add Chapter14

Chapter14/sequencer/libs/etl/include/etl/gcd.h

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+///\file
+
+/******************************************************************************
+The MIT License(MIT)
+
+Embedded Template Library.
+https://github.com/ETLCPP/etl
+https://www.etlcpp.com
+
+Copyright(c) 2024 John Wellbelove
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files(the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and / or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions :
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+******************************************************************************/
+
+#ifndef ETL_GDC_INCLUDED
+#define ETL_GDC_INCLUDED
+
+#include "type_traits.h"
+#include "absolute.h"
+#include "static_assert.h"
+
+namespace etl
+{
+  //***************************************************************************
+  // Greatest Common Divisor.
+  // For unsigned types.
+  //***************************************************************************
+  template <typename T>
+  ETL_NODISCARD
+  ETL_CONSTEXPR14
+  typename etl::enable_if<etl::is_unsigned<T>::value, T>::type
+    gcd(T a, T b) ETL_NOEXCEPT
+  {
+    ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Integral type required");
+
+    if ((a == 0 || b == 0))
+    {
+      return (a + b);
+    }
+
+    while (b != 0) 
+    {
+      T t = b;
+      b = a % b;
+      a = t;
+    }
+    
+    return a;
+  }
+
+  //***************************************************************************
+  // Greatest Common Divisor.
+  // For signed types.
+  //***************************************************************************
+  template <typename T>
+  ETL_NODISCARD
+  ETL_CONSTEXPR14
+  typename etl::enable_if<etl::is_signed<T>::value, T>::type
+    gcd(T a, T b) ETL_NOEXCEPT
+  {
+    ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Integral type required");
+
+    typedef typename etl::make_unsigned<T>::type utype;
+
+    utype ua = etl::absolute_unsigned(a);
+    utype ub = etl::absolute_unsigned(b);
+
+    return static_cast<T>(gcd(ua, ub));
+  }
+
+#if ETL_USING_CPP11
+  #if ETL_HAS_INITIALIZER_LIST
+  //***************************************************************************
+  // Greatest Common Divisor.
+  // Non-recursive, using an initializer_list.
+  // Top level variadic function.
+  //***************************************************************************
+  template<typename T, typename... TRest>
+  ETL_NODISCARD
+  ETL_CONSTEXPR14
+  T gcd(T first, TRest... rest) ETL_NOEXCEPT
+  {
+    T result = first;
+
+    for (T value : {rest...})
+    {
+      result = gcd(result, value);
+
+      if (result == 1)
+      {
+        // Early termination: if the GCD is one, it will remain one
+        // no matter what other numbers are processed.
+        return 1;
+      }
+    }
+
+    return result;
+  }
+  #else
+  //***************************************************************************
+  // Greatest Common Divisor.
+  // Recursive.
+  // Top level variadic function.
+  //***************************************************************************
+  template<typename T, typename... TRest>
+  ETL_NODISCARD
+  ETL_CONSTEXPR14
+  T gcd(T a, T b, TRest... rest) ETL_NOEXCEPT
+  {
+    T gcd_ab = gcd(a, b);
+
+    if (gcd_ab == 1)
+    {
+      // Early termination: if the GCD is one, it will remain one
+      // no matter what other numbers are processed.
+      return 1;
+    }
+    else
+    {
+      return gcd(gcd_ab, rest...);
+    }
+  }
+  #endif
+#endif
+}
+
+#endif
+