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/*
* Author: Sven Gothel <sgothel@jausoft.com>
* Copyright (c) 2020 Gothel Software e.K.
* Copyright (c) 2020 ZAFENA AB
*
* 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 JAU_BASIC_INT_MATH_HPP_
#define JAU_BASIC_INT_MATH_HPP_
#include <cmath>
namespace jau {
/**
// *************************************************
// *************************************************
// *************************************************
*/
/**
* Natural 'size_t' alternative using 'unsigned int' as its natural sized type.
* <p>
* The leading 'n' stands for natural.
* </p>
* <p>
* This is a compromise to indicate intend,
* but to avoid handling a multiple sized 'size_t' footprint where not desired.
* </p>
*/
typedef unsigned int nsize_t;
/**
* Natural 'ssize_t' alternative using 'signed int' as its natural sized type.
* <p>
* The leading 'n' stands for natural.
* </p>
* <p>
* This is a compromise to indicate intend,
* but to avoid handling a multiple sized 'ssize_t' footprint where not desired.
* </p>
*/
typedef signed int snsize_t;
/**
// *************************************************
// *************************************************
// *************************************************
*/
/**
* Returns the value of the sign function.
* <pre>
* -1 for x < 0
* 0 for x = 0
* 1 for x > 0
* </pre>
* Implementation is type safe.
* @tparam T an integral number type
* @param x the integral number
* @return function result
*/
template <typename T>
constexpr snsize_t sign(const T x) noexcept
{
return (T(0) < x) - (x < T(0));
}
/**
* Safely inverts the sign of an integral number.
* <p>
* Implementation takes special care to have T_MIN, i.e. std::numeric_limits<T>::min(),
* converted to T_MAX, i.e. std::numeric_limits<T>::max().<br>
* This is necessary since <code>T_MAX < | -T_MIN |</code> and the result would
* not fit in the return type T otherwise.
* </p>
* Hence for the extreme minimum case:
* <pre>
* jau::invert_sign<int32_t>(INT32_MIN) = | INT32_MIN | - 1 = INT32_MAX
* </pre>
* Otherwise with x < 0:
* <pre>
* jau::invert_sign<int32_t>(x) = | x | = -x
* </pre>
* and x >= 0:
* <pre>
* jau::invert_sign<int32_t>(x) = -x
* </pre>
* @tparam T
* @param x
* @return
*/
template <typename T>
constexpr T invert_sign(const T x) noexcept
{
return std::numeric_limits<T>::min() == x ? std::numeric_limits<T>::max() : -x;
}
/**
* Returns the absolute value of an integral number
* <p>
* Implementation uses jau::invert_sign() to have a safe absolute value conversion, if required.
* </p>
* @tparam T an integral number type
* @param x the integral number
* @return function result
*/
template <typename T>
constexpr T abs(const T x) noexcept
{
return sign(x) < 0 ? invert_sign<T>( x ) : x;
}
/**
* Returns the number of decimal digits of the given integral value number using std::log10<T>().<br>
* If sign_is_digit == true (default), treats a potential negative sign as a digit.
* <pre>
* x < 0: 1 + (int) ( log10( -x ) ) + ( sign_is_digit ? 1 : 0 )
* x = 0: 1
* x > 0: 1 + (int) ( log10( x ) )
* </pre>
* Implementation uses jau::invert_sign() to have a safe absolute value conversion, if required.
* <p>
* Convenience method, reusing precomputed sign of value to avoid redundant computations.
* </p>
* @tparam T an integral integer type
* @param x the integral integer
* @param x_sign the pre-determined sign of the given value x
* @param sign_is_digit if true and value is negative, adds one to result for sign. Defaults to true.
* @return digit count
*/
template<typename T>
constexpr nsize_t digits10(const T x, const snsize_t x_sign, const bool sign_is_digit=true) noexcept
{
if( x_sign == 0 ) {
return 1;
}
if( x_sign < 0 ) {
return 1 + static_cast<nsize_t>( std::log10<T>( invert_sign<T>( x ) ) ) + ( sign_is_digit ? 1 : 0 );
} else {
return 1 + static_cast<nsize_t>( std::log10<T>( x ) );
}
}
/**
* Returns the number of decimal digits of the given integral value number using std::log10<T>().
* If sign_is_digit == true (default), treats a potential negative sign as a digit.
* <pre>
* x < 0: 1 + (int) ( log10( -x ) ) + ( sign_is_digit ? 1 : 0 )
* x = 0: 1
* x > 0: 1 + (int) ( log10( x ) )
* </pre>
* Implementation uses jau::invert_sign() to have a safe absolute value conversion, if required.
* @tparam T an integral integer type
* @param x the integral integer
* @param sign_is_digit if true and value is negative, adds one to result for sign. Defaults to true.
* @return digit count
*/
template<typename T>
constexpr nsize_t digits10(const T x, const bool sign_is_digit=true) noexcept
{
return digits10<T>(x, jau::sign<T>(x), sign_is_digit);
}
} // namespace jau
#endif /* JAU_BASIC_INT_MATH_HPP_ */
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