completed arithmetic and transcendental

src/ForwardModeAD.chpl

@@ -33,9 +33,6 @@ module ForwardModeAD {
   }
 
   proc main() {
-    var x = new DualNumber(0.0, 0.0);
-    var y = new DualNumber(1e-16, -1e-16);
-    writeln(isclose(0.0, 1e-16, atol=1e-10));
-    writeln(isclose(x, y, atol=1e-10));
+    var x = new DualNumber(-1, 0.0);
   }
 }

src/arithmetic.chpl

@@ -27,4 +27,11 @@ module arithmetic {
         return new DualNumber(prim(a) ** b, b * (prim(a) ** (b - 1)) * dual(a));
     }
 
+    proc sqrt(a : DualNumber) {
+        return new DualNumber(sqrt(prim(a)), 0.5 * dual(a) / sqrt(prim(a)));
+    }
+
+    proc cbrt(a : DualNumber) {
+        return new DualNumber(cbrt(prim(a)), 1.0 / 3.0 * dual(a) / cbrt(prim(a) ** 2));
+    }
 }

src/transcendental.chpl

@@ -1,17 +1,28 @@
 module transcendental {
     use ForwardModeAD;
 
+    operator **(a : real, b : DualNumber) {
+        return new DualNumber(a ** prim(b), log(a) * (a ** prim(b)) * dual(b));
+    }
+
+
+    operator **(a : DualNumber, b : DualNumber) {
+        var f = prim(a) ** prim(b);
+        var df = f * (dual(b) * log(prim(a)) + prim(b) * dual(a) / prim(a)); 
+        return new DualNumber(f, df);
+    }
+
     proc exp(a : DualNumber) { return new DualNumber(exp(prim(a)), dual(a) * exp(prim(a))); }
 
-    proc exp2(a : DualNumber) {}
+    proc exp2(a : DualNumber) {return new DualNumber(exp2(prim(a)), ln_2 * exp2(prim(a)) * dual(a));}
 
-    proc expm1(a : DualNumber) {}
+    proc expm1(a : DualNumber) {return new DualNumber(expm1(prim(a)), exp(prim(a)) * dual(a));}
 
     proc log(a : DualNumber) { return new DualNumber(log(prim(a)), dual(a) / prim(a)); }
 
-    proc log2(a : DualNumber) {}
+    proc log2(a : DualNumber) {return new DualNumber(log2(prim(a)), dual(a)/(prim(a) * ln_2));}
 
-    proc log10(a : DualNumber) {}
+    proc log10(a : DualNumber) {return new DualNumber(log10(prim(a)), dual(a) / (prim(a) * ln_10));}
 
-    proc log1p(a : DualNumber) {}
+    proc log1p(a : DualNumber) {return new DualNumber(log1p(prim(a)), dual(a) / (prim(a) + 1));}
 }

test/test_dual_algebra.chpl

@@ -30,6 +30,9 @@ proc test_arithmetic_operations(test : borrowed Test) throws {
 
     test.assertEqual(y ** 3, new DualNumber(27, 108));
     test.assertEqual(y ** 0.4, new DualNumber(1.5518455739153598, 0.8276509727548587));
+
+    test.assertEqual(sqrt(y), new DualNumber(sqrt(3), 2.0 / sqrt(3)));
+    test.assertEqual(cbrt(y), new DualNumber(cbrt(3), 4.0 / 3.0 / cbrt(9)));
 }
 
 
@@ -46,7 +49,23 @@ proc test_trigonometric_operations(test : borrowed Test) throws {
 }
 
 proc test_transcendental_functions(test : borrowed Test) throws {
-
+    var x = new DualNumber(2, 3);
+
+    test.assertEqual(2 ** x, new DualNumber(4, 12 * ln_2));
+
+    test.assertEqual(x ** x, new DualNumber(4, 12 * (ln_2 + 1)));
+
+    test.assertEqual(exp(x), new DualNumber(exp(2), 3 * exp(2)));
+
+    test.assertEqual(exp2(x), new DualNumber(4, 12 * ln_2));
+
+    test.assertEqual(expm1(x), new DualNumber(expm1(2), 3 * exp(2)));
+
+    test.assertEqual(log(x), new DualNumber(ln_2, 1.5));
+
+    test.assertEqual(log2(x), new DualNumber(1, 1.5 / ln_2));
+
+    test.assertEqual(log1p(x), new DualNumber(log1p(2), 1));
 }
 
 proc test_hyperbolic_functions(test : borrowed Test) throws {