add nextafter for bfloat16

Eigen/src/Core/arch/Default/BFloat16.h

diff --git a/Eigen/src/Core/arch/Default/BFloat16.h b/Eigen/src/Core/arch/Default/BFloat16.h
index b9f886f..b8d3b4f 100644
--- a/Eigen/src/Core/arch/Default/BFloat16.h
+++ b/Eigen/src/Core/arch/Default/BFloat16.h
@@ -763,6 +763,31 @@
   return Eigen::bfloat16_impl::raw_bfloat16_as_uint16(src);
 }
 
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 nextafter(const bfloat16& from, const bfloat16& to) {
+  if (numext::isnan EIGEN_NOT_A_MACRO(from)) {
+    return from;
+  }
+  if (numext::isnan EIGEN_NOT_A_MACRO(to)) {
+    return to;
+  }
+  if (from == to) {
+    return to;
+  }
+  uint16_t from_bits = numext::bit_cast<uint16_t>(from);
+  bool from_sign = from_bits >> 15;
+  // Whether we are adjusting toward the infinity with the same sign as from.
+  bool toward_inf = (to > from) == !from_sign;
+  if (toward_inf) {
+    ++from_bits;
+  } else if ((from_bits & 0x7fff) == 0) {
+    // Adjusting away from inf, but from is zero, so just toggle the sign.
+    from_bits ^= 0x8000;
+  } else {
+    --from_bits;
+  }
+  return numext::bit_cast<bfloat16>(from_bits);
+}
+
 }  // namespace numext
 }  // namespace Eigen
 

test/bfloat16_float.cpp

diff --git a/test/bfloat16_float.cpp b/test/bfloat16_float.cpp
index 5be49d9..12d6d86 100644
--- a/test/bfloat16_float.cpp
+++ b/test/bfloat16_float.cpp
@@ -353,6 +353,40 @@
   VERIFY_IS_APPROX(Ch.noalias() += Ah * Bh, (Cf.noalias() += Af * Bf).cast<bfloat16>());
 }
 
+void test_nextafter() {
+  VERIFY((numext::isnan)(numext::nextafter(std::numeric_limits<bfloat16>::quiet_NaN(), bfloat16(1.0f))));
+  VERIFY((numext::isnan)(numext::nextafter(bfloat16(1.0f), std::numeric_limits<bfloat16>::quiet_NaN())));
+  VERIFY(numext::nextafter(bfloat16(0.0f), bfloat16(0.0f)) == bfloat16(0.0f));
+  VERIFY(numext::nextafter(bfloat16(1.0f), bfloat16(1.0f)) == bfloat16(1.0f));
+  VERIFY(numext::nextafter(bfloat16(-1.0f), bfloat16(-1.0f)) == bfloat16(-1.0f));
+  VERIFY(numext::nextafter(std::numeric_limits<bfloat16>::infinity(), std::numeric_limits<bfloat16>::infinity()) ==
+         std::numeric_limits<bfloat16>::infinity());
+  VERIFY(numext::nextafter(std::numeric_limits<bfloat16>::infinity(), bfloat16(0.0f)) ==
+         (std::numeric_limits<bfloat16>::max)());
+  VERIFY(numext::nextafter(-std::numeric_limits<bfloat16>::infinity(), bfloat16(0.0f)) ==
+         -(std::numeric_limits<bfloat16>::max)());
+  VERIFY(numext::nextafter(bfloat16(1.0f), std::numeric_limits<bfloat16>::infinity()) ==
+         bfloat16(1.0f) + std::numeric_limits<bfloat16>::epsilon());
+  VERIFY(numext::nextafter(bfloat16(1.0f), -std::numeric_limits<bfloat16>::infinity()) ==
+         bfloat16(1.0f) - std::numeric_limits<bfloat16>::epsilon() / bfloat16(2.0f));
+  VERIFY(numext::nextafter(bfloat16(-1.0f), -std::numeric_limits<bfloat16>::infinity()) ==
+         bfloat16(-1.0f) - std::numeric_limits<bfloat16>::epsilon());
+  VERIFY(numext::nextafter(bfloat16(-1.0f), std::numeric_limits<bfloat16>::infinity()) ==
+         bfloat16(-1.0f) + std::numeric_limits<bfloat16>::epsilon() / bfloat16(2.0f));
+  VERIFY(numext::nextafter((std::numeric_limits<bfloat16>::max)(), std::numeric_limits<bfloat16>::infinity()) ==
+         std::numeric_limits<bfloat16>::infinity());
+  VERIFY(numext::nextafter(-(std::numeric_limits<bfloat16>::max)(), -std::numeric_limits<bfloat16>::infinity()) ==
+         -std::numeric_limits<bfloat16>::infinity());
+  VERIFY_BFLOAT16_BITS_EQUAL(numext::nextafter(bfloat16(0.0f), bfloat16(1.0f)), 0x0001);
+  VERIFY_BFLOAT16_BITS_EQUAL(numext::nextafter(bfloat16(-0.0f), bfloat16(1.0f)), 0x0000);
+  VERIFY_BFLOAT16_BITS_EQUAL(numext::nextafter(bfloat16(0.0f), bfloat16(-1.0f)), 0x8000);
+  VERIFY_BFLOAT16_BITS_EQUAL(numext::nextafter(bfloat16(-0.0f), bfloat16(-1.0f)), 0x8001);
+  VERIFY_BFLOAT16_BITS_EQUAL(numext::nextafter(bfloat16(0.0f), bfloat16(-0.0f)), 0x8000);
+  VERIFY_BFLOAT16_BITS_EQUAL(numext::nextafter(bfloat16(-0.0f), bfloat16(0.0f)), 0x0000);
+  VERIFY_BFLOAT16_BITS_EQUAL(numext::nextafter(bfloat16(0.0f), bfloat16(0.0f)), 0x0000);
+  VERIFY_BFLOAT16_BITS_EQUAL(numext::nextafter(bfloat16(-0.0f), bfloat16(-0.0f)), 0x8000);
+}
+
 EIGEN_DECLARE_TEST(bfloat16_float) {
   CALL_SUBTEST(test_numtraits());
   for (int i = 0; i < g_repeat; i++) {
@@ -363,5 +397,6 @@
     CALL_SUBTEST(test_trigonometric_functions());
     CALL_SUBTEST(test_array());
     CALL_SUBTEST(test_product());
+    CALL_SUBTEST(test_nextafter());
   }
 }