test: derivative-of-^ via log() and derivative-of-sqrt — real + complex

src/cpp/cseval/cseval.hpp

@@ -209,7 +209,6 @@ right path of the derivative");
   // exponentiation for the computation of the derivative (left path)
   static Real _pow1(Real a, Real b) { return (b * _pow(a, b - ONE)); }
   // exponentiation for the computation of the derivative (right path)
-  // TODO test log()
   static Real _pow2(Real a, Real b) { return (_log(a) * _pow(a, b)); }
   //- general static methods
 
@@ -282,7 +281,6 @@ the natural logarithm derivative");
   }
   // "sqrt" - square root
   static Real _sqrt(Real a) { return sqrt(a); }
-  // TODO test _sqrt_d()
   // "sqrt" for the derivative
   static Real _sqrt_d(Real a, Real) {
     if (sqrt(a) == ZERO) {

src/cpp/cseval/cseval_complex.hpp

@@ -210,7 +210,6 @@ right path of the derivative");
   // exponentiation for the computation of the derivative (left path)
   static Complex _pow1(Complex a, Complex b) { return (b * _pow(a, b - ONE)); }
   // exponentiation for the computation of the derivative (right path)
-  // TODO test log()
   static Complex _pow2(Complex a, Complex b) { return (_log(a) * _pow(a, b)); }
   //- general static methods
 
@@ -283,7 +282,6 @@ the natural logarithm derivative");
   }
   // "sqrt" - square root
   static Complex _sqrt(Complex a) { return sqrt(a); }
-  // TODO test _sqrt_d()
   // "sqrt" for the derivative
   static Complex _sqrt_d(Complex a, Complex) {
     if (sqrt(a) == ZERO) {

tests/test_derivative_coverage.py

@@ -0,0 +1,45 @@
+"""Regression: derivative-of-^ uses log(), derivative-of-sqrt fires.
+
+Closes TODOs:
+  src/cpp/cseval/cseval.hpp:212          (// TODO test log())
+  src/cpp/cseval/cseval.hpp:285          (// TODO test _sqrt_d())
+  src/cpp/cseval/cseval_complex.hpp:213  (// TODO test log())
+  src/cpp/cseval/cseval_complex.hpp:286  (// TODO test _sqrt_d())
+
+The `^` derivative's right path is `_pow2(a, b) = log(a) * pow(a, b)`,
+which is only reached when the exponent is itself a function of the
+differentiation variable. The `_sqrt_d` path is reached for d(sqrt(x))/dx.
+Both fire on the real and complex evaluation paths.
+"""
+
+from formula import Solver
+
+
+def test_pow_derivative_via_log_real():
+    # d(x^y)/dy = log(x) * x^y.  At x=2, y=3:  log(2)*8 = 5.5451774444795625...
+    result = Solver("x^y", precision=24)(
+        {"x": "2", "y": "3"}, derivative="y"
+    )
+    assert result.startswith("5.545177444479562475337856")
+
+
+def test_pow_derivative_via_log_complex():
+    # Same identity through the complex path. The presence of 'i' in the
+    # expression forces complex evaluation, so _pow2 in cseval_complex.hpp
+    # runs instead of the real twin.
+    result = Solver("(2+i*0)^y", precision=24)(
+        {"y": "3"}, derivative="y"
+    )
+    assert result.startswith("5.5451774444795624753378")
+
+
+def test_sqrt_derivative_real():
+    # d(sqrt(x))/dx = 1/(2*sqrt(x)).  At x=4:  1/(2*2) = 0.25.
+    result = Solver("sqrt(x)", precision=24)({"x": "4"}, derivative="x")
+    assert result == "0.25"
+
+
+def test_sqrt_derivative_complex():
+    # Same identity through the complex path (forced by 'i' in the expression).
+    result = Solver("sqrt(x+i*0)", precision=24)({"x": "4"}, derivative="x")
+    assert result.startswith("0.25")