diff --git a/docs/source/api/basic_functions.rst b/docs/source/api/basic_functions.rst
index 63d0e20..58cd2bb 100644
--- a/docs/source/api/basic_functions.rst
+++ b/docs/source/api/basic_functions.rst
@@ -39,6 +39,10 @@ Basic functions
 .. doxygenfunction:: fmod(const T1, const T2)
    :project: gcem
 
+.. _hypot-func-ref:
+.. doxygenfunction:: hypot(const T1, const T2)
+   :project: gcem
+
 .. _log-function-reference:
 .. doxygenfunction:: log(const T)
    :project: gcem
diff --git a/docs/source/api/math_index.rst b/docs/source/api/math_index.rst
index 51a1844..5d06871 100644
--- a/docs/source/api/math_index.rst
+++ b/docs/source/api/math_index.rst
@@ -61,6 +61,8 @@ Mathematical functions
 +---------------------------------------+----------------------------------------------------+
 | :ref:`fmod <fmod-func-ref>`           | remainder of division function                     |
 +---------------------------------------+----------------------------------------------------+
+| :ref:`hypot <hypot-func-ref>`         | Pythagorean addition function                      |
++---------------------------------------+----------------------------------------------------+
 | :ref:`log <log-function-reference>`   | natural logarithm function                         |
 +---------------------------------------+----------------------------------------------------+
 | :ref:`log1p <log1p-func-ref>`         | natural logarithm 1 plus argument function         |
diff --git a/include/gcem.hpp b/include/gcem.hpp
index 6aa367d..cb28ff0 100644
--- a/include/gcem.hpp
+++ b/include/gcem.hpp
@@ -46,6 +46,7 @@ namespace gcem
     #include "gcem_incl/min.hpp"
     #include "gcem_incl/sqrt.hpp"
     #include "gcem_incl/inv_sqrt.hpp"
+    #include "gcem_incl/hypot.hpp"
 
     #include "gcem_incl/find_exponent.hpp"
     #include "gcem_incl/find_fraction.hpp"
diff --git a/include/gcem_incl/gcem_options.hpp b/include/gcem_incl/gcem_options.hpp
index f26eaf8..cd2747c 100644
--- a/include/gcem_incl/gcem_options.hpp
+++ b/include/gcem_incl/gcem_options.hpp
@@ -53,7 +53,7 @@
 #endif
 
 #ifndef GCEM_VERSION_MINOR
-    #define GCEM_VERSION_MINOR 15
+    #define GCEM_VERSION_MINOR 16
 #endif
 
 #ifndef GCEM_VERSION_PATCH
diff --git a/include/gcem_incl/hypot.hpp b/include/gcem_incl/hypot.hpp
new file mode 100644
index 0000000..5a805ed
--- /dev/null
+++ b/include/gcem_incl/hypot.hpp
@@ -0,0 +1,90 @@
+/*################################################################################
+  ##
+  ##   Copyright (C) 2016-2022 Keith O'Hara
+  ##
+  ##   This file is part of the GCE-Math C++ library.
+  ##
+  ##   Licensed under the Apache License, Version 2.0 (the "License");
+  ##   you may not use this file except in compliance with the License.
+  ##   You may obtain a copy of the License at
+  ##
+  ##       http://www.apache.org/licenses/LICENSE-2.0
+  ##
+  ##   Unless required by applicable law or agreed to in writing, software
+  ##   distributed under the License is distributed on an "AS IS" BASIS,
+  ##   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+  ##   See the License for the specific language governing permissions and
+  ##   limitations under the License.
+  ##
+  ################################################################################*/
+
+/*
+ * compile-time Pythagorean addition function
+ */
+
+// see: https://en.wikipedia.org/wiki/Pythagorean_addition
+
+#ifndef _gcem_hypot_HPP
+#define _gcem_hypot_HPP
+
+namespace internal
+{
+
+template<typename T>
+constexpr
+T
+hypot_compute(const T x, const T ydx)
+noexcept
+{
+    return abs(x) * sqrt( T(1) + (ydx * ydx) );
+}
+
+template<typename T>
+constexpr
+T
+hypot_vals_check(const T x, const T y)
+noexcept
+{
+    return( any_nan(x, y) ? \
+                GCLIM<T>::quiet_NaN() :
+            //
+            any_inf(x,y) ? \
+                GCLIM<T>::infinity() :
+            // indistinguishable from zero or one
+            GCLIM<T>::min() > abs(x) ? \
+                abs(y) :
+            GCLIM<T>::min() > abs(y) ? \
+                abs(x) :
+            // else
+            hypot_compute(x, y/x) );
+}
+
+template<typename T1, typename T2, typename TC = common_return_t<T1,T2>>
+constexpr
+TC
+hypot_type_check(const T1 x, const T2 y)
+noexcept
+{
+    return hypot_vals_check(static_cast<TC>(x),static_cast<TC>(y));
+}
+
+}
+
+/**
+ * Compile-time Pythagorean addition function
+ *
+ * @param x a real-valued input.
+ * @param y a real-valued input.
+ * @return Computes \f$ x \oplus y = \sqrt{x^2 + y^2} \f$.
+ */
+
+template<typename T1, typename T2>
+constexpr
+common_return_t<T1,T2>
+hypot(const T1 x, const T2 y)
+noexcept
+{
+    return internal::hypot_type_check(x,y);
+}
+
+#endif
diff --git a/tests/Makefile b/tests/Makefile
index 664806d..f67cf5d 100644
--- a/tests/Makefile
+++ b/tests/Makefile
@@ -98,6 +98,9 @@ fmod:
 gcd:
 	$(GCEM_MAKE_CALL)
 
+hypot:
+	$(GCEM_MAKE_CALL)
+
 incomplete_beta:
 	$(GCEM_MAKE_CALL)
 
diff --git a/tests/hypot.cpp b/tests/hypot.cpp
new file mode 100644
index 0000000..1bfc9f1
--- /dev/null
+++ b/tests/hypot.cpp
@@ -0,0 +1,75 @@
+/*################################################################################
+  ##
+  ##   Copyright (C) 2016-2022 Keith O'Hara
+  ##
+  ##   This file is part of the GCE-Math C++ library.
+  ##
+  ##   Licensed under the Apache License, Version 2.0 (the "License");
+  ##   you may not use this file except in compliance with the License.
+  ##   You may obtain a copy of the License at
+  ##
+  ##       http://www.apache.org/licenses/LICENSE-2.0
+  ##
+  ##   Unless required by applicable law or agreed to in writing, software
+  ##   distributed under the License is distributed on an "AS IS" BASIS,
+  ##   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+  ##   See the License for the specific language governing permissions and
+  ##   limitations under the License.
+  ##
+  ################################################################################*/
+
+#define TEST_PRINT_PRECISION_1 6
+#define TEST_PRINT_PRECISION_2 18
+
+#include "gcem_tests.hpp"
+
+int main()
+{
+    print_begin("hypot");
+
+    //
+
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      0.0L,           0.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,     -0.0L,           0.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      0.0L,          -0.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,     -0.0L,          -0.0L);
+
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      0.2L,           0.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,     -0.2L,           0.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      0.001L,         0.001L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      0.49L,          0.49L);
+
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,     -0.5L,          -0.5L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      0.5L,          -0.5L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,     -0.5L,           0.5L);
+
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      9.6L,           8.4L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      1.0L,           0.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      0.0L,           1.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,     -1.0L,           0.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      0.0L,          -1.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      1.0L,           3.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,     -5.0L,           2.5L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,  -1000.0L,          -0.001L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,      0.1337L,  -123456.0L);
+
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot, TEST_POSINF,        2.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,        2.0L, TEST_POSINF);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot, TEST_POSINF, TEST_POSINF);
+
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot, TEST_NEGINF,        2.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,        2.0L, TEST_NEGINF);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot, TEST_NEGINF, TEST_NEGINF);
+
+    //
+
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot, TEST_NAN,     1.0L);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot,     1.0L, TEST_NAN);
+    GCEM_TEST_COMPARE_VALS(gcem::hypot,std::hypot, TEST_NAN, TEST_NAN);
+
+    //
+
+    print_final("hypot");
+
+    return 0;
+}