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/* $Id */

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/**

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 * @file

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 * Implements a Fixed-point data type.

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 * This files defines a new data type

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 * "FixedT<Tstorage, Tdec_bits>", which can be used to compute fractional

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 * numbers without having to worry about network stability (because

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 * there is no real rounding taking place.

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 * Use "Fixed" for the defaults values (48 bits integral part, 16 bits

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 * fractional part) or "FixedT<typename, int>" for flexible sizes. "int"

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 * number of bits are taken from a variable of "typename" for the fractional

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 * representation, the rest stays available for the integral part.

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 * @warning More than 16 bits fractional should not be used when working

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 * with large integers.

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 * @warning More than 31 fractional bits are not supported, and will

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 * trigger a compiler warning with appropriate settings.

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 * @warning There are no warnings for buffer overflows. Those are very likely

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 * to happen with divisions, as those first shift the numerator by the number

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 * of fractional bits. Use multiplication with the reciprocal whereever

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 * it is possible.

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 * @warning Please use signed variables for storage at the moment ONLY

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 *

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 * Variables can be initialized:

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 * 	- with integers: "FixedT<int, 9> a = -5"

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 * 	- with fractionals: "FixedT<int64, 11> b(7, 2);" where the first number is

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 * the numerator and the second is the denominator.

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 * 	- not at all: "Fixed c;", which will automatically set c to zero.

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 *

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 * @example fixed_ex.cpp How to initialize Fixed-point data types

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 */

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/* Included to overload the stream operator << */

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#include <iostream>

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/* Needed for some ottd-specific data types */

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#include "stdafx.h"

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/**

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 * Base Class for storing fixed-point data types.

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 * Fixed-point data types are stored in a single integer-type variable

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 * (Tstorage) of which a certain number of bits (Tdec_bits) is used to

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 * represent the fractional part of the number.

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 */

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template <typename Tstorage, int Tdec_bits>

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class FixedRawT {

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public:

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	/** The number of bits that represent the fractional */

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	static const int dec_bits = Tdec_bits;

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	/** The storage of the number itself */

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	Tstorage m_data;

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	/**

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	 * Basic constructor for integer arguments.

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	 * @param value The raw value to which we want to initialize

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	 */

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	template <typename T>

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	FixedRawT(T value) : m_data(value) {}

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	/**

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	 * Make sure that a Fixed variable is always inizialized to zero by default.

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	 * We need this ctor so that we can declare variable without

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	 * the need to initialize it explicitly

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	 */

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	FixedRawT() : m_data (0) {}

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	/**

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	 * Returns the biggest integral number we can represent

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	 */

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	int64 FIXED_MAX() const { return m_maximum; }

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	/**

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	 * Returns the biggest integral number we can represent

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	 */

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	int64 FIXED_MIN() const { return m_minimum; }

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private:

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	/** The largest number we can hold */

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	static const int64 m_maximum = +(1ULL << ((sizeof(Tstorage) * 8) - Tdec_bits - 1)) - 1;

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	/** The smallest number we can hold */

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	static const int64 m_minimum = -(1ULL << ((sizeof(Tstorage) * 8) - Tdec_bits - 1)) - 0;

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};

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/* forward-declare some structs */

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template <typename Tstorage, int Tdec_bits> class FixedT;

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template <typename T> struct FixedHelperT;

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/**

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 * Specialization of FixedHelperT. Used to decimal-align two variables of Fixed type.

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 */

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template <typename Tstorage, int Tdec_bits> struct FixedHelperT<FixedRawT<Tstorage, Tdec_bits> >

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{

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	/** The number of bits used for the fraction */

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	static const int dec_bits = Tdec_bits;

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	/**

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	 * Gives the raw data of a FixedRaw

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	 * @param t The number to return

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	 */

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	static int64 Raw(const FixedRawT<Tstorage, Tdec_bits>& t) {return (int64)t.m_data;}

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	/**

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	 * Returns the data from FixedRawT aligned so that it is aligned to a given number

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	 * @param t    The number to be aligned

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	 * @param bits The number of bits in the fractional part to be aligned to

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	 */

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	static int64 Raw(const FixedRawT<Tstorage, Tdec_bits>& t, int bits)

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	{

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		return (((int64)t.m_data) << (bits > Tdec_bits ? bits - Tdec_bits : 0)) >> (bits < Tdec_bits ? Tdec_bits - bits : 0);

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	}

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};

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/**

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 * Specialization of FixedHelperT. Used to decimal-align two variables of Fixed type.

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 */

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template <typename Tstorage, int Tdec_bits> struct FixedHelperT<FixedT<Tstorage, Tdec_bits> > : public FixedHelperT<FixedRawT<Tstorage, Tdec_bits> > {};

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/**

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 * General implementation of FixedHelperT. This tempate makes sure that

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 * some number supplied is properly aligned at the decimal

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 */

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template <typename T> struct FixedHelperT

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{

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	/** This version of FixedHelperT is only used for full integers, so assume the number of dec_bits to be zero */

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	static const int dec_bits = 0;

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	/** Converts a full integer to one that has a given number of fractional bits, assumes

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	 * the number of fractional bits to be zero.

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	 * @param t the number to be converted

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	 */

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	static int64 Raw(const T& t) {return (int64)t;}

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	/**

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	 * Converts a full integer to one that has a given number of fractional bits

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	 * @param bits the number of bits for the fraction

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	 * @param t    the number to be converted

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	 */

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	static int64 Raw(const T& t, int bits) {return ((int64)t) << bits;}

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};

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/**

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 * A class that defines a fixed-point data type, which a variable length and precision.

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 * The data type that is defined is a fixed-point variable that has and number of Tdec_bits

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 * bits to represent the fractional part, the remaining bits of Tstorage are then used for

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 * the integer part of the number. This means, we always need to make a trade-off between

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 * the precision we want (higher number in Tdec_bits) and the range (smaller number of

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 * Tdec_bits). This class here only defines the constructors and the operators, everything

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 * else is happning in helper classes.

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 * @note for usage of fprintf and similar, explicit casts are needed (double or int64).

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 */

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template <typename Tstorage, int Tdec_bits> class FixedT : public FixedRawT<Tstorage, Tdec_bits> {

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/* private block up here, because we need the typedef later on */

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private:

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	/** We shortcut the underlying data type to "Raw", to save typing */

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	typedef FixedRawT<Tstorage, Tdec_bits> Raw;

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public:

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	/**

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	 * Ctor for assignment with other, non floating, variable types

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	 * @param value The Value we should assign to the Fixed

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	 */

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	template <typename T> FixedT(T value) : Raw(FixedHelperT<T>::Raw(value, Tdec_bits)) {}

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	/** As a constructor without initializing, just use the one that Raw uses. Sets a variable to zero */

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	FixedT() : Raw() {}

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	/**

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	 * Ctor for use with a fraction, useful for initing a variable to a non-integer number at declaration.

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	 * @param numerator   The Nominator of the fraction

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	 * @param denominator The Denominator of the fraction

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	 */

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	FixedT(int numerator, int denominator) {Raw::m_data = ((int64)numerator << Raw::dec_bits) / (int64)denominator;}

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	/**

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	 * Equality operator

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	 * @param comparator The non-floating point variable we want to compare against

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	 */

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	template <typename T>

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	bool operator ==(const T &comparator) const { return Raw::m_data == (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }

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	/**

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	 * Inequality operator

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	 * @param comparator The non-floating point variable we want to compare against

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	 */

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	template <typename T>

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	bool operator !=(const T &comparator) const { return Raw::m_data != (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }

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	/**

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	 * Greater or equal operator

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	 * @param comparator The non-floating point variable we want to compare against

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	 */

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	template <typename T>

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	bool operator >=(const T &comparator) const { return Raw::m_data >= (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }

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	/**

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	 * Less or equal operator

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	 * @param comparator The non-floating point variable we want to compare against

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	 */

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	template <typename T>

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	bool operator <=(const T &comparator) const { return Raw::m_data <= (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }

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	/**

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	 * Greater than operator

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	 * @param comparator The non-floating point variable we want to compare against

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	 */

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	template <typename T>

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	bool operator >(const T &comparator) const { return Raw::m_data > (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }

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	/**

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	 * Less than operator

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	 * @param comparator The non-floating point variable we want to compare against

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	 */

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	template <typename T>

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	bool operator <(const T &comparator) const { return Raw::m_data < (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }

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	/**

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	 * Addition for Fixed-point data types

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	 * @param value The non-floating point number to add

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	 */

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	template <typename T> FixedT operator +(const T &value) const

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	{

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		return Raw(Raw::m_data + (Tstorage)FixedHelperT<T>::Raw(value, Tdec_bits));

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	}

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	/**

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	 * Subtraction for Fixed-point data types

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	 * @param value The non-floating point number to subtract

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	 */

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	template <typename T> FixedT operator -(const T &value) const

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	{

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		return Raw(Raw::m_data - (Tstorage)FixedHelperT<T>::Raw(value, Tdec_bits));

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	}

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	/**

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	 * A simple multiplication for non-floating data types

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	 * @param value The non floating-point factor

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	 */

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	template <typename T> FixedT operator *(const T &value) const

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	{

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		return Raw( (((int64)Raw::m_data) * FixedHelperT<T>::Raw(value)) >> FixedHelperT<T>::dec_bits);

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	}

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	/**

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	 * A simple division for non-floating data types

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	 * @param value The non floating-point divisor

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	 */

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	template <typename T> FixedT operator /(const T &value) const

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	{

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		return Raw( (((int64)Raw::m_data) << FixedHelperT<T>::dec_bits) / FixedHelperT<T>::Raw(value));

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	}

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	/**

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	 * Addition-assignment for Fixed-point data types

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	 * @param value The non-floating point number to add

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	 */

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	template <typename T> FixedT& operator +=(const T &value)

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	{

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		Raw::m_data = Raw::m_data + (Tstorage)FixedHelperT<T>::Raw(value, Tdec_bits);

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		return *this;

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	}

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	/**

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	 * Subtract-assignment for Fixed-point data types

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	 * @param value The non-floating point number to subtract

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	 */

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	template <typename T> FixedT& operator -=(const T &value)

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	{

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		Raw::m_data = Raw::m_data - (Tstorage)FixedHelperT<T>::Raw(value, Tdec_bits);

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		return *this;

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	}

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	/**

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	 * Multiply-assignment for Fixed-point data types

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	 * @param value The non-floating point number to multiply

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	 */

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	template <typename T> FixedT& operator *=(const T &value)

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	{

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		Raw::m_data = (Raw::m_data * (Tstorage)FixedHelperT<T>::Raw(value)) >> FixedHelperT<T>::dec_bits;

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		return *this;

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	}

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	/**

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	 * Divide-assignment for Fixed-point data types

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	 * @param value The non-floating point number to use as divisor

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	 */

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	template <typename T> FixedT& operator /=(const T &value)

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	{

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		Raw::m_data = (Raw::m_data << FixedHelperT<T>::dec_bits) / (Tstorage)FixedHelperT<T>::Raw(value);

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		return *this;

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	}

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	/**

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	 * Stream operator, used for floating point output

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	 * @param os    The stream we are going to write to

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	 * @param value The Fixed-point variable we want to write in the stream

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	 */

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	friend std::ostream& operator << (std::ostream &os, const FixedT &value) { os << (double)value.m_data / (1ULL << Raw::dec_bits); return os; }

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};

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