text: /*
   * Copyright (c) 2017 ARM Limited.
   *
   * SPDX-License-Identifier: MIT
   *
   * 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 __ARM_COMPUTE_TEST_VALIDATION_FIXEDPOINT_H__
  #define __ARM_COMPUTE_TEST_VALIDATION_FIXEDPOINT_H__
  
  #include "Utils.h"
  
  #include <cassert>
  #include <cstdint>
  #include <cstdlib>
  #include <limits>
  #include <string>
  #include <type_traits>
  
  namespace arm_compute
  {
  namespace test
  {
  namespace fixed_point_arithmetic
  {
  namespace detail
  {
  // Forward declare structs
  struct functions;
  template <typename T>
  struct constant_expr;
  }
  
  /** Fixed point traits */
  namespace traits
  {
  // Promote types
  // *INDENT-OFF*
  // clang-format off
  template <typename T> struct promote { };
  template <> struct promote<uint8_t> { using type = uint16_t; };
  template <> struct promote<int8_t> { using type = int16_t; };
  template <> struct promote<uint16_t> { using type = uint32_t; };
  template <> struct promote<int16_t> { using type = int32_t; };
  template <> struct promote<uint32_t> { using type = uint64_t; };
  template <> struct promote<int32_t> { using type = int64_t; };
  template <> struct promote<uint64_t> { using type = uint64_t; };
  template <> struct promote<int64_t> { using type = int64_t; };
  // clang-format on
  // *INDENT-ON*
  }
  
  /** Strongly typed enum class representing the overflow policy */
  enum class OverflowPolicy
  {
      WRAP,    /**< Wrap policy */
      SATURATE /**< Saturate policy */
  };
  /** Strongly typed enum class representing the rounding policy */
  enum class RoundingPolicy
  {
      TO_ZERO,        /**< Round to zero policy */
      TO_NEAREST_EVEN /**< Round to nearest even policy */
  };
  
  /** Arbitrary fixed-point arithmetic class */
  template <typename T>
  class fixed_point
  {
  public:
      // Static Checks
      static_assert(std::is_integral<T>::value, "Type is not an integer");
  
      // Friends
      friend struct detail::functions;
      friend struct detail::constant_expr<T>;
  
      /** Constructor (from different fixed point type)
       *
       * @param[in] val Fixed point
       * @param[in] p   Fixed point precision
       */
      template <typename U>
      fixed_point(fixed_point<U> val, uint8_t p)
          : _value(0), _fixed_point_position(p)
      {
          assert(p > 0 && p < std::numeric_limits<T>::digits);
          T v = 0;
  
          if(std::numeric_limits<T>::digits < std::numeric_limits<U>::digits)
          {
              val.rescale(p);
              v = detail::constant_expr<T>::saturate_cast(val.raw());
          }
          else
          {
              auto v_cast = static_cast<fixed_point<T>>(val);
              v_cast.rescale(p);
              v = v_cast.raw();
          }
          _value = static_cast<T>(v);
      }
      /** Constructor (from integer)
       *
       * @param[in] val    Integer value to be represented as fixed point
       * @param[in] p      Fixed point precision
       * @param[in] is_raw If true val is a raw fixed point value else an integer
       */
      template <typename U, typename = typename std::enable_if<std::is_integral<U>::value>::type>
      fixed_point(U val, uint8_t p, bool is_raw = false)
          : _value(val << p), _fixed_point_position(p)
      {
          if(is_raw)
          {
              _value = val;
          }
      }
      /** Constructor (from float)
       *
       * @param[in] val Float value to be represented as fixed point
       * @param[in] p   Fixed point precision
       */
      fixed_point(float val, uint8_t p)
          : _value(detail::constant_expr<T>::to_fixed(val, p)), _fixed_point_position(p)
      {
          assert(p > 0 && p < std::numeric_limits<T>::digits);
      }
      /** Constructor (from float string)
       *
       * @param[in] str Float string to be represented as fixed point
       * @param[in] p   Fixed point precision
       */
      fixed_point(std::string str, uint8_t p)
          : _value(detail::constant_expr<T>::to_fixed(arm_compute::test::cpp11::stof(str), p)), _fixed_point_position(p)
      {
          assert(p > 0 && p < std::numeric_limits<T>::digits);
      }
      /** Default copy constructor */
      fixed_point &operator=(const fixed_point &) = default;
      /** Default move constructor */
      fixed_point &operator=(fixed_point &&) = default;
      /** Default copy assignment operator */
      fixed_point(const fixed_point &) = default;
      /** Default move assignment operator */
      fixed_point(fixed_point &&) = default;
  
      /** Float conversion operator
       *
       * @return Float representation of fixed point
       */
      operator float() const
      {
          return detail::constant_expr<T>::to_float(_value, _fixed_point_position);
      }
      /** Integer conversion operator
       *
       * @return Integer representation of fixed point
       */
      template <typename U, typename = typename std::enable_if<std::is_integral<T>::value>::type>
      operator U() const
      {
          return detail::constant_expr<T>::to_int(_value, _fixed_point_position);
      }
      /** Convert to different fixed point of different type but same precision
       *
       * @note Down-conversion might fail.
       */
      template <typename U>
      operator fixed_point<U>()
      {
          U val = static_cast<U>(_value);
          if(std::numeric_limits<U>::digits < std::numeric_limits<T>::digits)
          {
              val = detail::constant_expr<U>::saturate_cast(_value);
          }
          return fixed_point<U>(val, _fixed_point_position, true);
      }
  
      /** Arithmetic += assignment operator
       *
       * @param[in] rhs Fixed point operand
       *
       * @return Reference to this fixed point
       */
      template <typename U>
      fixed_point<T> &operator+=(const fixed_point<U> &rhs)
      {
          fixed_point<T> val(rhs, _fixed_point_position);
          _value += val.raw();
          return *this;
      }
      /** Arithmetic -= assignment operator
       *
       * @param[in] rhs Fixed point operand
       *
       * @return Reference to this fixed point
       */
      template <typename U>
      fixed_point<T> &operator-=(const fixed_point<U> &rhs)
      {
          fixed_point<T> val(rhs, _fixed_point_position);
          _value -= val.raw();
          return *this;
      }
  
      /** Raw value accessor
       *
       * @return Raw fixed point value
       */
      T raw() const
      {
          return _value;
      }
      /** Precision accessor
       *
       * @return Precision of fixed point
       */
      uint8_t precision() const
      {
          return _fixed_point_position;
      }
      /** Rescale a fixed point to a new precision
       *
       * @param[in] p New fixed point precision
       */
      void rescale(uint8_t p)
      {
          assert(p > 0 && p < std::numeric_limits<T>::digits);
  
          if(p > _fixed_point_position)
          {
              _value <<= (p - _fixed_point_position);
          }
          else if(p < _fixed_point_position)
          {
              _value >>= (_fixed_point_position - p);
          }
  
          _fixed_point_position = p;
      }
  
  private:
      T       _value;                /**< Fixed point raw value */
      uint8_t _fixed_point_position; /**< Fixed point precision */
  };
  
  namespace detail
  {
  /** Count the number of leading zero bits in the given value.
   *
   * @param[in] value Input value.
   *
   * @return Number of leading zero bits.
   */
  template <typename T>
  constexpr int clz(T value)
  {
      using unsigned_T = typename std::make_unsigned<T>::type;
      // __builtin_clz is available for int. Need to correct reported number to
      // match the original type.
      return __builtin_clz(value) - (32 - std::numeric_limits<unsigned_T>::digits);
  }
  
  template <typename T>
  struct constant_expr
  {
      /** Calculate representation of 1 in fixed point given a fixed point precision
       *
       * @param[in] p Fixed point precision
       *
       * @return Representation of value 1 in fixed point.
       */
      static constexpr T fixed_one(uint8_t p)
      {
          return (1 << p);
      }
      /** Calculate fixed point precision step given a fixed point precision
       *
       * @param[in] p Fixed point precision
       *
       * @return Fixed point precision step
       */
      static constexpr float fixed_step(uint8_t p)
      {
          return (1.0f / static_cast<float>(1 << p));
      }
  
      /** Convert a fixed point value to float given its precision.
       *
       * @param[in] val Fixed point value
       * @param[in] p   Fixed point precision
       *
       * @return Float representation of the fixed point number
       */
      static constexpr float to_float(T val, uint8_t p)
      {
          return static_cast<float>(val * fixed_step(p));
      }
      /** Convert a fixed point value to integer given its precision.
       *
       * @param[in] val Fixed point value
       * @param[in] p   Fixed point precision
       *
       * @return Integer of the fixed point number
       */
      static constexpr T to_int(T val, uint8_t p)
      {
          return val >> p;
      }
      /** Convert a single precision floating point value to a fixed point representation given its precision.
       *
       * @param[in] val Floating point value
       * @param[in] p   Fixed point precision
       *
       * @return The raw fixed point representation
       */
      static constexpr T to_fixed(float val, uint8_t p)
      {
          return static_cast<T>(val * fixed_one(p) + ((val >= 0) ? 0.5 : -0.5));
      }
      /** Clamp value between two ranges
       *
       * @param[in] val Value to clamp
       * @param[in] min Minimum value to clamp to
       * @param[in] max Maximum value to clamp to
       *
       * @return clamped value
       */
      static constexpr T clamp(T val, T min, T max)
      {
          return std::min(std::max(val, min), max);
      }
      /** Saturate given number
       *
       * @param[in] val Value to saturate
       *
       * @return Saturated value
       */
      template <typename U>
      static constexpr T saturate_cast(U val)
      {
          return static_cast<T>(std::min<U>(std::max<U>(val, static_cast<U>(std::numeric_limits<T>::min())), static_cast<U>(std::numeric_limits<T>::max())));
      }
  };
  struct functions
  {
      /** Output stream operator
       *
       * @param[in] s Output stream
       * @param[in] x Fixed point value
       *
       * @return Reference output to updated stream
       */
      template <typename T, typename U, typename traits>
      static std::basic_ostream<T, traits> &write(std::basic_ostream<T, traits> &s, fixed_point<U> &x)
      {
          return s << static_cast<float>(x);
      }
      /** Signbit of a fixed point number.
       *
       * @param[in] x Fixed point number
       *
       * @return True if negative else false.
       */
      template <typename T>
      static bool signbit(fixed_point<T> x)
      {
          return ((x._value >> std::numeric_limits<T>::digits) != 0);
      }
      /** Checks if two fixed point numbers are equal
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return True if fixed points are equal else false
       */
      template <typename T>
      static bool isequal(fixed_point<T> x, fixed_point<T> y)
      {
          uint8_t p = std::min(x._fixed_point_position, y._fixed_point_position);
          x.rescale(p);
          y.rescale(p);
          return (x._value == y._value);
      }
      /** Checks if two fixed point number are not equal
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return True if fixed points are not equal else false
       */
      template <typename T>
      static bool isnotequal(fixed_point<T> x, fixed_point<T> y)
      {
          return !isequal(x, y);
      }
      /** Checks if one fixed point is greater than the other
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return True if fixed point is greater than other
       */
      template <typename T>
      static bool isgreater(fixed_point<T> x, fixed_point<T> y)
      {
          uint8_t p = std::min(x._fixed_point_position, y._fixed_point_position);
          x.rescale(p);
          y.rescale(p);
          return (x._value > y._value);
      }
      /** Checks if one fixed point is greater or equal than the other
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return True if fixed point is greater or equal than other
       */
      template <typename T>
      static bool isgreaterequal(fixed_point<T> x, fixed_point<T> y)
      {
          uint8_t p = std::min(x._fixed_point_position, y._fixed_point_position);
          x.rescale(p);
          y.rescale(p);
          return (x._value >= y._value);
      }
      /** Checks if one fixed point is less than the other
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return True if fixed point is less than other
       */
      template <typename T>
      static bool isless(fixed_point<T> x, fixed_point<T> y)
      {
          uint8_t p = std::min(x._fixed_point_position, y._fixed_point_position);
          x.rescale(p);
          y.rescale(p);
          return (x._value < y._value);
      }
      /** Checks if one fixed point is less or equal than the other
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return True if fixed point is less or equal than other
       */
      template <typename T>
      static bool islessequal(fixed_point<T> x, fixed_point<T> y)
      {
          uint8_t p = std::min(x._fixed_point_position, y._fixed_point_position);
          x.rescale(p);
          y.rescale(p);
          return (x._value <= y._value);
      }
      /** Checks if one fixed point is less or greater than the other
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return True if fixed point is less or greater than other
       */
      template <typename T>
      static bool islessgreater(fixed_point<T> x, fixed_point<T> y)
      {
          return isnotequal(x, y);
      }
      /** Clamp fixed point to specific range.
       *
       * @param[in] x   Fixed point operand
       * @param[in] min Minimum value to clamp to
       * @param[in] max Maximum value to clamp to
       *
       * @return Clamped result
       */
      template <typename T>
      static fixed_point<T> clamp(fixed_point<T> x, T min, T max)
      {
          return fixed_point<T>(constant_expr<T>::clamp(x._value, min, max), x._fixed_point_position, true);
      }
      /** Negate number
       *
       * @param[in] x Fixed point operand
       *
       * @return Negated fixed point result
       */
      template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T>
      static fixed_point<T> negate(fixed_point<T> x)
      {
          using promoted_T = typename traits::promote<T>::type;
          promoted_T val   = -x._value;
          if(OP == OverflowPolicy::SATURATE)
          {
              val = constant_expr<T>::saturate_cast(val);
          }
          return fixed_point<T>(static_cast<T>(val), x._fixed_point_position, true);
      }
      /** Perform addition among two fixed point numbers
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return Result fixed point with precision equal to minimum precision of both operands
       */
      template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T>
      static fixed_point<T> add(fixed_point<T> x, fixed_point<T> y)
      {
          uint8_t p = std::min(x._fixed_point_position, y._fixed_point_position);
          x.rescale(p);
          y.rescale(p);
          if(OP == OverflowPolicy::SATURATE)
          {
              using type = typename traits::promote<T>::type;
              type val   = static_cast<type>(x._value) + static_cast<type>(y._value);
              val        = constant_expr<T>::saturate_cast(val);
              return fixed_point<T>(static_cast<T>(val), p, true);
          }
          else
          {
              return fixed_point<T>(x._value + y._value, p, true);
          }
      }
      /** Perform subtraction among two fixed point numbers
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return Result fixed point with precision equal to minimum precision of both operands
       */
      template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T>
      static fixed_point<T> sub(fixed_point<T> x, fixed_point<T> y)
      {
          uint8_t p = std::min(x._fixed_point_position, y._fixed_point_position);
          x.rescale(p);
          y.rescale(p);
          if(OP == OverflowPolicy::SATURATE)
          {
              using type = typename traits::promote<T>::type;
              type val   = static_cast<type>(x._value) - static_cast<type>(y._value);
              val        = constant_expr<T>::saturate_cast(val);
              return fixed_point<T>(static_cast<T>(val), p, true);
          }
          else
          {
              return fixed_point<T>(x._value - y._value, p, true);
          }
      }
      /** Perform multiplication among two fixed point numbers
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return Result fixed point with precision equal to minimum precision of both operands
       */
      template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T>
      static fixed_point<T> mul(fixed_point<T> x, fixed_point<T> y)
      {
          using promoted_T        = typename traits::promote<T>::type;
          uint8_t    p_min        = std::min(x._fixed_point_position, y._fixed_point_position);
          uint8_t    p_max        = std::max(x._fixed_point_position, y._fixed_point_position);
          promoted_T round_factor = (1 << (p_max - 1));
          promoted_T val          = ((static_cast<promoted_T>(x._value) * static_cast<promoted_T>(y._value)) + round_factor) >> p_max;
          if(OP == OverflowPolicy::SATURATE)
          {
              val = constant_expr<T>::saturate_cast(val);
          }
          return fixed_point<T>(static_cast<T>(val), p_min, true);
      }
      /** Perform division among two fixed point numbers
       *
       * @param[in] x First fixed point operand
       * @param[in] y Second fixed point operand
       *
       * @return Result fixed point with precision equal to minimum precision of both operands
       */
      template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T>
      static fixed_point<T> div(fixed_point<T> x, fixed_point<T> y)
      {
          using promoted_T = typename traits::promote<T>::type;
          uint8_t    p     = std::min(x._fixed_point_position, y._fixed_point_position);
          promoted_T denom = static_cast<promoted_T>(y._value);
          if(denom != 0)
          {
              promoted_T val = (static_cast<promoted_T>(x._value) << std::max(x._fixed_point_position, y._fixed_point_position)) / denom;
              if(OP == OverflowPolicy::SATURATE)
              {
                  val = constant_expr<T>::saturate_cast(val);
              }
              return fixed_point<T>(static_cast<T>(val), p, true);
          }
          else
          {
              T val = (x._value < 0) ? std::numeric_limits<T>::min() : std::numeric_limits<T>::max();
              return fixed_point<T>(val, p, true);
          }
      }
      /** Shift left
       *
       * @param[in] x     Fixed point operand
       * @param[in] shift Shift value
       *
       * @return Shifted value
       */
      template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T>
      static fixed_point<T> shift_left(fixed_point<T> x, size_t shift)
      {
          using promoted_T = typename traits::promote<T>::type;
          promoted_T val   = static_cast<promoted_T>(x._value) << shift;
          if(OP == OverflowPolicy::SATURATE)
          {
              val = constant_expr<T>::saturate_cast(val);
          }
          return fixed_point<T>(static_cast<T>(val), x._fixed_point_position, true);
      }
      /** Shift right
       *
       * @param[in] x     Fixed point operand
       * @param[in] shift Shift value
       *
       * @return Shifted value
       */
      template <typename T>
      static fixed_point<T> shift_right(fixed_point<T> x, size_t shift)
      {
          return fixed_point<T>(x._value >> shift, x._fixed_point_position, true);
      }
      /** Calculate absolute value
       *
       * @param[in] x Fixed point operand
       *
       * @return Absolute value of operand
       */
      template <typename T>
      static fixed_point<T> abs(fixed_point<T> x)
      {
          using promoted_T = typename traits::promote<T>::type;
          T val            = (x._value < 0) ? constant_expr<T>::saturate_cast(-static_cast<promoted_T>(x._value)) : x._value;
          return fixed_point<T>(val, x._fixed_point_position, true);
      }
      /** Calculate the logarithm of a fixed point number
       *
       * @param[in] x Fixed point operand
       *
       * @return Logarithm value of operand
       */
      template <typename T>
      static fixed_point<T> log(fixed_point<T> x)
      {
          uint8_t p         = x._fixed_point_position;
          auto    const_one = fixed_point<T>(static_cast<T>(1), p);
  
          // Logarithm of 1 is zero and logarithm of negative values is not defined in R, so return 0.
          // Also, log(x) == -log(1/x) for 0 < x < 1.
          if(isequal(x, const_one) || islessequal(x, fixed_point<T>(static_cast<T>(0), p)))
          {
              return fixed_point<T>(static_cast<T>(0), p, true);
          }
          else if(isless(x, const_one))
          {
              return mul(log(div(const_one, x)), fixed_point<T>(-1, p));
          }
  
          // Remove even powers of 2
          T shift_val = 31 - __builtin_clz(x._value >> p);
          x           = shift_right(x, shift_val);
          x           = sub(x, const_one);
  
          // Constants
          auto ln2 = fixed_point<T>(0.6931471, p);
          auto A   = fixed_point<T>(1.4384189, p);
          auto B   = fixed_point<T>(-0.67719, p);
          auto C   = fixed_point<T>(0.3218538, p);
          auto D   = fixed_point<T>(-0.0832229, p);
  
          // Polynomial expansion
          auto sum = add(mul(x, D), C);
          sum      = add(mul(x, sum), B);
          sum      = add(mul(x, sum), A);
          sum      = mul(x, sum);
  
          return mul(add(sum, fixed_point<T>(static_cast<T>(shift_val), p)), ln2);
      }
      /** Calculate the exponential of a fixed point number.
       *
       * exp(x) = exp(floor(x)) * exp(x - floor(x))
       *        = pow(2, floor(x) / ln(2)) * exp(x - floor(x))
       *        = exp(x - floor(x)) << (floor(x) / ln(2))
       *
       * @param[in] x Fixed point operand
       *
       * @return Exponential value of operand
       */
      template <typename T>
      static fixed_point<T> exp(fixed_point<T> x)
      {
          uint8_t p = x._fixed_point_position;
          // Constants
          auto const_one = fixed_point<T>(1, p);
          auto ln2       = fixed_point<T>(0.6931471, p);
          auto inv_ln2   = fixed_point<T>(1.442695, p);
          auto A         = fixed_point<T>(0.9978546, p);
          auto B         = fixed_point<T>(0.4994721, p);
          auto C         = fixed_point<T>(0.1763723, p);
          auto D         = fixed_point<T>(0.0435108, p);
  
          T scaled_int_part = detail::constant_expr<T>::to_int(mul(x, inv_ln2)._value, p);
  
          // Polynomial expansion
          auto frac_part = sub(x, mul(ln2, fixed_point<T>(scaled_int_part, p)));
          auto taylor    = add(mul(frac_part, D), C);
          taylor         = add(mul(frac_part, taylor), B);
          taylor         = add(mul(frac_part, taylor), A);
          taylor         = mul(frac_part, taylor);
          taylor         = add(taylor, const_one);
  
          // Saturate value
          if(static_cast<T>(clz(taylor.raw())) <= scaled_int_part)
          {
              return fixed_point<T>(std::numeric_limits<T>::max(), p, true);
          }
  
          return (scaled_int_part < 0) ? shift_right(taylor, -scaled_int_part) : shift_left(taylor, scaled_int_part);
      }
      /** Calculate the inverse square root of a fixed point number
       *
       * @param[in] x Fixed point operand
       *
       * @return Inverse square root value of operand
       */
      template <typename T>
      static fixed_point<T> inv_sqrt(fixed_point<T> x)
      {
          const uint8_t p     = x._fixed_point_position;
          int8_t        shift = std::numeric_limits<T>::digits - (p + detail::clz(x._value));
  
          shift += std::numeric_limits<T>::is_signed ? 1 : 0;
  
          const auto           three_half = fixed_point<T>(1.5f, p);
          fixed_point<T>       a          = shift < 0 ? shift_left(x, -shift) : shift_right(x, shift);
          const fixed_point<T> x_half     = shift_right(a, 1);
  
          // We need three iterations to find the result
          for(int i = 0; i < 3; ++i)
          {
              a = mul(a, sub(three_half, mul(x_half, mul(a, a))));
          }
  
          return (shift < 0) ? shift_left(a, -shift >> 1) : shift_right(a, shift >> 1);
      }
      /** Calculate the hyperbolic tangent of a fixed point number
       *
       * @param[in] x Fixed point operand
       *
       * @return Hyperbolic tangent of the operand
       */
      template <typename T>
      static fixed_point<T> tanh(fixed_point<T> x)
      {
          uint8_t p = x._fixed_point_position;
          // Constants
          auto const_one = fixed_point<T>(1, p);
          auto const_two = fixed_point<T>(2, p);
  
          auto exp2x = exp(const_two * x);
          auto num   = exp2x - const_one;
          auto den   = exp2x + const_one;
          auto tanh  = num / den;
  
          return tanh;
      }
      /** Calculate the a-th power of a fixed point number.
       *
       *  The power is computed as x^a = e^(log(x) * a)
       *
       * @param[in] x Fixed point operand
       * @param[in] a Fixed point exponent
       *
       * @return a-th power of the operand
       */
      template <typename T>
      static fixed_point<T> pow(fixed_point<T> x, fixed_point<T> a)
      {
          return exp(log(x) * a);
      }
  };
  
  template <typename T>
  bool operator==(const fixed_point<T> &lhs, const fixed_point<T> &rhs)
  {
      return functions::isequal(lhs, rhs);
  }
  template <typename T>
  bool operator!=(const fixed_point<T> &lhs, const fixed_point<T> &rhs)
  {
      return !operator==(lhs, rhs);
  }
  template <typename T>
  bool operator<(const fixed_point<T> &lhs, const fixed_point<T> &rhs)
  {
      return functions::isless(lhs, rhs);
  }
  template <typename T>
  bool operator>(const fixed_point<T> &lhs, const fixed_point<T> &rhs)
  {
      return operator<(rhs, lhs);
  }
  template <typename T>
  bool operator<=(const fixed_point<T> &lhs, const fixed_point<T> &rhs)
  {
      return !operator>(lhs, rhs);
  }
  template <typename T>
  bool operator>=(const fixed_point<T> &lhs, const fixed_point<T> &rhs)
  {
      return !operator<(lhs, rhs);
  }
  template <typename T>
  fixed_point<T> operator+(const fixed_point<T> &lhs, const fixed_point<T> &rhs)
  {
      return functions::add(lhs, rhs);
  }
  template <typename T>
  fixed_point<T> operator-(const fixed_point<T> &lhs, const fixed_point<T> &rhs)
  {
      return functions::sub(lhs, rhs);
  }
  template <typename T>
  fixed_point<T> operator-(const fixed_point<T> &rhs)
  {
      return functions::negate(rhs);
  }
  template <typename T>
  fixed_point<T> operator*(fixed_point<T> x, fixed_point<T> y)
  {
      return functions::mul(x, y);
  }
  template <typename T>
  fixed_point<T> operator/(fixed_point<T> x, fixed_point<T> y)
  {
      return functions::div(x, y);
  }
  template <typename T>
  fixed_point<T> operator>>(fixed_point<T> x, size_t shift)
  {
      return functions::shift_right(x, shift);
  }
  template <typename T>
  fixed_point<T> operator<<(fixed_point<T> x, size_t shift)
  {
      return functions::shift_left(x, shift);
  }
  template <typename T, typename U, typename traits>
  std::basic_ostream<T, traits> &operator<<(std::basic_ostream<T, traits> &s, fixed_point<U> x)
  {
      return functions::write(s, x);
  }
  template <typename T>
  inline fixed_point<T> min(fixed_point<T> x, fixed_point<T> y)
  {
      return x > y ? y : x;
  }
  template <typename T>
  inline fixed_point<T> max(fixed_point<T> x, fixed_point<T> y)
  {
      return x > y ? x : y;
  }
  template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T>
  inline fixed_point<T> add(fixed_point<T> x, fixed_point<T> y)
  {
      return functions::add<OP>(x, y);
  }
  template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T>
  inline fixed_point<T> sub(fixed_point<T> x, fixed_point<T> y)
  {
      return functions::sub<OP>(x, y);
  }
  template <OverflowPolicy OP = OverflowPolicy::SATURATE, typename T>
  inline fixed_point<T> mul(fixed_point<T> x, fixed_point<T> y)
  {
      return functions::mul<OP>(x, y);
  }
  template <typename T>
  inline fixed_point<T> div(fixed_point<T> x, fixed_point<T> y)
  {
      return functions::div(x, y);
  }
  template <typename T>
  inline fixed_point<T> abs(fixed_point<T> x)
  {
      return functions::abs(x);
  }
  template <typename T>
  inline fixed_point<T> clamp(fixed_point<T> x, T min, T max)
  {
      return functions::clamp(x, min, max);
  }
  template <typename T>
  inline fixed_point<T> exp(fixed_point<T> x)
  {
      return functions::exp(x);
  }
  template <typename T>
  inline fixed_point<T> log(fixed_point<T> x)
  {
      return functions::log(x);
  }
  template <typename T>
  inline fixed_point<T> inv_sqrt(fixed_point<T> x)
  {
      return functions::inv_sqrt(x);
  }
  template <typename T>
  inline fixed_point<T> tanh(fixed_point<T> x)
  {
      return functions::tanh(x);
  }
  template <typename T>
  inline fixed_point<T> pow(fixed_point<T> x, fixed_point<T> a)
  {
      return functions::pow(x, a);
  }
  } // namespace detail
  
  // Expose operators
  using detail::operator==;
  using detail::operator!=;
  using detail::operator<;
  using detail::operator>;
  using detail::operator<=;
  using detail::operator>=;
  using detail::operator+;
  using detail::operator-;
  using detail::operator*;
  using detail::operator/;
  using detail::operator>>;
  using detail::operator<<;
  
  // Expose additional functions
  using detail::min;
  using detail::max;
  using detail::add;
  using detail::sub;
  using detail::mul;
  using detail::div;
  using detail::abs;
  using detail::clamp;
  using detail::exp;
  using detail::log;
  using detail::inv_sqrt;
  using detail::tanh;
  using detail::pow;
  } // namespace fixed_point_arithmetic
  } // namespace test
  } // namespace arm_compute
  #endif /*__ARM_COMPUTE_TEST_VALIDATION_FIXEDPOINT_H__ */
  