(svn r9026) [gamebalance] -Add: Added a new data type that allows fixed-point computations, as to enable computing non-integral numbers without worrying about the FPU rounding differences and, thus, desyncs. It is fully doxygenned, read the usage there. Thanks a bunch to KUDr for helping me with templates
/* $Id */
/**
* @file
* Implements a Fixed-point data type.
* This files defines a new data type
* "FixedT<Tstorage, Tdec_bits>", which can be used to compute fractional
* numbers without having to worry about network stability (because
* there is no real rounding taking place.
* Use "Fixed" for the defaults values (48 bits integral part, 16 bits
* fractional part) or "FixedT<typename, int>" for flexible sizes. "int"
* number of bits are taken from a variable of "typename" for the fractional
* representation, the rest stays available for the integral part.
* @warning More than 16 bits fractional should not be used when working
* with large integers.
* @warning More than 31 fractional bits are not supported, and will
* trigger a compiler warning with appropriate settings.
* @warning There are no warnings for buffer overflows. Those are very likely
* to happen with divisions, as those first shift the numerator by the number
* of fractional bits. Use multiplication with the reciprocal whereever
* it is possible.
* @warning Please use signed variables for storage at the moment ONLY
*
* Variables can be initialized:
* - with integers: "FixedT<int, 9> a = -5"
* - with fractionals: "FixedT<int64, 11> b(7, 2);" where the first number is
* the numerator and the second is the denominator.
* - not at all: "Fixed c;", which will automatically set c to zero.
*
* @example fixed_ex.cpp How to initialize Fixed-point data types
*/
/* Included to overload the stream operator << */
#include <iostream>
/* Needed for some ottd-specific data types */
#include "stdafx.h"
/**
* Base Class for storing fixed-point data types.
* Fixed-point data types are stored in a single integer-type variable
* (Tstorage) of which a certain number of bits (Tdec_bits) is used to
* represent the fractional part of the number.
*/
template <typename Tstorage, int Tdec_bits>
class FixedRawT {
public:
/** The number of bits that represent the fractional */
static const int dec_bits = Tdec_bits;
/** The storage of the number itself */
Tstorage m_data;
/**
* Basic constructor for integer arguments.
* @param value The raw value to which we want to initialize
*/
template <typename T>
FixedRawT(T value) : m_data(value) {}
/**
* Make sure that a Fixed variable is always inizialized to zero by default.
* We need this ctor so that we can declare variable without
* the need to initialize it explicitly
*/
FixedRawT() : m_data (0) {}
/**
* Returns the biggest integral number we can represent
*/
int64 FIXED_MAX() const { return m_maximum; }
/**
* Returns the biggest integral number we can represent
*/
int64 FIXED_MIN() const { return m_minimum; }
private:
/** The largest number we can hold */
static const int64 m_maximum = +(1ULL << ((sizeof(Tstorage) * 8) - Tdec_bits - 1)) - 1;
/** The smallest number we can hold */
static const int64 m_minimum = -(1ULL << ((sizeof(Tstorage) * 8) - Tdec_bits - 1)) - 0;
};
/* forward-declare some structs */
template <typename Tstorage, int Tdec_bits> class FixedT;
template <typename T> struct FixedHelperT;
/**
* Specialization of FixedHelperT. Used to decimal-align two variables of Fixed type.
*/
template <typename Tstorage, int Tdec_bits> struct FixedHelperT<FixedRawT<Tstorage, Tdec_bits> >
{
/** The number of bits used for the fraction */
static const int dec_bits = Tdec_bits;
/**
* Gives the raw data of a FixedRaw
* @param t The number to return
*/
static int64 Raw(const FixedRawT<Tstorage, Tdec_bits>& t) {return (int64)t.m_data;}
/**
* Returns the data from FixedRawT aligned so that it is aligned to a given number
* @param t The number to be aligned
* @param bits The number of bits in the fractional part to be aligned to
*/
static int64 Raw(const FixedRawT<Tstorage, Tdec_bits>& t, int bits)
{
return (((int64)t.m_data) << (bits > Tdec_bits ? bits - Tdec_bits : 0)) >> (bits < Tdec_bits ? Tdec_bits - bits : 0);
}
};
/**
* Specialization of FixedHelperT. Used to decimal-align two variables of Fixed type.
*/
template <typename Tstorage, int Tdec_bits> struct FixedHelperT<FixedT<Tstorage, Tdec_bits> > : public FixedHelperT<FixedRawT<Tstorage, Tdec_bits> > {};
/**
* General implementation of FixedHelperT. This tempate makes sure that
* some number supplied is properly aligned at the decimal
*/
template <typename T> struct FixedHelperT
{
/** This version of FixedHelperT is only used for full integers, so assume the number of dec_bits to be zero */
static const int dec_bits = 0;
/** Converts a full integer to one that has a given number of fractional bits, assumes
* the number of fractional bits to be zero.
* @param t the number to be converted
*/
static int64 Raw(const T& t) {return (int64)t;}
/**
* Converts a full integer to one that has a given number of fractional bits
* @param bits the number of bits for the fraction
* @param t the number to be converted
*/
static int64 Raw(const T& t, int bits) {return ((int64)t) << bits;}
};
/**
* A class that defines a fixed-point data type, which a variable length and precision.
* The data type that is defined is a fixed-point variable that has and number of Tdec_bits
* bits to represent the fractional part, the remaining bits of Tstorage are then used for
* the integer part of the number. This means, we always need to make a trade-off between
* the precision we want (higher number in Tdec_bits) and the range (smaller number of
* Tdec_bits). This class here only defines the constructors and the operators, everything
* else is happning in helper classes.
* @note for usage of fprintf and similar, explicit casts are needed (double or int64).
*/
template <typename Tstorage, int Tdec_bits> class FixedT : public FixedRawT<Tstorage, Tdec_bits> {
/* private block up here, because we need the typedef later on */
private:
/** We shortcut the underlying data type to "Raw", to save typing */
typedef FixedRawT<Tstorage, Tdec_bits> Raw;
public:
/**
* Ctor for assignment with other, non floating, variable types
* @param value The Value we should assign to the Fixed
*/
template <typename T> FixedT(T value) : Raw(FixedHelperT<T>::Raw(value, Tdec_bits)) {}
/** As a constructor without initializing, just use the one that Raw uses. Sets a variable to zero */
FixedT() : Raw() {}
/**
* Ctor for use with a fraction, useful for initing a variable to a non-integer number at declaration.
* @param numerator The Nominator of the fraction
* @param denominator The Denominator of the fraction
*/
FixedT(int numerator, int denominator) {Raw::m_data = ((int64)numerator << Raw::dec_bits) / (int64)denominator;}
/**
* Equality operator
* @param comparator The non-floating point variable we want to compare against
*/
template <typename T>
bool operator ==(const T &comparator) const { return Raw::m_data == (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }
/**
* Inequality operator
* @param comparator The non-floating point variable we want to compare against
*/
template <typename T>
bool operator !=(const T &comparator) const { return Raw::m_data != (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }
/**
* Greater or equal operator
* @param comparator The non-floating point variable we want to compare against
*/
template <typename T>
bool operator >=(const T &comparator) const { return Raw::m_data >= (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }
/**
* Less or equal operator
* @param comparator The non-floating point variable we want to compare against
*/
template <typename T>
bool operator <=(const T &comparator) const { return Raw::m_data <= (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }
/**
* Greater than operator
* @param comparator The non-floating point variable we want to compare against
*/
template <typename T>
bool operator >(const T &comparator) const { return Raw::m_data > (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }
/**
* Less than operator
* @param comparator The non-floating point variable we want to compare against
*/
template <typename T>
bool operator <(const T &comparator) const { return Raw::m_data < (Tstorage)FixedHelperT<T>::Raw(comparator, Tdec_bits); }
/**
* Addition for Fixed-point data types
* @param value The non-floating point number to add
*/
template <typename T> FixedT operator +(const T &value) const
{
return Raw(Raw::m_data + (Tstorage)FixedHelperT<T>::Raw(value, Tdec_bits));
}
/**
* Subtraction for Fixed-point data types
* @param value The non-floating point number to subtract
*/
template <typename T> FixedT operator -(const T &value) const
{
return Raw(Raw::m_data - (Tstorage)FixedHelperT<T>::Raw(value, Tdec_bits));
}
/**
* A simple multiplication for non-floating data types
* @param value The non floating-point factor
*/
template <typename T> FixedT operator *(const T &value) const
{
return Raw( (((int64)Raw::m_data) * FixedHelperT<T>::Raw(value)) >> FixedHelperT<T>::dec_bits);
}
/**
* A simple division for non-floating data types
* @param value The non floating-point divisor
*/
template <typename T> FixedT operator /(const T &value) const
{
return Raw( (((int64)Raw::m_data) << FixedHelperT<T>::dec_bits) / FixedHelperT<T>::Raw(value));
}
/**
* Addition-assignment for Fixed-point data types
* @param value The non-floating point number to add
*/
template <typename T> FixedT& operator +=(const T &value)
{
Raw::m_data = Raw::m_data + (Tstorage)FixedHelperT<T>::Raw(value, Tdec_bits);
return *this;
}
/**
* Subtract-assignment for Fixed-point data types
* @param value The non-floating point number to subtract
*/
template <typename T> FixedT& operator -=(const T &value)
{
Raw::m_data = Raw::m_data - (Tstorage)FixedHelperT<T>::Raw(value, Tdec_bits);
return *this;
}
/**
* Multiply-assignment for Fixed-point data types
* @param value The non-floating point number to multiply
*/
template <typename T> FixedT& operator *=(const T &value)
{
Raw::m_data = (Raw::m_data * (Tstorage)FixedHelperT<T>::Raw(value)) >> FixedHelperT<T>::dec_bits;
return *this;
}
/**
* Divide-assignment for Fixed-point data types
* @param value The non-floating point number to use as divisor
*/
template <typename T> FixedT& operator /=(const T &value)
{
Raw::m_data = (Raw::m_data << FixedHelperT<T>::dec_bits) / (Tstorage)FixedHelperT<T>::Raw(value);
return *this;
}
/**
* Stream operator, used for floating point output
* @param os The stream we are going to write to
* @param value The Fixed-point variable we want to write in the stream
*/
friend std::ostream& operator << (std::ostream &os, const FixedT &value) { os << (double)value.m_data / (1ULL << Raw::dec_bits); return os; }
};