Add sinh, cosh, tanh and tan functions to automatic differentiation

Change-Id: I6eb43fe9b340d4074ed3eed1461dda315f6e8ce8

include/ceres/jet.h

diff --git a/include/ceres/jet.h b/include/ceres/jet.h
index 000bd1c..7299a48 100644
--- a/include/ceres/jet.h
+++ b/include/ceres/jet.h
@@ -405,7 +405,6 @@
 // double-valued and Jet-valued functions, but we are not allowed to put
 // Jet-valued functions inside namespace std.
 //
-// Missing: cosh, sinh, tanh, tan
 // TODO(keir): Switch to "using".
 inline double abs     (double x) { return std::abs(x);      }
 inline double log     (double x) { return std::log(x);      }
@@ -415,6 +414,11 @@
 inline double acos    (double x) { return std::acos(x);     }
 inline double sin     (double x) { return std::sin(x);      }
 inline double asin    (double x) { return std::asin(x);     }
+inline double tan     (double x) { return std::tan(x);      }
+inline double atan    (double x) { return std::atan(x);     }
+inline double sinh    (double x) { return std::sinh(x);     }
+inline double cosh    (double x) { return std::cosh(x);     }
+inline double tanh    (double x) { return std::tanh(x);     }
 inline double pow  (double x, double y) { return std::pow(x, y);   }
 inline double atan2(double y, double x) { return std::atan2(y, x); }
 
@@ -495,6 +499,58 @@
   return g;
 }
 
+// tan(a + h) ~= tan(a) + (1 + tan(a)^2) h
+template <typename T, int N> inline
+Jet<T, N> tan(const Jet<T, N>& f) {
+  Jet<T, N> g;
+  g.a = tan(f.a);
+  double tan_a = tan(f.a);
+  const T tmp = T(1.0) + tan_a * tan_a;
+  g.v = tmp * f.v;
+  return g;
+}
+
+// atan(a + h) ~= atan(a) + 1 / (1 + a^2) h
+template <typename T, int N> inline
+Jet<T, N> atan(const Jet<T, N>& f) {
+  Jet<T, N> g;
+  g.a = atan(f.a);
+  const T tmp = T(1.0) / (T(1.0) + f.a * f.a);
+  g.v = tmp * f.v;
+  return g;
+}
+
+// sinh(a + h) ~= sinh(a) + cosh(a) h
+template <typename T, int N> inline
+Jet<T, N> sinh(const Jet<T, N>& f) {
+  Jet<T, N> g;
+  g.a = sinh(f.a);
+  const T cosh_a = cosh(f.a);
+  g.v = cosh_a * f.v;
+  return g;
+}
+
+// cosh(a + h) ~= cosh(a) + sinh(a) h
+template <typename T, int N> inline
+Jet<T, N> cosh(const Jet<T, N>& f) {
+  Jet<T, N> g;
+  g.a = cosh(f.a);
+  const T sinh_a = sinh(f.a);
+  g.v = sinh_a * f.v;
+  return g;
+}
+
+// tanh(a + h) ~= tanh(a) + (1 - tanh(a)^2) h
+template <typename T, int N> inline
+Jet<T, N> tanh(const Jet<T, N>& f) {
+  Jet<T, N> g;
+  g.a = tanh(f.a);
+  double tanh_fa = tanh(f.a);
+  const T tmp = 1 - tanh_fa * tanh_fa;
+  g.v = tmp * f.v;
+  return g;
+}
+
 // Jet Classification. It is not clear what the appropriate semantics are for
 // these classifications. This picks that IsFinite and isnormal are "all"
 // operations, i.e. all elements of the jet must be finite for the jet itself
@@ -645,6 +701,11 @@
 template<typename T, int N> inline       Jet<T, N>  ei_log (const Jet<T, N>& x) { return log(x);         }  // NOLINT
 template<typename T, int N> inline       Jet<T, N>  ei_sin (const Jet<T, N>& x) { return sin(x);         }  // NOLINT
 template<typename T, int N> inline       Jet<T, N>  ei_cos (const Jet<T, N>& x) { return cos(x);         }  // NOLINT
+template<typename T, int N> inline       Jet<T, N>  ei_tan (const Jet<T, N>& x) { return tan(x);         }  // NOLINT
+template<typename T, int N> inline       Jet<T, N>  ei_atan(const Jet<T, N>& x) { return atan(x);        }  // NOLINT
+template<typename T, int N> inline       Jet<T, N>  ei_sinh(const Jet<T, N>& x) { return sinh(x);        }  // NOLINT
+template<typename T, int N> inline       Jet<T, N>  ei_cosh(const Jet<T, N>& x) { return cosh(x);        }  // NOLINT
+template<typename T, int N> inline       Jet<T, N>  ei_tanh(const Jet<T, N>& x) { return tanh(x);        }  // NOLINT
 template<typename T, int N> inline       Jet<T, N>  ei_pow (const Jet<T, N>& x, Jet<T, N> y) { return pow(x, y); }  // NOLINT
 
 // Note: This has to be in the ceres namespace for argument dependent lookup to

internal/ceres/jet_test.cc

diff --git a/internal/ceres/jet_test.cc b/internal/ceres/jet_test.cc
index 0dd4336..6b8cf17 100644
--- a/internal/ceres/jet_test.cc
+++ b/internal/ceres/jet_test.cc
@@ -142,6 +142,38 @@
     ExpectJetsClose(u, t);
   }
 
+  { // Check that tan(x) = sin(x) / cos(x).
+    J z = tan(x);
+    J w = sin(x) / cos(x);
+    VL << "z = " << z;
+    VL << "w = " << w;
+    ExpectJetsClose(z, w);
+  }
+
+  { // Check that tan(atan(x)) = x.
+    J z = tan(atan(x));
+    J w = x;
+    VL << "z = " << z;
+    VL << "w = " << w;
+    ExpectJetsClose(z, w);
+  }
+
+  { // Check that cosh(x)*cosh(x) - sinh(x)*sinh(x) = 1
+    J z = cosh(x) * cosh(x);
+    J w = sinh(x) * sinh(x);
+    VL << "z = " << z;
+    VL << "w = " << w;
+    ExpectJetsClose(z - w, J(1.0));
+  }
+
+  { // Check that tanh(x + y) = (tanh(x) + tanh(y)) / (1 + tanh(x) tanh(y))
+    J z = tanh(x + y);
+    J w = (tanh(x) + tanh(y)) / (J(1.0) + tanh(x) * tanh(y));
+    VL << "z = " << z;
+    VL << "w = " << w;
+    ExpectJetsClose(z, w);
+  }
+
   { // Check that pow(x, 1) == x.
     VL << "x = " << x;