add atan function for ADScalar

include/a2ddefs.h

@@ -265,6 +265,11 @@ A2D_FUNCTION T fabs(T val) {
   return std::fabs(val);
 }
 
+template <typename T, std::enable_if_t<is_scalar_type<T>::value, bool> = true>
+A2D_FUNCTION T fsgn(T val) {
+  return std::copysign(1.0, val);
+}
+
 template <typename T, std::enable_if_t<is_scalar_type<T>::value, bool> = true>
 A2D_FUNCTION T sqrt(T val) {
 #ifndef __CUDACC__
@@ -329,7 +334,7 @@ A2D_FUNCTION T acos(T val) {
 }
 
 template <class ForwardIt, class T>
-A2D_FUNCTION void fill(ForwardIt first, ForwardIt last, const T& value) {
+A2D_FUNCTION void fill(ForwardIt first, ForwardIt last, const T &value) {
 #ifdef __CUDACC__
   thrust::fill(first, last, value);
 #else

include/ad/core/a2dsymmatveccore.h

@@ -20,7 +20,7 @@ A2D_FUNCTION void SymMatVecCore3x3(const T A[], const T x[], T b[]) {
 }
 
 template <typename T, bool additive = false>
-A2D_FUNCTION void SymMatVecCoreScale3x3(const T& scale, const T A[],
+A2D_FUNCTION void SymMatVecCoreScale3x3(const T &scale, const T A[],
                                         const T x[], T b[]) {
   // compute b = A * x
   if constexpr (additive) {

include/adscalar.h

@@ -297,6 +297,21 @@ A2D_FUNCTION inline ADScalar<X, M> operator/(const ADScalar<X, M> &l,
   return out;
 }
 
+// sign function
+// template <class X, int M>
+// A2D_FUNCTION inline ADScalar<X, M> fsgn(const ADScalar<X, M> &r) {
+//   X sign = 1.0;
+//   if (r.value < 0.0) {
+//     sign = -1.0;
+//   }
+//   // device compatible fsgn
+//   ADScalar<X, M> out(::fsgn(r.value));
+//   for (int i = 0; i < M; i++) {
+//     out.deriv[i] = sign * r.deriv[i];
+//   }
+//   return out;
+// }
+
 // fabs, sqrt
 template <class X, int M>
 A2D_FUNCTION inline ADScalar<X, M> fabs(const ADScalar<X, M> &r) {
@@ -371,6 +386,43 @@ A2D_FUNCTION inline ADScalar<X, M> cos(const ADScalar<X, M> &r) {
   return out;
 }
 
+template <class X, int M>
+A2D_FUNCTION inline ADScalar<X, M> atan(const ADScalar<X, M> &r) {
+  // device compatible sin, cos
+  ADScalar<X, M> out(::atan(r.value));
+  X d = 1.0 / (1.0 + r.value * r.value);  // 1/(1+x^2)
+  for (int i = 0; i < M; i++) {
+    out.deriv[i] = d * r.deriv[i];
+  }
+  return out;
+}
+
+template <class X, int M>
+A2D_FUNCTION inline ADScalar<X, M> atan2(const ADScalar<X, M> &y,
+                                         const ADScalar<X, M> &x) {
+  /** atan2(y,x) => theta */
+  ADScalar<X, M> out(::atan2(y.value, x.value));
+  X denom = x.value * x.value + y.value * y.value;
+  X dx = -y.value / denom;
+  X dy = x.value / denom;
+
+  for (int i = 0; i < M; i++) {
+    out.deriv[i] = dx * x.deriv[0] + dy * y.deriv[0];
+  }
+  return out;
+}
+
+template <class X, int M>
+A2D_FUNCTION inline ADScalar<X, M> tanh(const ADScalar<X, M> &r) {
+  // for smooth sign function essentially
+  ADScalar<X, M> out(::tanh(r.value));
+  X d = 1.0 / ::cosh(r.value) / ::cosh(r.value);
+  for (int i = 0; i < M; i++) {
+    out.deriv[i] = d * r.deriv[i];
+  }
+  return out;
+}
+
 // for A2D Objects
 
 // template <int N>