[SYCL] Improve the accuracy of host sycl::cospi (#9575)

Signed-off-by: Michael Aziz <michael.aziz@intel.com>

Author: 0x12CC

sycl/source/detail/builtins_math.cpp

@@ -36,7 +36,9 @@ template <typename T> inline T __atan2pi(T x, T y) {
   return std::atan2(x, y) / M_PI;
 }
 
-template <typename T> inline T __cospi(T x) { return std::cos(M_PI * x); }
+template <typename T> inline T __cospi(T x) {
+  return std::sin(M_PI * (0.5 - x));
+}
 
 template <typename T> T inline __fract(T x, T *iptr) {
   T f = std::floor(x);

sycl/test-e2e/Basic/built-ins/host_math.cpp

@@ -0,0 +1,40 @@
+// RUN: %{build} -o %t.out
+// RUN: %{run} %t.out
+
+#include <iomanip>
+#include <iostream>
+#include <sycl.hpp>
+
+template <typename T> T get_ulp_std(T x) {
+  const T inf = std::numeric_limits<T>::infinity();
+  const T negative = std::fabs(std::nextafter(x, -inf) - x);
+  const T positive = std::fabs(std::nextafter(x, inf) - x);
+  return std::fmin(negative, positive);
+}
+
+void testCospi() {
+  const double value = 0.4863334355; // some random value
+  const double reference =
+      0.042921588887841428949787569990803604014217853546142578125; // calculated
+                                                                   // with
+                                                                   // oclmath
+  const unsigned int ulpsExpected =
+      4; // according to section 4.17.5 of the SYCL 2020 spec, math functions
+         // correspond to those from OpenCL 1.2 spec, so this accuracy comes
+         // from the OpenCL 1.2 spec
+  const double differenceExpected = ulpsExpected * get_ulp_std(reference);
+  const double hostDifference = std::fabs(sycl::cospi(value) - reference);
+
+  std::cout << std::setprecision(17) << "cospi: " << '\n'
+            << "ref:\t" << reference << '\n'
+            << "host:\t" << sycl::cospi(value) << '\n'
+            << "diff host:\t " << hostDifference << '\n'
+            << "expected:\t" << differenceExpected << std::endl;
+
+  assert(hostDifference <= differenceExpected && "Host result incorrect");
+}
+
+int main() {
+  testCospi();
+  return 0;
+}