[SYCL][E2E] Add more checks to exp-std-complex-edge-cases.hpp (#16020)

To cover the rest of checks from
https://en.cppreference.com/w/cpp/numeric/complex/exp

Author: KornevNikita

sycl/test-e2e/DeviceLib/exp/exp-std-complex-edge-cases.hpp

@@ -199,12 +199,18 @@ template <typename T> bool test() {
 
     sycl::buffer<std::complex<T>> data(testcases, sycl::range{N});
     sycl::buffer<std::complex<T>> results(sycl::range{N});
+    sycl::buffer<std::complex<T>> exp_conj(sycl::range{N});
+    sycl::buffer<std::complex<T>> conj_exp(sycl::range{N});
 
     q.submit([&](sycl::handler &cgh) {
        sycl::accessor acc_data(data, cgh, sycl::read_only);
-       sycl::accessor acc(results, cgh, sycl::write_only);
+       sycl::accessor acc_results(results, cgh, sycl::write_only);
+       sycl::accessor acc_exp_conj(exp_conj, cgh, sycl::write_only);
+       sycl::accessor acc_conj_exp(conj_exp, cgh, sycl::write_only);
        cgh.parallel_for(sycl::range{N}, [=](sycl::item<1> it) {
-         acc[it] = std::exp(acc_data[it]);
+         acc_results[it] = std::exp(acc_data[it]);
+         acc_exp_conj[it] = std::exp(std::conj(acc_data[it]));
+         acc_conj_exp[it] = std::conj(std::exp(acc_data[it]));
        });
      }).wait_and_throw();
 
@@ -219,9 +225,18 @@ template <typename T> bool test() {
 
     // Based on https://en.cppreference.com/w/cpp/numeric/complex/exp
     // z below refers to the argument passed to std::exp(complex<T>)
-    sycl::host_accessor acc(results);
+    sycl::host_accessor acc_results(results);
+    sycl::host_accessor acc_exp_conj(exp_conj);
+    sycl::host_accessor acc_conj_exp(conj_exp);
     for (unsigned i = 0; i < N; ++i) {
-      std::complex<T> r = acc[i];
+      // std::exp(std::conj(z)) == std::conj(std::exp(z))
+      // NAN is not equal to NAN in floating-point arithmetic, therefore compare
+      // only results without NAN
+      if (!std::isnan(acc_exp_conj[i].real()) &&
+          !std::isnan(acc_exp_conj[i].imag()))
+        CHECK(acc_exp_conj[i] == acc_conj_exp[i], passed, i);
+
+      std::complex<T> r = acc_results[i];
       // If z is (+/-0, +0), the result is (1, +0)
       if (testcases[i].real() == 0 && testcases[i].imag() == 0 &&
           !std::signbit(testcases[i].imag())) {
@@ -247,6 +262,33 @@ template <typename T> bool test() {
         CHECK(r.imag() == 0, passed, i);
         CHECK(std::signbit(testcases[i].imag()) == std::signbit(r.imag()),
               passed, i);
+        // If z is (-inf, y) (for any finite y), the result is +0cis(y) where
+        // cis(y) is cos(y) + isin(y)
+      } else if (std::isinf(testcases[i].real()) &&
+                 std::signbit(testcases[i].real()) &&
+                 std::isfinite(testcases[i].imag())) {
+        CHECK(r.real() == 0, passed, i)
+        CHECK(std::signbit(r.real()) ==
+                  std::signbit(std::cos(testcases[i].imag())),
+              passed, i)
+        CHECK(r.imag() == 0, passed, i)
+        CHECK(std::signbit(r.imag()) ==
+                  std::signbit(std::sin(testcases[i].imag())),
+              passed, i)
+        // If z is (+inf, y) (for any finite nonzero y), the result is +∞cis(y)
+        // where cis(y) is cos(y) + isin(y)
+      } else if (std::isinf(testcases[i].real()) &&
+                 !std::signbit(testcases[i].real()) &&
+                 std::isfinite(testcases[i].imag()) &&
+                 testcases[i].imag() != 0) {
+        CHECK(std::isinf(r.real()), passed, i)
+        CHECK(std::signbit(r.real()) ==
+                  std::signbit(std::cos(testcases[i].imag())),
+              passed, i)
+        CHECK(std::isinf(r.imag()), passed, i)
+        CHECK(std::signbit(r.imag()) ==
+                  std::signbit(std::sin(testcases[i].imag())),
+              passed, i)
         // If z is (-inf, +inf), the result is (+/-0, +/-0) (signs are
         // unspecified)
       } else if (std::isinf(testcases[i].real()) && testcases[i].real() < 0 &&