diff --git a/libc/config/linux/aarch64/entrypoints.txt b/libc/config/linux/aarch64/entrypoints.txt
--- a/libc/config/linux/aarch64/entrypoints.txt
+++ b/libc/config/linux/aarch64/entrypoints.txt
@@ -32,6 +32,9 @@
     libc.src.math.floor
     libc.src.math.floorf
     libc.src.math.floorl
+    libc.src.math.fmax
+    libc.src.math.fmaxf
+    libc.src.math.fmaxl
     libc.src.math.fmin
     libc.src.math.fminf
     libc.src.math.fminl
diff --git a/libc/config/linux/api.td b/libc/config/linux/api.td
--- a/libc/config/linux/api.td
+++ b/libc/config/linux/api.td
@@ -163,6 +163,9 @@
    "floor",
    "floorf",
    "floorl",
+   "fmax",
+   "fmaxf",
+   "fmaxl",
    "fmin",
    "fminf",
    "fminl",
diff --git a/libc/config/linux/x86_64/entrypoints.txt b/libc/config/linux/x86_64/entrypoints.txt
--- a/libc/config/linux/x86_64/entrypoints.txt
+++ b/libc/config/linux/x86_64/entrypoints.txt
@@ -68,6 +68,9 @@
     libc.src.math.fmin
     libc.src.math.fminf
     libc.src.math.fminl
+    libc.src.math.fmax
+    libc.src.math.fmaxf
+    libc.src.math.fmaxl
     libc.src.math.frexp
     libc.src.math.frexpf
     libc.src.math.frexpl
diff --git a/libc/spec/stdc.td b/libc/spec/stdc.td
--- a/libc/spec/stdc.td
+++ b/libc/spec/stdc.td
@@ -209,6 +209,10 @@
           FunctionSpec<"fminf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
           FunctionSpec<"fminl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoubleType>]>,
 
+          FunctionSpec<"fmax", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,
+          FunctionSpec<"fmaxf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<FloatType>]>,
+          FunctionSpec<"fmaxl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<LongDoubleType>]>,
+
           FunctionSpec<"frexp", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<IntPtr>]>,
           FunctionSpec<"frexpf", RetValSpec<FloatType>, [ArgSpec<FloatType>, ArgSpec<IntPtr>]>,
           FunctionSpec<"frexpl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>, ArgSpec<IntPtr>]>,
diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt
--- a/libc/src/math/CMakeLists.txt
+++ b/libc/src/math/CMakeLists.txt
@@ -449,3 +449,39 @@
   COMPILE_OPTIONS
     -O2
 )
+
+add_entrypoint_object(
+  fmax
+  SRCS
+    fmax.cpp
+  HDRS
+    fmax.h
+  DEPENDS
+    libc.utils.FPUtil.fputil
+  COMPILE_OPTIONS
+    -O2
+)
+
+add_entrypoint_object(
+  fmaxf
+  SRCS
+    fmaxf.cpp
+  HDRS
+    fmaxf.h
+  DEPENDS
+    libc.utils.FPUtil.fputil
+  COMPILE_OPTIONS
+    -O2
+)
+
+add_entrypoint_object(
+  fmaxl
+  SRCS
+    fmaxl.cpp
+  HDRS
+    fmaxl.h
+  DEPENDS
+    libc.utils.FPUtil.fputil
+  COMPILE_OPTIONS
+    -O2
+)
diff --git a/libc/src/math/fmax.h b/libc/src/math/fmax.h
new file mode 100644
--- /dev/null
+++ b/libc/src/math/fmax.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for fmax --------------------------*- 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_FMAX_H
+#define LLVM_LIBC_SRC_MATH_FMAX_H
+
+namespace __llvm_libc {
+
+double fmax(double x, double y);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_FMAX_H
diff --git a/libc/src/math/fmax.cpp b/libc/src/math/fmax.cpp
new file mode 100644
--- /dev/null
+++ b/libc/src/math/fmax.cpp
@@ -0,0 +1,18 @@
+//===-- Implementation of fmax 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/__support/common.h"
+#include "utils/FPUtil/BasicOperations.h"
+
+namespace __llvm_libc {
+
+double LLVM_LIBC_ENTRYPOINT(fmax)(double x, double y) {
+  return fputil::fmax(x, y);
+}
+
+} // namespace __llvm_libc
diff --git a/libc/src/math/fmaxf.h b/libc/src/math/fmaxf.h
new file mode 100644
--- /dev/null
+++ b/libc/src/math/fmaxf.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for fmaxf -------------------------*- 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_FMAXF_H
+#define LLVM_LIBC_SRC_MATH_FMAXF_H
+
+namespace __llvm_libc {
+
+float fmaxf(float x, float y);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_FMAXF_H
diff --git a/libc/src/math/fmaxf.cpp b/libc/src/math/fmaxf.cpp
new file mode 100644
--- /dev/null
+++ b/libc/src/math/fmaxf.cpp
@@ -0,0 +1,18 @@
+//===-- Implementation of fmaxf 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/__support/common.h"
+#include "utils/FPUtil/BasicOperations.h"
+
+namespace __llvm_libc {
+
+float LLVM_LIBC_ENTRYPOINT(fmaxf)(float x, float y) {
+  return fputil::fmax(x, y);
+}
+
+} // namespace __llvm_libc
diff --git a/libc/src/math/fmaxl.h b/libc/src/math/fmaxl.h
new file mode 100644
--- /dev/null
+++ b/libc/src/math/fmaxl.h
@@ -0,0 +1,18 @@
+//===-- Implementation header for fmaxl -------------------------*- 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_FMAXL_H
+#define LLVM_LIBC_SRC_MATH_FMAXL_H
+
+namespace __llvm_libc {
+
+long double fmaxl(long double x, long double y);
+
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_SRC_MATH_FMAXL_H
diff --git a/libc/src/math/fmaxl.cpp b/libc/src/math/fmaxl.cpp
new file mode 100644
--- /dev/null
+++ b/libc/src/math/fmaxl.cpp
@@ -0,0 +1,18 @@
+//===-- Implementation of fmaxl 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/__support/common.h"
+#include "utils/FPUtil/BasicOperations.h"
+
+namespace __llvm_libc {
+
+long double LLVM_LIBC_ENTRYPOINT(fmaxl)(long double x, long double y) {
+  return fputil::fmax(x, y);
+}
+
+} // namespace __llvm_libc
diff --git a/libc/test/src/math/CMakeLists.txt b/libc/test/src/math/CMakeLists.txt
--- a/libc/test/src/math/CMakeLists.txt
+++ b/libc/test/src/math/CMakeLists.txt
@@ -472,4 +472,40 @@
     libc.include.math
     libc.src.math.fminl
     libc.utils.FPUtil.fputil
-)
\ No newline at end of file
+)
+
+add_math_unittest(
+  fmaxf_test
+  SUITE
+    libc_math_unittests
+  SRCS
+    fmaxf_test.cpp
+  DEPENDS
+    libc.include.math
+    libc.src.math.fmaxf
+    libc.utils.FPUtil.fputil
+)
+
+add_math_unittest(
+  fmax_test
+  SUITE
+    libc_math_unittests
+  SRCS
+    fmax_test.cpp
+  DEPENDS
+    libc.include.math
+    libc.src.math.fmax
+    libc.utils.FPUtil.fputil
+)
+
+add_math_unittest(
+  fmaxl_test
+  SUITE
+    libc_math_unittests
+  SRCS
+    fmaxl_test.cpp
+  DEPENDS
+    libc.include.math
+    libc.src.math.fmaxl
+    libc.utils.FPUtil.fputil
+)
diff --git a/libc/test/src/math/fmax_test.cpp b/libc/test/src/math/fmax_test.cpp
new file mode 100644
--- /dev/null
+++ b/libc/test/src/math/fmax_test.cpp
@@ -0,0 +1,73 @@
+//===-- Unittests for fmax -----------------------------------------------===//
+//
+// 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 "include/math.h"
+#include "src/math/fmax.h"
+#include "utils/FPUtil/FPBits.h"
+#include "utils/UnitTest/Test.h"
+
+using FPBits = __llvm_libc::fputil::FPBits<double>;
+
+double nan = FPBits::buildNaN(1);
+double inf = FPBits::inf();
+double negInf = FPBits::negInf();
+
+TEST(FmaxTest, NaNArg) {
+  EXPECT_EQ(inf, __llvm_libc::fmax(nan, inf));
+  EXPECT_EQ(negInf, __llvm_libc::fmax(negInf, nan));
+  EXPECT_EQ(0.0, __llvm_libc::fmax(nan, 0.0));
+  EXPECT_EQ(-0.0, __llvm_libc::fmax(-0.0, nan));
+  EXPECT_EQ(-1.2345, __llvm_libc::fmax(nan, -1.2345));
+  EXPECT_EQ(1.2345, __llvm_libc::fmax(1.2345, nan));
+  EXPECT_NE(isnan(__llvm_libc::fmax(nan, nan)), 0);
+}
+
+TEST(FmaxTest, InfArg) {
+  EXPECT_EQ(inf, __llvm_libc::fmax(negInf, inf));
+  EXPECT_EQ(inf, __llvm_libc::fmax(inf, 0.0));
+  EXPECT_EQ(inf, __llvm_libc::fmax(-0.0, inf));
+  EXPECT_EQ(inf, __llvm_libc::fmax(inf, 1.2345));
+  EXPECT_EQ(inf, __llvm_libc::fmax(-1.2345, inf));
+}
+
+TEST(FmaxTest, NegInfArg) {
+  EXPECT_EQ(inf, __llvm_libc::fmax(inf, negInf));
+  EXPECT_EQ(0.0, __llvm_libc::fmax(negInf, 0.0));
+  EXPECT_EQ(-0.0, __llvm_libc::fmax(-0.0, negInf));
+  EXPECT_EQ(-1.2345, __llvm_libc::fmax(negInf, -1.2345));
+  EXPECT_EQ(1.2345, __llvm_libc::fmax(1.2345, negInf));
+}
+
+TEST(FmaxTest, BothZero) {
+  EXPECT_EQ(0.0, __llvm_libc::fmax(0.0, 0.0));
+  EXPECT_EQ(0.0, __llvm_libc::fmax(-0.0, 0.0));
+  EXPECT_EQ(0.0, __llvm_libc::fmax(0.0, -0.0));
+  EXPECT_EQ(-0.0, __llvm_libc::fmax(-0.0, -0.0));
+}
+
+TEST(FmaxTest, InDoubleRange) {
+  using UIntType = FPBits::UIntType;
+  constexpr UIntType count = 10000001;
+  constexpr UIntType step = UIntType(-1) / count;
+  for (UIntType i = 0, v = 0, w = UIntType(-1); i <= count;
+       ++i, v += step, w -= step) {
+    double x = FPBits(v), y = FPBits(w);
+    if (isnan(x) || isinf(x))
+      continue;
+    if (isnan(y) || isinf(y))
+      continue;
+    if ((x == 0) && (y == 0))
+      continue;
+
+    if (x > y) {
+      ASSERT_EQ(x, __llvm_libc::fmax(x, y));
+    } else {
+      ASSERT_EQ(y, __llvm_libc::fmax(x, y));
+    }
+  }
+}
diff --git a/libc/test/src/math/fmaxf_test.cpp b/libc/test/src/math/fmaxf_test.cpp
new file mode 100644
--- /dev/null
+++ b/libc/test/src/math/fmaxf_test.cpp
@@ -0,0 +1,73 @@
+//===-- Unittests for fmaxf -----------------------------------------------===//
+//
+// 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 "include/math.h"
+#include "src/math/fmaxf.h"
+#include "utils/FPUtil/FPBits.h"
+#include "utils/UnitTest/Test.h"
+
+using FPBits = __llvm_libc::fputil::FPBits<float>;
+
+float nan = FPBits::buildNaN(1);
+float inf = FPBits::inf();
+float negInf = FPBits::negInf();
+
+TEST(FmaxfTest, NaNArg) {
+  EXPECT_EQ(inf, __llvm_libc::fmaxf(nan, inf));
+  EXPECT_EQ(negInf, __llvm_libc::fmaxf(negInf, nan));
+  EXPECT_EQ(0.0f, __llvm_libc::fmaxf(nan, 0.0f));
+  EXPECT_EQ(-0.0f, __llvm_libc::fmaxf(-0.0f, nan));
+  EXPECT_EQ(-1.2345f, __llvm_libc::fmaxf(nan, -1.2345f));
+  EXPECT_EQ(1.2345f, __llvm_libc::fmaxf(1.2345f, nan));
+  EXPECT_NE(isnan(__llvm_libc::fmaxf(nan, nan)), 0);
+}
+
+TEST(FmaxfTest, InfArg) {
+  EXPECT_EQ(inf, __llvm_libc::fmaxf(negInf, inf));
+  EXPECT_EQ(inf, __llvm_libc::fmaxf(inf, 0.0f));
+  EXPECT_EQ(inf, __llvm_libc::fmaxf(-0.0f, inf));
+  EXPECT_EQ(inf, __llvm_libc::fmaxf(inf, 1.2345f));
+  EXPECT_EQ(inf, __llvm_libc::fmaxf(-1.2345f, inf));
+}
+
+TEST(FmaxfTest, NegInfArg) {
+  EXPECT_EQ(inf, __llvm_libc::fmaxf(inf, negInf));
+  EXPECT_EQ(0.0f, __llvm_libc::fmaxf(negInf, 0.0f));
+  EXPECT_EQ(-0.0f, __llvm_libc::fmaxf(-0.0f, negInf));
+  EXPECT_EQ(-1.2345f, __llvm_libc::fmaxf(negInf, -1.2345f));
+  EXPECT_EQ(1.2345f, __llvm_libc::fmaxf(1.2345f, negInf));
+}
+
+TEST(FmaxfTest, BothZero) {
+  EXPECT_EQ(0.0f, __llvm_libc::fmaxf(0.0f, 0.0f));
+  EXPECT_EQ(0.0f, __llvm_libc::fmaxf(-0.0f, 0.0f));
+  EXPECT_EQ(0.0f, __llvm_libc::fmaxf(0.0f, -0.0f));
+  EXPECT_EQ(-0.0f, __llvm_libc::fmaxf(-0.0f, -0.0f));
+}
+
+TEST(FmaxfTest, InFloatRange) {
+  using UIntType = FPBits::UIntType;
+  constexpr UIntType count = 10000001;
+  constexpr UIntType step = UIntType(-1) / count;
+  for (UIntType i = 0, v = 0, w = UIntType(-1); i <= count;
+       ++i, v += step, w -= step) {
+    float x = FPBits(v), y = FPBits(w);
+    if (isnan(x) || isinf(x))
+      continue;
+    if (isnan(y) || isinf(y))
+      continue;
+    if ((x == 0) && (y == 0))
+      continue;
+
+    if (x > y) {
+      ASSERT_EQ(x, __llvm_libc::fmaxf(x, y));
+    } else {
+      ASSERT_EQ(y, __llvm_libc::fmaxf(x, y));
+    }
+  }
+}
diff --git a/libc/test/src/math/fmaxl_test.cpp b/libc/test/src/math/fmaxl_test.cpp
new file mode 100644
--- /dev/null
+++ b/libc/test/src/math/fmaxl_test.cpp
@@ -0,0 +1,73 @@
+//===-- Unittests for fmaxl -----------------------------------------------===//
+//
+// 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 "include/math.h"
+#include "src/math/fmaxl.h"
+#include "utils/FPUtil/FPBits.h"
+#include "utils/UnitTest/Test.h"
+
+using FPBits = __llvm_libc::fputil::FPBits<long double>;
+
+long double nan = FPBits::buildNaN(1);
+long double inf = FPBits::inf();
+long double negInf = FPBits::negInf();
+
+TEST(FmaxlTest, NaNArg) {
+  EXPECT_EQ(inf, __llvm_libc::fmaxl(nan, inf));
+  EXPECT_EQ(negInf, __llvm_libc::fmaxl(negInf, nan));
+  EXPECT_EQ(0.0L, __llvm_libc::fmaxl(nan, 0.0L));
+  EXPECT_EQ(-0.0L, __llvm_libc::fmaxl(-0.0L, nan));
+  EXPECT_EQ(-1.2345L, __llvm_libc::fmaxl(nan, -1.2345L));
+  EXPECT_EQ(1.2345L, __llvm_libc::fmaxl(1.2345L, nan));
+  EXPECT_NE(isnan(__llvm_libc::fmaxl(nan, nan)), 0);
+}
+
+TEST(FmaxlTest, InfArg) {
+  EXPECT_EQ(inf, __llvm_libc::fmaxl(negInf, inf));
+  EXPECT_EQ(inf, __llvm_libc::fmaxl(inf, 0.0L));
+  EXPECT_EQ(inf, __llvm_libc::fmaxl(-0.0L, inf));
+  EXPECT_EQ(inf, __llvm_libc::fmaxl(inf, 1.2345L));
+  EXPECT_EQ(inf, __llvm_libc::fmaxl(-1.2345L, inf));
+}
+
+TEST(FmaxlTest, NegInfArg) {
+  EXPECT_EQ(inf, __llvm_libc::fmaxl(inf, negInf));
+  EXPECT_EQ(0.0L, __llvm_libc::fmaxl(negInf, 0.0L));
+  EXPECT_EQ(-0.0L, __llvm_libc::fmaxl(-0.0L, negInf));
+  EXPECT_EQ(-1.2345L, __llvm_libc::fmaxl(negInf, -1.2345L));
+  EXPECT_EQ(1.2345L, __llvm_libc::fmaxl(1.2345L, negInf));
+}
+
+TEST(FmaxlTest, BothZero) {
+  EXPECT_EQ(0.0L, __llvm_libc::fmaxl(0.0L, 0.0L));
+  EXPECT_EQ(0.0L, __llvm_libc::fmaxl(-0.0L, 0.0L));
+  EXPECT_EQ(0.0L, __llvm_libc::fmaxl(0.0L, -0.0L));
+  EXPECT_EQ(-0.0L, __llvm_libc::fmaxl(-0.0L, -0.0L));
+}
+
+TEST(FmaxlTest, InLongDoubleRange) {
+  using UIntType = FPBits::UIntType;
+  constexpr UIntType count = 10000001;
+  constexpr UIntType step = UIntType(-1) / count;
+  for (UIntType i = 0, v = 0, w = UIntType(-1); i <= count;
+       ++i, v += step, w -= step) {
+    long double x = FPBits(v), y = FPBits(w);
+    if (isnan(x) || isinf(x))
+      continue;
+    if (isnan(y) || isinf(y))
+      continue;
+    if ((x == 0) && (y == 0))
+      continue;
+
+    if (x > y) {
+      ASSERT_EQ(x, __llvm_libc::fmaxl(x, y));
+    } else {
+      ASSERT_EQ(y, __llvm_libc::fmaxl(x, y));
+    }
+  }
+}
diff --git a/libc/utils/FPUtil/BasicOperations.h b/libc/utils/FPUtil/BasicOperations.h
--- a/libc/utils/FPUtil/BasicOperations.h
+++ b/libc/utils/FPUtil/BasicOperations.h
@@ -43,6 +43,25 @@
   }
 }
 
+template <typename T,
+          cpp::EnableIfType<cpp::IsFloatingPointType<T>::Value, int> = 0>
+static inline T fmax(T x, T y) {
+  FPBits<T> bitx(x), bity(y);
+
+  if (bitx.isNaN()) {
+    return y;
+  } else if (bity.isNaN()) {
+    return x;
+  } else if (bitx.sign != bity.sign) {
+    // To make sure that fmax(+0, -0) == +0 == fmax(-0, +0), whenever x and
+    // y has different signs and both are not NaNs, we return the number
+    // with positive sign.
+    return (bitx.sign ? y : x);
+  } else {
+    return (x > y ? x : y);
+  }
+}
+
 } // namespace fputil
 } // namespace __llvm_libc