Changing input argument to match gcc (k vs m). Updated documentation …

…to mention that it is an argument of k.

Docs/sphinx_documentation/source/Basics.rst

@@ -595,7 +595,7 @@ numbers can be computed with ``min`` and ``max``, respectively.  It supports
 the Heaviside step function, ``heaviside(x1,x2)`` that gives ``0``, ``x2``,
 ``1``, for ``x1 < 0``, ``x1 = 0`` and ``x1 > 0``, respectively.
 It supports the Bessel function of the first kind of order ``n``
-``jn(n,x)``. Complete elliptic integrals of the first and second kind, ``comp_ellint_1`` and ``comp_ellint_2``,
+``jn(n,x)``. Complete elliptic integrals of the first and second kind, ``comp_ellint_1(k)`` and ``comp_ellint_2(k)``,
 are supported.
 There is ``if(a,b,c)`` that gives ``b`` or ``c`` depending on the value of
 ``a``.  A number of comparison operators are supported, including ``<``,

Src/Base/AMReX_Math.H

@@ -228,13 +228,17 @@ std::uint64_t umulhi (std::uint64_t a, std::uint64_t b)
 
 template <typename T>
 AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
-T comp_ellint_1 (T m)
+T comp_ellint_1 (T k)
 {
     // Computing K based on DLMF
     // https://dlmf.nist.gov/19.8
     T tol = 1e-12;
+    if constexpr (std::is_same<T, float>::value) {
+        tol = 1e-6;
+    }
+
     T a0 = 1.0;
-    T g0 = std::sqrt(1.0 - m);
+    T g0 = std::sqrt(1.0 - k*k);
     T a, g;
 
     // Find Arithmetic Geometric mean
@@ -251,16 +255,19 @@ T comp_ellint_1 (T m)
 
 template <typename T>
 AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
-T comp_ellint_2 (T m)
+T comp_ellint_2 (T k)
 {
     // Computing E based on DLMF
     // https://dlmf.nist.gov/19.8
-    T Kcomp = amrex::Math::comp_ellint_1<T>(m);
+    T Kcomp = amrex::Math::comp_ellint_1<T>(k);
     T tol = 1e-12;
+    if constexpr (std::is_same<T, float>::value) {
+        tol = 1e-6;
+    }
 
     // Step Zero
     T a0 = 1.0;
-    T g0 = std::sqrt(1.0 - m);
+    T g0 = std::sqrt(1.0 - k*k);
     T cn = std::sqrt(a0*a0 - g0*g0);
 
     // Step 1