[libcxx][test][z/OS] Fix hermite.pass.cpp for HEX float (#101019)

The HEX float on z/OS does not have infinity nor NaN. In addition, the
limits are smaller before the overflow occurs in mathematical
calculations. This PR accounts for this.

FYI, this LIT test was recently added in PR
[89982](#89982)

Author: zibi2

libcxx/test/std/numerics/c.math/hermite.pass.cpp

@@ -26,7 +26,16 @@
 
 #include "type_algorithms.h"
 
-inline constexpr unsigned g_max_n = 128;
+template <class Real>
+constexpr unsigned get_maximal_order() {
+  if constexpr (std::numeric_limits<Real>::is_iec559)
+    return 128;
+  else { // Workaround for z/OS HexFloat.
+    // Note |H_n(x)| < 10^75 for n < 39 and x in sample_points().
+    static_assert(std::numeric_limits<Real>::max_exponent10 == 75);
+    return 39;
+  }
+}
 
 template <class T>
 std::array<T, 11> sample_points() {
@@ -203,16 +212,21 @@ std::vector<T> get_roots(unsigned n) {
 
 template <class Real>
 void test() {
-  { // checks if NaNs are reported correctly (i.e. output == input for input == NaN)
+  if constexpr (
+      std::numeric_limits<Real>::has_quiet_NaN &&
+      std::numeric_limits<
+          Real>::has_signaling_NaN) { // checks if NaNs are reported correctly (i.e. output == input for input == NaN)
     using nl = std::numeric_limits<Real>;
     for (Real NaN : {nl::quiet_NaN(), nl::signaling_NaN()})
-      for (unsigned n = 0; n < g_max_n; ++n)
+      for (unsigned n = 0; n < get_maximal_order<Real>(); ++n)
         assert(std::isnan(std::hermite(n, NaN)));
   }
 
-  { // simple sample points for n=0..127 should not produce NaNs.
+  if constexpr (std::numeric_limits<Real>::has_quiet_NaN &&
+                std::numeric_limits<
+                    Real>::has_signaling_NaN) { // simple sample points for n=0..127 should not produce NaNs.
     for (Real x : sample_points<Real>())
-      for (unsigned n = 0; n < g_max_n; ++n)
+      for (unsigned n = 0; n < get_maximal_order<Real>(); ++n)
         assert(!std::isnan(std::hermite(n, x)));
   }
 
@@ -237,21 +251,21 @@ void test() {
 
   { // checks std::hermitef for bitwise equality with std::hermite(unsigned, float)
     if constexpr (std::is_same_v<Real, float>)
-      for (unsigned n = 0; n < g_max_n; ++n)
+      for (unsigned n = 0; n < get_maximal_order<Real>(); ++n)
         for (float x : sample_points<float>())
           assert(std::hermite(n, x) == std::hermitef(n, x));
   }
 
   { // checks std::hermitel for bitwise equality with std::hermite(unsigned, long double)
     if constexpr (std::is_same_v<Real, long double>)
-      for (unsigned n = 0; n < g_max_n; ++n)
+      for (unsigned n = 0; n < get_maximal_order<Real>(); ++n)
         for (long double x : sample_points<long double>())
           assert(std::hermite(n, x) == std::hermitel(n, x));
   }
 
   { // Checks if the characteristic recurrence relation holds:    H_{n+1}(x) = 2x H_n(x) - 2n H_{n-1}(x)
     for (Real x : sample_points<Real>()) {
-      for (unsigned n = 1; n < g_max_n - 1; ++n) {
+      for (unsigned n = 1; n < get_maximal_order<Real>() - 1; ++n) {
         Real H_next            = std::hermite(n + 1, x);
         Real H_next_recurrence = 2 * (x * std::hermite(n, x) - n * std::hermite(n - 1, x));
 
@@ -289,22 +303,23 @@ void test() {
     }
   }
 
-  { // check input infinity is handled correctly
+  if constexpr (std::numeric_limits<Real>::has_infinity) { // check input infinity is handled correctly
     Real inf = std::numeric_limits<Real>::infinity();
-    for (unsigned n = 1; n < g_max_n; ++n) {
+    for (unsigned n = 1; n < get_maximal_order<Real>(); ++n) {
       assert(std::hermite(n, +inf) == inf);
       assert(std::hermite(n, -inf) == ((n & 1) ? -inf : inf));
     }
   }
 
-  { // check: if overflow occurs that it is mapped to the correct infinity
+  if constexpr (std::numeric_limits<
+                    Real>::has_infinity) { // check: if overflow occurs that it is mapped to the correct infinity
     if constexpr (std::is_same_v<Real, double>) {
       // Q: Why only double?
       // A: The numeric values (e.g. overflow threshold `n`) below are different for other types.
       static_assert(sizeof(double) == 8);
-      for (unsigned n = 0; n < g_max_n; ++n) {
+      for (unsigned n = 0; n < get_maximal_order<Real>(); ++n) {
         // Q: Why n=111 and x=300?
-        // A: Both are chosen s.t. the first overlow occurs for some `n<g_max_n`.
+        // A: Both are chosen s.t. the first overlow occurs for some `n<get_maximal_order<Real>()`.
         if (n < 111) {
           assert(std::isfinite(std::hermite(n, +300.0)));
           assert(std::isfinite(std::hermite(n, -300.0)));
@@ -329,7 +344,7 @@ struct TestInt {
   template <class Integer>
   void operator()() {
     // checks that std::hermite(unsigned, Integer) actually wraps std::hermite(unsigned, double)
-    for (unsigned n = 0; n < g_max_n; ++n)
+    for (unsigned n = 0; n < get_maximal_order<double>(); ++n)
       for (Integer x : {-42, -7, -5, -1, 0, 1, 5, 7, 42})
         assert(std::hermite(n, x) == std::hermite(n, static_cast<double>(x)));
   }