Implementation of Bessel functions of second kind (yn) (AMReX-Codes#4234

)

## Summary
This merge request adds support for the Bessel function of the second
kind (Yn) to the AMReX parser. The implementation allows users to
evaluate the Yn(x) function directly in runtime expressions, enhancing
the mathematical capabilities of AMReX.

## Additional background
The Bessel function of the second kind is widely used in solving partial
differential equations, particularly in problems involving cylindrical
or spherical symmetry. Adding this function expands the parser's
usability in scientific and engineering applications where such
functions are essential. The implementation leverages standard
mathematical libraries for accurate computation.

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(k)`` and ``comp_ellint_2(k)``,
+``jn(n,x)``, and the Bessel function of the second kind of order ``n`` ``yn(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/Parser/AMReX_Parser_Y.H

@@ -91,6 +91,7 @@ enum parser_f2_t {  // Built-in functions with two arguments
     PARSER_OR,
     PARSER_HEAVISIDE,
     PARSER_JN,
+    PARSER_YN,
     PARSER_MIN,
     PARSER_MAX,
     PARSER_FMOD
@@ -116,6 +117,7 @@ std::string_view parser_f2_s[] =
     "or",
     "heaviside",
     "jn",
+    "yn",
     "min",
     "max",
     "fmod"
@@ -400,6 +402,21 @@ T parser_math_jn (int a, T b)
 #endif
 }
 
+template <typename T>
+AMREX_GPU_HOST_DEVICE AMREX_NO_INLINE
+T parser_math_yn (int a, T b)
+{
+#if defined AMREX_USE_SYCL || defined __MINGW32__
+    amrex::ignore_unused(a,b);
+    // neither yn(f) nor std::cyl_bessel_y work yet
+    // https://github.com/oneapi-src/oneAPI-spec/issues/308
+    AMREX_ALWAYS_ASSERT_WITH_MESSAGE(false, "parser: yn in SYCL not supported yet");
+    return 0.0;
+#else
+    return yn(a, b);
+#endif
+}
+
 AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE double
 parser_call_f1 (enum parser_f1_t type, double a)
 {
@@ -460,6 +477,8 @@ parser_call_f2 (enum parser_f2_t type, double a, double b)
         return (a < 0.0) ? 0.0 : ((a > 0.0) ? 1.0 : b);
     case PARSER_JN:
         return parser_math_jn<double>(int(a),b);
+    case PARSER_YN:
+        return parser_math_yn<double>(int(a),b);
     case PARSER_MIN:
         return (a < b) ? a : b;
     case PARSER_MAX:

Src/Base/Parser/amrex_parser.l

@@ -70,6 +70,7 @@ EXP	([Ee][-+]?[0-9]+)
 "pow"         { amrex_parserlval.f2 = amrex::PARSER_POW;       return F2; }
 "heaviside"   { amrex_parserlval.f2 = amrex::PARSER_HEAVISIDE; return F2; }
 "jn"          { amrex_parserlval.f2 = amrex::PARSER_JN;        return F2; }
+"yn"          { amrex_parserlval.f2 = amrex::PARSER_YN;        return F2; }
 "min"         { amrex_parserlval.f2 = amrex::PARSER_MIN;       return F2; }
 "max"         { amrex_parserlval.f2 = amrex::PARSER_MAX;       return F2; }
 "fmod"        { amrex_parserlval.f2 = amrex::PARSER_FMOD;      return F2; }