-0.2)), next(Math.asin(0.5)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.asin(nsf.single(-1.1, 1.1)),
+        nsf.single(prev(Math.asin(-1)), next(Math.asin(1)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.asin(nsf.single(-1.1, -0.5)),
+        nsf.single(prev(Math.asin(-1)), next(Math.asin(-0.5)))
+    );
+
+    assert.deepStrictEqual(
+        nsf.asin(nsf.single(0.5, 1.5)),
+        nsf.single(prev(Math.asin(0.5)), next(Math.asin(1)))
+    );
+
+    assert.deepStrictEqual(nsf.asin(nsf.single(-1.2, -1.1)), nsf.EMPTY);
+    assert.deepStrictEqual(nsf.asin(nsf.single(1.1, 1.2)), nsf.EMPTY);
+});