[libc][math][c++23] Add bfloat16 support in LLVM libc

[krishna2803]

This PR enables support for BFloat16 type in LLVM libc along with support for testing BFloat16 functions via MPFR.

cc @overmighty @lntue

[github-actions]

⚠️ C/C++ code formatter, clang-format found issues in your code. ⚠️

You can test this locally with the following command:

git-clang-format --diff HEAD~1 HEAD --extensions h,cpp -- libc/cmake/modules/compiler_features/check_bfloat16.cpp libc/src/__support/FPUtil/bfloat16.h libc/test/src/__support/FPUtil/bfloat16_test.cpp libc/src/__support/CPP/type_traits/is_floating_point.h libc/src/__support/FPUtil/FPBits.h libc/src/__support/FPUtil/cast.h libc/src/__support/FPUtil/dyadic_float.h libc/src/__support/macros/properties/types.h libc/utils/MPFRWrapper/MPCommon.cpp libc/utils/MPFRWrapper/MPCommon.h

View the diff from clang-format here.

diff --git a/libc/test/src/__support/FPUtil/bfloat16_test.cpp b/libc/test/src/__support/FPUtil/bfloat16_test.cpp
index 3bfabf3fd..14f06c305 100644
--- a/libc/test/src/__support/FPUtil/bfloat16_test.cpp
+++ b/libc/test/src/__support/FPUtil/bfloat16_test.cpp
@@ -24,7 +24,6 @@ static constexpr uint16_t POS_STOP = 0x7f80U;
 static constexpr uint16_t NEG_START = 0x8000U;
 static constexpr uint16_t NEG_STOP = 0xff80;
 
-
 using MPFRNumber = LIBC_NAMESPACE::testing::mpfr::MPFRNumber;
 
 // TODO: better naming?
@@ -32,7 +31,7 @@ TEST_F(LlvmLibcBfloat16ExhaustiveTest, PositiveRange) {
   for (uint16_t bits = POS_START; bits <= POS_STOP; bits++) {
     bfloat16 bf16_num{bits};
     MPFRNumber mpfr_num{bf16_num};
-    
+
     // bfloat16 to float
     float mpfr_float = mpfr_num.as<float>();
     ASSERT_FP_EQ(mpfr_float, bf16_num.as_float());
@@ -49,7 +48,7 @@ TEST_F(LlvmLibcBfloat16ExhaustiveTest, NegativeRange) {
   for (uint16_t bits = NEG_START; bits <= NEG_STOP; bits++) {
     bfloat16 bf16_num{bits};
     MPFRNumber mpfr_num{bf16_num};
-    
+
     // bfloat16 to float
     float mpfr_float = mpfr_num.as<float>();
     ASSERT_FP_EQ(mpfr_float, bf16_num.as_float());

[lntue]

You can leave the cmake detection changes to other PR:

  CheckCompilerFeatures.cmake
  check_bfloat16.cpp
  entrypoints.txt

[lntue]

we should implement floating point equality of the same type in FPBits, and it should follow IEEE 754 rules for equality (aka not bit identical in some cases).

[lntue]

Add unit tests to make sure the class and the MPFR utility work.