[libc][math] Implement nexttoward functions (#72763)

Implements the `nexttoward`, `nexttowardf` and `nexttowardl` functions.
Also, raise excepts required by the standard in `nextafter` functions.

cc: @lntue

libc/config/darwin/arm/entrypoints.txt

@@ -199,6 +199,9 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.nextafter
     libc.src.math.nextafterf
     libc.src.math.nextafterl
+    libc.src.math.nexttoward
+    libc.src.math.nexttowardf
+    libc.src.math.nexttowardl
     libc.src.math.powf
     libc.src.math.remainderf
     libc.src.math.remainder

libc/config/darwin/x86_64/entrypoints.txt

@@ -178,6 +178,9 @@ set(TARGET_LIBM_ENTRYPOINTS
     #libc.src.math.nextafter
     #libc.src.math.nextafterf
     #libc.src.math.nextafterl
+    #libc.src.math.nexttoward
+    #libc.src.math.nexttowardf
+    #libc.src.math.nexttowardl
     #libc.src.math.remainderf
     #libc.src.math.remainder
     #libc.src.math.remainderl

libc/config/gpu/entrypoints.txt

@@ -219,6 +219,8 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.nearbyintf
     libc.src.math.nextafter
     libc.src.math.nextafterf
+    libc.src.math.nexttoward
+    libc.src.math.nexttowardf
     libc.src.math.pow
     libc.src.math.powf
     libc.src.math.remainder

libc/config/linux/aarch64/entrypoints.txt

@@ -316,6 +316,9 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.nextafter
     libc.src.math.nextafterf
     libc.src.math.nextafterl
+    libc.src.math.nexttoward
+    libc.src.math.nexttowardf
+    libc.src.math.nexttowardl
     libc.src.math.powf
     libc.src.math.remainderf
     libc.src.math.remainder

libc/config/linux/riscv/entrypoints.txt

@@ -325,6 +325,9 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.nextafter
     libc.src.math.nextafterf
     libc.src.math.nextafterl
+    libc.src.math.nexttoward
+    libc.src.math.nexttowardf
+    libc.src.math.nexttowardl
     libc.src.math.powf
     libc.src.math.remainderf
     libc.src.math.remainder

libc/config/linux/x86_64/entrypoints.txt

@@ -329,6 +329,9 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.nextafter
     libc.src.math.nextafterf
     libc.src.math.nextafterl
+    libc.src.math.nexttoward
+    libc.src.math.nexttowardf
+    libc.src.math.nexttowardl
     libc.src.math.powf
     libc.src.math.remainderf
     libc.src.math.remainder

libc/config/windows/entrypoints.txt

@@ -198,6 +198,9 @@ set(TARGET_LIBM_ENTRYPOINTS
     libc.src.math.nextafter
     libc.src.math.nextafterf
     libc.src.math.nextafterl
+    libc.src.math.nexttoward
+    libc.src.math.nexttowardf
+    libc.src.math.nexttowardl
     libc.src.math.powf
     libc.src.math.remainderf
     libc.src.math.remainder

libc/docs/math/index.rst

@@ -230,11 +230,11 @@ Basic Operations
 +--------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | nextafterl   | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +--------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
-| nexttoward   |         |         |         |         |         |         |         |         |         |         |         |         |
+| nexttoward   | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +--------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
-| nexttowardf  |         |         |         |         |         |         |         |         |         |         |         |         |
+| nexttowardf  | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +--------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
-| nexttowardl  |         |         |         |         |         |         |         |         |         |         |         |         |
+| nexttowardl  | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +--------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
 | remainder    | |check| | |check| |         | |check| | |check| |         |         | |check| |         |         |         |         |
 +--------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+

libc/spec/stdc.td

@@ -492,6 +492,10 @@ def StdC : StandardSpec<"stdc"> {
           FunctionSpec<"nextafter", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
           FunctionSpec<"nextafterl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoubleType>]>,
 
+          FunctionSpec<"nexttowardf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<LongDoubleType>]>,
+          FunctionSpec<"nexttoward", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<LongDoubleType>]>,
+          FunctionSpec<"nexttowardl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoubleType>]>,
+
           FunctionSpec<"powf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
           FunctionSpec<"pow", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
 

libc/src/__support/FPUtil/CMakeLists.txt

@@ -96,6 +96,7 @@ add_header_library(
   HDRS
     ManipulationFunctions.h
   DEPENDS
+    .fenv_impl
     .fp_bits
     .nearest_integer_operations
     .normal_float

libc/src/__support/FPUtil/ManipulationFunctions.h

@@ -10,12 +10,14 @@
 #define LLVM_LIBC_SRC___SUPPORT_FPUTIL_MANIPULATIONFUNCTIONS_H
 
 #include "FPBits.h"
+#include "FloatProperties.h"
 #include "NearestIntegerOperations.h"
 #include "NormalFloat.h"
 #include "PlatformDefs.h"
 
 #include "src/__support/CPP/bit.h"
 #include "src/__support/CPP/type_traits.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/macros/attributes.h"
 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
 
@@ -169,8 +171,50 @@ LIBC_INLINE T nextafter(T from, T to) {
     int_val = (to_bits.uintval() & sign_mask) + UIntType(1);
   }
 
+  UIntType exponent_bits = int_val & FloatProperties<T>::EXPONENT_MASK;
+  if (exponent_bits == UIntType(0))
+    raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
+  else if (exponent_bits == FloatProperties<T>::EXPONENT_MASK)
+    raise_except_if_required(FE_OVERFLOW | FE_INEXACT);
+
+  return cpp::bit_cast<T>(int_val);
+}
+
+template <typename T>
+LIBC_INLINE cpp::enable_if_t<cpp::is_floating_point_v<T>, T>
+nexttoward(T from, long double to) {
+  FPBits<T> from_bits(from);
+  if (from_bits.is_nan())
+    return from;
+
+  FPBits<long double> to_bits(to);
+  if (to_bits.is_nan())
+    return to;
+
+  if ((long double)from == to)
+    return to;
+
+  using UIntType = typename FPBits<T>::UIntType;
+  UIntType int_val = from_bits.uintval();
+  if (from != T(0.0)) {
+    if ((from < to) == (from > T(0.0))) {
+      ++int_val;
+    } else {
+      --int_val;
+    }
+  } else {
+    int_val = FPBits<T>::MIN_SUBNORMAL;
+    if (to_bits.get_sign())
+      int_val |= FloatProperties<T>::SIGN_MASK;
+  }
+
+  UIntType exponent_bits = int_val & FloatProperties<T>::EXPONENT_MASK;
+  if (exponent_bits == UIntType(0))
+    raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
+  else if (exponent_bits == FloatProperties<T>::EXPONENT_MASK)
+    raise_except_if_required(FE_OVERFLOW | FE_INEXACT);
+
   return cpp::bit_cast<T>(int_val);
-  // TODO: Raise floating point exceptions as required by the standard.
 }
 
 } // namespace fputil

libc/src/__support/FPUtil/x86_64/NextAfterLongDouble.h

@@ -16,6 +16,7 @@
 #endif
 
 #include "src/__support/CPP/bit.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
 #include "src/__support/FPUtil/FPBits.h"
 
 #include <stdint.h>
@@ -59,6 +60,8 @@ LIBC_INLINE long double nextafter(long double from, long double to) {
         // which is what is expected. Since NaNs are handling separately,
         // it will never overflow "beyond" infinity.
         from_bits.set_unbiased_exponent(from_bits.get_unbiased_exponent() + 1);
+        if (from_bits.is_inf())
+          raise_except_if_required(FE_OVERFLOW | FE_INEXACT);
         return from_bits;
       } else {
         ++int_val;
@@ -105,6 +108,8 @@ LIBC_INLINE long double nextafter(long double from, long double to) {
         // which is what is expected. Since NaNs are handling separately,
         // it will never overflow "beyond" infinity.
         from_bits.set_unbiased_exponent(from_bits.get_unbiased_exponent() + 1);
+        if (from_bits.is_inf())
+          raise_except_if_required(FE_OVERFLOW | FE_INEXACT);
         return from_bits;
       } else {
         ++int_val;
@@ -112,8 +117,12 @@ LIBC_INLINE long double nextafter(long double from, long double to) {
     }
   }
 
+  UIntType implicit_bit =
+      int_val & (UIntType(1) << MantissaWidth<long double>::VALUE);
+  if (implicit_bit == UIntType(0))
+    raise_except_if_required(FE_UNDERFLOW | FE_INEXACT);
+
   return cpp::bit_cast<long double>(int_val);
-  // TODO: Raise floating point exceptions as required by the standard.
 }
 
 } // namespace fputil

libc/src/math/CMakeLists.txt

@@ -187,6 +187,10 @@ add_math_entrypoint_object(nextafter)
 add_math_entrypoint_object(nextafterf)
 add_math_entrypoint_object(nextafterl)
 
+add_math_entrypoint_object(nexttoward)
+add_math_entrypoint_object(nexttowardf)
+add_math_entrypoint_object(nexttowardl)
+
 add_math_entrypoint_object(pow)
 add_math_entrypoint_object(powf)
 

libc/src/math/generic/CMakeLists.txt

@@ -1474,6 +1474,42 @@ add_entrypoint_object(
     -O2
 )
 
+add_entrypoint_object(
+  nexttoward
+  SRCS
+    nexttoward.cpp
+  HDRS
+    ../nexttoward.h
+  DEPENDS
+    libc.src.__support.FPUtil.manipulation_functions
+  COMPILE_OPTIONS
+    -O3
+)
+
+add_entrypoint_object(
+  nexttowardf
+  SRCS
+    nexttowardf.cpp
+  HDRS
+    ../nexttowardf.h
+  DEPENDS
+    libc.src.__support.FPUtil.manipulation_functions
+  COMPILE_OPTIONS
+    -O3
+)
+
+add_entrypoint_object(
+  nexttowardl
+  SRCS
+    nexttowardl.cpp
+  HDRS
+    ../nexttowardl.h
+  DEPENDS
+    libc.src.__support.FPUtil.manipulation_functions
+  COMPILE_OPTIONS
+    -O3
+)
+
 add_entrypoint_object(
   fmod
   SRCS

libc/src/math/generic/nexttoward.cpp

@@ -0,0 +1,19 @@
+//===-- Implementation of nexttoward function -----------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/nexttoward.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(double, nexttoward, (double x, long double y)) {
+  return fputil::nexttoward(x, y);
+}
+
+} // namespace LIBC_NAMESPACE

libc/src/math/generic/nexttowardf.cpp

@@ -0,0 +1,19 @@
+//===-- Implementation of nexttowardf function ----------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/nexttowardf.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(float, nexttowardf, (float x, long double y)) {
+  return fputil::nexttoward(x, y);
+}
+
+} // namespace LIBC_NAMESPACE

libc/src/math/generic/nexttowardl.cpp

@@ -0,0 +1,22 @@
+//===-- Implementation of nexttowardl function ----------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/nexttowardl.h"
+#include "src/__support/FPUtil/ManipulationFunctions.h"
+#include "src/__support/common.h"
+
+namespace LIBC_NAMESPACE {
+
+LLVM_LIBC_FUNCTION(long double, nexttowardl, (long double x, long double y)) {
+  // We can reuse the nextafter implementation because nexttoward behaves
+  // exactly same as nextafter in case of long doubles. Also, we have explcitly
+  // handled the special 80-bit long doubles in nextafter implementation.
+  return fputil::nextafter(x, y);
+}
+
+} // namespace LIBC_NAMESPACE

libc/src/math/nexttoward.h

@@ -0,0 +1,18 @@
+//===-- Implementation header for nexttoward --------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_MATH_NEXTTOWARD_H
+#define LLVM_LIBC_SRC_MATH_NEXTTOWARD_H
+
+namespace LIBC_NAMESPACE {
+
+double nexttoward(double x, long double y);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_NEXTTOWARD_H

libc/src/math/nexttowardf.h

@@ -0,0 +1,18 @@
+//===-- Implementation header for nexttowardf -------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_MATH_NEXTTOWARDF_H
+#define LLVM_LIBC_SRC_MATH_NEXTTOWARDF_H
+
+namespace LIBC_NAMESPACE {
+
+float nexttowardf(float x, long double y);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_NEXTTOWARDF_H

libc/src/math/nexttowardl.h

@@ -0,0 +1,18 @@
+//===-- Implementation header for nexttowardl -------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC_MATH_NEXTTOWARDL_H
+#define LLVM_LIBC_SRC_MATH_NEXTTOWARDL_H
+
+namespace LIBC_NAMESPACE {
+
+long double nexttowardl(long double x, long double y);
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC_MATH_NEXTTOWARDL_H

libc/test/src/math/smoke/CMakeLists.txt

@@ -1251,6 +1251,54 @@ add_fp_unittest(
     libc.src.__support.FPUtil.fp_bits
 )
 
+# FIXME: These tests are currently spurious for NVPTX.
+if(NOT LIBC_GPU_TARGET_ARCHITECTURE_IS_NVPTX)
+  add_fp_unittest(
+    nexttoward_test
+    SUITE
+      libc-math-smoke-tests
+    SRCS
+      nexttoward_test.cpp
+    HDRS
+      NextTowardTest.h
+    DEPENDS
+      libc.include.math
+      libc.src.math.nexttoward
+      libc.src.__support.FPUtil.basic_operations
+      libc.src.__support.FPUtil.fp_bits
+  )
+
+  add_fp_unittest(
+    nexttowardf_test
+    SUITE
+      libc-math-smoke-tests
+    SRCS
+      nexttowardf_test.cpp
+    HDRS
+      NextTowardTest.h
+    DEPENDS
+      libc.include.math
+      libc.src.math.nexttowardf
+      libc.src.__support.FPUtil.basic_operations
+      libc.src.__support.FPUtil.fp_bits
+  )
+endif()
+
+add_fp_unittest(
+  nexttowardl_test
+  SUITE
+    libc-math-smoke-tests
+  SRCS
+    nexttowardl_test.cpp
+  HDRS
+    NextTowardTest.h
+  DEPENDS
+    libc.include.math
+    libc.src.math.nexttowardl
+    libc.src.__support.FPUtil.basic_operations
+    libc.src.__support.FPUtil.fp_bits
+)
+
 # TODO(lntue): The current implementation of fputil::general::fma<float> is only
 # correctly rounded for the default rounding mode round-to-nearest tie-to-even.
 add_fp_unittest(

libc/test/src/math/smoke/NextTowardTest.h

@@ -0,0 +1,223 @@
+//===-- Utility class to test different flavors of nexttoward ---*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_TEST_SRC_MATH_NEXTTOWARDTEST_H
+#define LLVM_LIBC_TEST_SRC_MATH_NEXTTOWARDTEST_H
+
+#include "src/__support/CPP/bit.h"
+#include "src/__support/CPP/type_traits.h"
+#include "src/__support/FPUtil/BasicOperations.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "test/UnitTest/FPMatcher.h"
+#include "test/UnitTest/Test.h"
+#include <fenv.h>
+#include <math.h>
+
+#define ASSERT_FP_EQ_WITH_EXCEPTION(result, expected, expected_exception)      \
+  ASSERT_FP_EQ(result, expected);                                              \
+  ASSERT_FP_EXCEPTION(expected_exception);                                     \
+  LIBC_NAMESPACE::fputil::clear_except(FE_ALL_EXCEPT)
+
+#define ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected)                          \
+  ASSERT_FP_EQ_WITH_EXCEPTION(result, expected, FE_INEXACT | FE_UNDERFLOW)
+
+#define ASSERT_FP_EQ_WITH_OVERFLOW(result, expected)                           \
+  ASSERT_FP_EQ_WITH_EXCEPTION(result, expected, FE_INEXACT | FE_OVERFLOW)
+
+template <typename T>
+class NextTowardTestTemplate : public LIBC_NAMESPACE::testing::Test {
+  using FPBits = LIBC_NAMESPACE::fputil::FPBits<T>;
+  using ToFPBits = LIBC_NAMESPACE::fputil::FPBits<long double>;
+  using MantissaWidth = LIBC_NAMESPACE::fputil::MantissaWidth<T>;
+  using UIntType = typename FPBits::UIntType;
+
+  static constexpr int BIT_WIDTH_OF_TYPE =
+      LIBC_NAMESPACE::fputil::FloatProperties<T>::BIT_WIDTH;
+
+  const T zero = T(FPBits::zero());
+  const T neg_zero = T(FPBits::neg_zero());
+  const T inf = T(FPBits::inf());
+  const T neg_inf = T(FPBits::neg_inf());
+  const T nan = T(FPBits::build_quiet_nan(1));
+
+  const long double to_zero = ToFPBits::zero();
+  const long double to_neg_zero = ToFPBits::neg_zero();
+  const long double to_nan = ToFPBits::build_quiet_nan(1);
+
+  const UIntType min_subnormal = FPBits::MIN_SUBNORMAL;
+  const UIntType max_subnormal = FPBits::MAX_SUBNORMAL;
+  const UIntType min_normal = FPBits::MIN_NORMAL;
+  const UIntType max_normal = FPBits::MAX_NORMAL;
+
+public:
+  typedef T (*NextTowardFunc)(T, long double);
+
+  void testNaN(NextTowardFunc func) {
+    ASSERT_FP_EQ(func(nan, 0), nan);
+    ASSERT_FP_EQ(func(0, to_nan), nan);
+  }
+
+  void testBoundaries(NextTowardFunc func) {
+    ASSERT_FP_EQ(func(zero, to_neg_zero), neg_zero);
+    ASSERT_FP_EQ(func(neg_zero, to_zero), zero);
+
+    // 'from' is zero|neg_zero.
+    T x = zero;
+    T result = func(x, 1);
+    UIntType expected_bits = 1;
+    T expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+
+    result = func(x, -1);
+    expected_bits = (UIntType(1) << (BIT_WIDTH_OF_TYPE - 1)) + 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+
+    x = neg_zero;
+    result = func(x, 1);
+    expected_bits = 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+
+    result = func(x, -1);
+    expected_bits = (UIntType(1) << (BIT_WIDTH_OF_TYPE - 1)) + 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+
+    // 'from' is max subnormal value.
+    x = LIBC_NAMESPACE::cpp::bit_cast<T>(max_subnormal);
+    result = func(x, 1);
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(min_normal);
+    ASSERT_FP_EQ(result, expected);
+
+    result = func(x, 0);
+    expected_bits = max_subnormal - 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+
+    x = -x;
+
+    result = func(x, -1);
+    expected_bits = (UIntType(1) << (BIT_WIDTH_OF_TYPE - 1)) + min_normal;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ(result, expected);
+
+    result = func(x, 0);
+    expected_bits =
+        (UIntType(1) << (BIT_WIDTH_OF_TYPE - 1)) + max_subnormal - 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+
+    // 'from' is min subnormal value.
+    x = LIBC_NAMESPACE::cpp::bit_cast<T>(min_subnormal);
+    result = func(x, 1);
+    expected_bits = min_subnormal + 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(func(x, 0), 0);
+
+    x = -x;
+    result = func(x, -1);
+    expected_bits =
+        (UIntType(1) << (BIT_WIDTH_OF_TYPE - 1)) + min_subnormal + 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(func(x, 0), T(-0.0));
+
+    // 'from' is min normal.
+    x = LIBC_NAMESPACE::cpp::bit_cast<T>(min_normal);
+    result = func(x, 0);
+    expected_bits = max_subnormal;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+
+    result = func(x, inf);
+    expected_bits = min_normal + 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ(result, expected);
+
+    x = -x;
+    result = func(x, 0);
+    expected_bits = (UIntType(1) << (BIT_WIDTH_OF_TYPE - 1)) + max_subnormal;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ_WITH_UNDERFLOW(result, expected);
+
+    result = func(x, -inf);
+    expected_bits = (UIntType(1) << (BIT_WIDTH_OF_TYPE - 1)) + min_normal + 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ(result, expected);
+
+    // 'from' is max normal
+    x = LIBC_NAMESPACE::cpp::bit_cast<T>(max_normal);
+    result = func(x, 0);
+    expected_bits = max_normal - 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ(result, expected);
+    ASSERT_FP_EQ_WITH_OVERFLOW(func(x, inf), inf);
+
+    x = -x;
+    result = func(x, 0);
+    expected_bits = (UIntType(1) << (BIT_WIDTH_OF_TYPE - 1)) + max_normal - 1;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ(result, expected);
+    ASSERT_FP_EQ_WITH_OVERFLOW(func(x, -inf), -inf);
+
+    // 'from' is infinity.
+    x = inf;
+    result = func(x, 0);
+    expected_bits = max_normal;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ(result, expected);
+    ASSERT_FP_EQ(func(x, inf), inf);
+
+    x = neg_inf;
+    result = func(x, 0);
+    expected_bits = (UIntType(1) << (BIT_WIDTH_OF_TYPE - 1)) + max_normal;
+    expected = LIBC_NAMESPACE::cpp::bit_cast<T>(expected_bits);
+    ASSERT_FP_EQ(result, expected);
+    ASSERT_FP_EQ(func(x, neg_inf), neg_inf);
+
+    // 'from' is a power of 2.
+    x = T(32.0);
+    result = func(x, 0);
+    FPBits x_bits = FPBits(x);
+    FPBits result_bits = FPBits(result);
+    ASSERT_EQ(result_bits.get_unbiased_exponent(),
+              uint16_t(x_bits.get_unbiased_exponent() - 1));
+    ASSERT_EQ(result_bits.get_mantissa(),
+              (UIntType(1) << MantissaWidth::VALUE) - 1);
+
+    result = func(x, 33.0);
+    result_bits = FPBits(result);
+    ASSERT_EQ(result_bits.get_unbiased_exponent(),
+              x_bits.get_unbiased_exponent());
+    ASSERT_EQ(result_bits.get_mantissa(), x_bits.get_mantissa() + UIntType(1));
+
+    x = -x;
+
+    result = func(x, 0);
+    result_bits = FPBits(result);
+    ASSERT_EQ(result_bits.get_unbiased_exponent(),
+              uint16_t(x_bits.get_unbiased_exponent() - 1));
+    ASSERT_EQ(result_bits.get_mantissa(),
+              (UIntType(1) << MantissaWidth::VALUE) - 1);
+
+    result = func(x, -33.0);
+    result_bits = FPBits(result);
+    ASSERT_EQ(result_bits.get_unbiased_exponent(),
+              x_bits.get_unbiased_exponent());
+    ASSERT_EQ(result_bits.get_mantissa(), x_bits.get_mantissa() + UIntType(1));
+  }
+};
+
+#define LIST_NEXTTOWARD_TESTS(T, func)                                         \
+  using LlvmLibcNextTowardTest = NextTowardTestTemplate<T>;                    \
+  TEST_F(LlvmLibcNextTowardTest, TestNaN) { testNaN(&func); }                  \
+  TEST_F(LlvmLibcNextTowardTest, TestBoundaries) { testBoundaries(&func); }
+
+#endif // LLVM_LIBC_TEST_SRC_MATH_NEXTTOWARDTEST_H

libc/test/src/math/smoke/nexttoward_test.cpp

@@ -0,0 +1,13 @@
+//===-- Unittests for nexttoward ------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "NextTowardTest.h"
+
+#include "src/math/nexttoward.h"
+
+LIST_NEXTTOWARD_TESTS(double, LIBC_NAMESPACE::nexttoward)

libc/test/src/math/smoke/nexttowardf_test.cpp

@@ -0,0 +1,13 @@
+//===-- Unittests for nexttowardf -----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "NextTowardTest.h"
+
+#include "src/math/nexttowardf.h"
+
+LIST_NEXTTOWARD_TESTS(float, LIBC_NAMESPACE::nexttowardf)

libc/test/src/math/smoke/nexttowardl_test.cpp

@@ -0,0 +1,13 @@
+//===-- Unittests for nexttowardl -----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "NextTowardTest.h"
+
+#include "src/math/nexttowardl.h"
+
+LIST_NEXTTOWARD_TESTS(long double, LIBC_NAMESPACE::nexttowardl)

utils/bazel/llvm-project-overlay/libc/BUILD.bazel

@@ -1872,6 +1872,12 @@ libc_math_function(name = "nextafterf")
 
 libc_math_function(name = "nextafterl")
 
+libc_math_function(name = "nexttoward")
+
+libc_math_function(name = "nexttowardf")
+
+libc_math_function(name = "nexttowardl")
+
 libc_math_function(name = "scalbn")
 
 libc_math_function(name = "scalbnf")