rmath.h

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#ifndef __math_h__
#define __math_h__

#include <string>
#include <float.h>

#include "asserts.h"
#include "types.h"
#include "estring.h"

/** A small set of numeric limits routines, since gcc prior to 3.x doesn't
 * have numeric_limits */

// ---------------------------------------------------------------------------

/** Find the maximum limit for a type, equivalent to
 * std::numeric_limits<T>.max() for systems that don't have the limits c++
 * header file. */
template<typename T>
static const T max_limit()
{
        T tmp = 0;
        static T max = 0;
        static bool found = false;

        if (found) {
                return(max);
        }
        
        tmp = 1;
        max = 0;
        while (tmp > max) {
                max = tmp;
                try {
                        tmp = (tmp * T(2)) + T(1);
                }
                catch(...) { }
        }
        found = true;
        return(max);
}

/** Find the maximum limit for a type, equivalent to
 * std::numeric_limits<T>.min() for systems that don't have the limits c++
 * header file.
 */
template<typename T>
static const T min_limit()
{
        T tmp = 0;
        static T min = 0;
        static bool found = false;

        if (found) {
                return(min);
        }
        
        tmp = -1;
        min = 0;
        while (tmp < min) {
                min = tmp;
                try {
                        tmp = (tmp * T(2)) - T(1);
                }
                catch(...) { }
        }
        
        try {
                tmp = - max_limit<T>() - T(1);
        }
        catch(...) { }
        if (tmp < min) {
                min = tmp;
        }

        found = true;
        return(min);
}

/** Return the largest possible number that a float may hold. */
#ifdef OSX_WORKAROUND
template<>
const float max_limit<float>();
#else
template<>
const float max_limit<float>()
{
        return(FLT_MAX);
}
#endif

/** Return the smallest positive number that a float may hold.
 *
 * Caveat: This is in contrast to other types, where min_limit<T>() will return
 * either 0 or the largest possible negative number that the type may hold.  If
 * you are looking for the largest possible negative number for any given type,
 * use lowest_value<T>() instead.
 */
#ifdef OSX_WORKAROUND
template<>
const float min_limit<float>();
#else
template<>
const float min_limit<float>()
{
        return(FLT_MIN);
}
#endif

/** Return the largest possible number that a double may hold. */
#ifdef OSX_WORKAROUND
template<>
const double max_limit<double>();
#else
template<>
const double max_limit<double>()
{
        return(DBL_MAX);
}
#endif

/** Return the smallest positive number that a double may hold.
 *
 * Caveat: This is in contrast to other types, where min_limit<T>() will return
 * either 0 or the largest possible negative number that the type may hold.  If
 * you are looking for the largest possible negative number for any given type,
 * use lowest_value<T>() instead.
 */
#ifdef OSX_WORKAROUND
template<>
const double min_limit<double>();
#else
template<>
const double min_limit<double>()
{
        return(DBL_MIN);
}
#endif

// ---------------------------------------------------------------------------

/** Return the max_limit of a variable.
 *
 * This is handy to have because it means
 * that the author may change the type of a variable without having to track
 * down all uses of max_limit or min_limit to change the type they measure.
 */
template<typename T>
static const T max_limit(const T& a_arg)
{
        T value;

        value = max_limit<T>();

        return(value);
}

/** Return the min_limit of a variable.
 *
 * This is handy to have because it means
 * that the author may change the type of a variable without having to track
 * down all uses of max_limit or min_limit to change the type they measure.
 */
template<typename T>
static const T min_limit(const T& a_arg)
{
        T value;

        value = min_limit<T>();

        return(value);
}

// ---------------------------------------------------------------------------

/** Return the maximum possible value a type may hold.
 *
 * This is just a convenience function to match lowest_value<T>().  All it does
 * is return the value of max_limit<T>().
 */
template<typename T>
static const T highest_value(void)
{
        T value;

        value = max_limit<T>();

        return(value);
}

/** Return the maximum possible value of a variable. */
template<typename T>
static const T highest_value(const T& a_arg)
{
        T value;

        value = highest_value<T>();

        return(value);
}

/** Return 0 for unsigned types, or the maximum negative value that the type
 * may hold.
 */
template<typename T>
static const T lowest_value(void)
{
        T value;

        value = -max_limit<T>();
        if (value > min_limit<T>())
                value = min_limit<T>();
        
        return(value);
}

/** Return 0 for unsigned types, or the maximum negative value that a variable
 * may hold.
 */
template<typename T>
static const T lowest_value(const T& a_arg)
{
        T value;

        value = lowest_value<T>();

        return(value);
}

// ---------------------------------------------------------------------------

/** Return the absolute value of a numeric type 
 *
 * Caveat: For some types, the maximum negative value is one larger than the
 * maximum positive value: specifically char.  Depending on the type and value,
 * it may be impossible to return the absolute value.  For such types under
 * such circumstances an exception is thrown.
 */
template<typename T>
T absolute(const T& a_num)
{
        T num;
        std::string es;

// std::cerr << "absolute(" << static_cast<long long>(a_num) << ") : BEGIN" << std::endl;
        num = a_num;
        if ((num < 0) && (num == min_limit<T>())) {
                TRY_nomem(es = "Absolute value is not containable by this type: ");
                if (is_char(num)) {
                        TRY_nomem(es += estring(static_cast<int>(num)));
                }
                else {
                        TRY_nomem(es += estring(num));
                }
                throw(ERROR(0,es));
        }
        if (num < 0) {
                num = -num;
                if (num < 0) {
                        TRY_nomem(es = "Absolute value is still negative: ");
                        if (is_char(num)) {
                                TRY_nomem(es += estring(static_cast<int>(num)));
                        }
                        else {
                                TRY_nomem(es += estring(num));
                        }
                        throw(INTERNAL_ERROR(0,es));
                }
// else std::cerr << "absolute(" << static_cast<long long>(a_num) << ") >= 0" << std::endl;
        }

// std::cerr << "absolute(" << static_cast<long long>(a_num) << ") = " << static_cast<long long>(num) << std::endl;
// std::cerr << "absolute(" << static_cast<long long>(a_num) << ") : END" << std::endl;
        return(num);
}

// ---------------------------------------------------------------------------

/** Safely manipulate numbers without worryiung about over/underflow error */
template<typename T>
class safe_num
{
public:
        /** C'tor */
        safe_num()
        {
                clear();
        }

        /** C'tor */
        safe_num(const T a_num)
        {
                clear();
                m_num = a_num;
        }

        /** C'tor */
        safe_num(const safe_num& a_class)
        {
                clear();
                m_num = a_class.value();
        }

        /** Clear the value */
        void clear(void)
        {
                m_num = static_cast<T>(0);
        }

        /** Return the value */
        const T value(void) const
        {
                return(m_num);
        }

        /** Assign a value */
        void assign(const T& a_arg)
        {
                m_num = a_arg;
        }

        /** Add a value */
        void add(const T& a_arg) 
        {
                bool overflow = false;
                T num;

                if (a_arg < static_cast<T>(0)) {
                        num = absolute(a_arg);
                        subtract(num);
                        return;
                }

                if (highest_value<T>() - a_arg < m_num)
                        overflow = true;

                if (overflow) {
                        estring es;

                        es = "Addition overflow error detected: ";
                        if (is_char(m_num))
                                es += estring(static_cast<int>(m_num));
                        else
                                es += estring(m_num);
                        es += " + ";
                        if (is_char(a_arg))
                                es += estring(static_cast<int>(a_arg));
                        else
                                es += estring(a_arg);
                        throw(INTERNAL_ERROR(0,es));
                }
                m_num += a_arg;
        }

        /** Subtract a value */
        void subtract(const T& a_arg) 
        {
                bool underflow = false;
                T num;

                if (a_arg < static_cast<T>(0)) {
                        num = absolute(a_arg);
                        add(num);
                        return;
                }

                if (lowest_value<T>() < 0) {
                        if (m_num < lowest_value<T>() + a_arg)
                                underflow = true;
                }
                else {
                        if (m_num - lowest_value<T>() < a_arg)
                                underflow = true;
                }

                if (underflow) {
                        estring es;

                        es = "Subtraction underflow error detected: ";
                        if (is_char(m_num))
                                es += estring(static_cast<int>(m_num));
                        else
                                es += estring(m_num);
                        es += " - ";
                        if (is_char(a_arg))
                                es += estring(static_cast<int>(a_arg));
                        else
                                es += estring(a_arg);
                        throw(INTERNAL_ERROR(0,es));
                }
                m_num -= a_arg;
        }

        /** Multiply by a value */
        void multiply(const T& a_arg) 
        {
                bool overflow = false;

                if ((a_arg == 0) || (m_num == 0) || (a_arg == 1) || (m_num == 1)) {
                        m_num *= a_arg;
                        return;
                }

                if ((lowest_value<T>() < 0) && (m_num < 0) && (a_arg < 0)) {
                        if (-highest_value<T>() > a_arg)
                                overflow = true;
                        if (-(highest_value<T>() / a_arg) < -m_num)
                                overflow = true;
                }
                else
                if ((lowest_value<T>() < 0) && (m_num < 0) && (a_arg >= 0)) {
                        if (lowest_value<T>() / a_arg > m_num)
                                overflow = true;
                }
                else
                if ((lowest_value<T>() < 0) && (m_num >= 0) && (a_arg < 0)) {
                        if (lowest_value<T>() / m_num > a_arg)
                                overflow = true;
                }
                else
                if ((lowest_value<T>() < 0) && (m_num >= 0) && (a_arg >= 0)) {
                        if (highest_value<T>() / a_arg < m_num)
                                overflow = true;
                }
                else
                if ((lowest_value<T>() >= 0) && (m_num >= 0) && (a_arg >= 0)) {
                        if (highest_value<T>() / a_arg < m_num)
                                overflow = true;
                }
                else {
                        // This should never happen
                        ASSERT(0);
                }

                if (overflow) {
                        estring es;

                        es = "Multiplication overflow error detected: ";
                        if (is_char(m_num))
                                es += estring(static_cast<int>(m_num));
                        else
                                es += estring(m_num);
                        es += " * ";
                        if (is_char(a_arg))
                                es += estring(static_cast<int>(a_arg));
                        else
                                es += estring(a_arg);
                        throw(INTERNAL_ERROR(0,es));
                }
                m_num *= a_arg;
        }

        /** Divide by a value */
        void divide(const T& a_arg) 
        {
                T num;

                if (a_arg == static_cast<T>(0)) {
                        estring es;

                        es = "Division by zero error detected: ";
                        if (is_char(m_num))
                                es += estring(static_cast<int>(m_num));
                        else
                                es += estring(m_num);
                        es += " / ";
                        if (is_char(a_arg))
                                es += estring(static_cast<int>(a_arg));
                        else
                                es += estring(a_arg);
                        throw(INTERNAL_ERROR(0,es));
                }

                num = m_num;
                num /= a_arg;
                if ((m_num < 0) && (a_arg < 0) && (num < 0)) {
                        estring es;

                        es = "Division result has incorrect sign: ";
                        if (is_char(m_num))
                                es += estring(static_cast<int>(m_num));
                        else
                                es += estring(m_num);
                        es += " / ";
                        if (is_char(a_arg))
                                es += estring(static_cast<int>(a_arg));
                        else
                                es += estring(a_arg);
                        es += " != ";
                        if (is_char(num))
                                es += estring(static_cast<int>(num));
                        else
                                es += estring(num);
                        throw(INTERNAL_ERROR(0,es));
                }

                m_num = num;
                return;
        }

        /** Assign a safe_num */
        void assign(const safe_num<T>& a_class) 
        {
                assign(a_class.value());
        }

        /** Add a safe_num */
        void add(const safe_num<T>& a_class) 
        {
                add(a_class.value());
        }

        /** Subtract a safe_num */
        void subtract(const safe_num<T>& a_class)
        {
                subtract(a_class.value());
        }

        /** Multiply by a safe_num */
        void multiply(const safe_num<T>& a_class) 
        {
                multiply(a_class.value());
        }

        /** Divide by a safe_num */
        void divide(const safe_num<T>& a_class)
        {
                divide(a_class.value());
        }

        /** Boolean operator */
        const bool operator==(const T& a_arg) const 
        {
                bool value;

                value = (m_num == a_arg);

                return(value);
        }

        /** Boolean operator */
        const bool operator==(const safe_num<T>& a_class) const 
        {
                bool value;

                value = (m_num == a_class.value());

                return(value);
        }

        /** Boolean operator */
        const bool operator!=(const T& a_arg) const
        {
                bool value;

                value = (m_num != a_arg);

                return(value);
        }

        /** Boolean operator */
        const bool operator!=(const safe_num<T>& a_class) const
        {
                bool value;

                value = (m_num != a_class.value());

                return(value);
        }

        /** Boolean operator */
        const bool operator<(const T& a_arg) const 
        {
                bool value;

                value = (m_num < a_arg);

                return(value);
        }

        /** Boolean operator */
        const bool operator<(const safe_num<T>& a_class) const
        {
                bool value;

                value = (m_num < a_class.value());

                return(value);
        }

        /** Boolean operator */
        const bool operator>(const T& a_arg) const
        {
                bool value;

                value = (m_num > a_arg);

                return(value);
        }

        /** Boolean operator */
        const bool operator>(const safe_num<T>& a_class) const 
        {
                bool value;

                value = (m_num > a_class.value());

                return(value);
        }

        /** Boolean operator */
        const bool operator<=(const T& a_arg) const
        {
                bool value;

                value = (m_num <= a_arg);

                return(value);
        }

        /** Boolean operator */
        const bool operator<=(const safe_num<T>& a_class) const
        {
                bool value;

                value = (m_num <= a_class.value());

                return(value);
        }

        /** Boolean operator */
        const bool operator>=(const T& a_arg) const
        {
                bool value;

                value = (m_num >= a_arg);

                return(value);
        }

        /** Boolean operator */
        const bool operator>=(const safe_num<T>& a_class) const
        {
                bool value;

                value = (m_num >= a_class.value());

                return(value);
        }

        /** Arithmetic operator */
        safe_num<T>& operator+=(safe_num<T> a_class)
        {
                add(a_class);

                return(*this);
        }

        /** Arithmetic operator */
        safe_num<T>& operator-=(safe_num<T> a_class)
        {
                subtract(a_class);

                return(*this);
        }

        /** Arithmetic operator */
        safe_num<T>& operator*=(safe_num<T> a_class)
        {
                multiply(a_class);

                return(*this);
        }

        /** Arithmetic operator */
        safe_num<T>& operator/=(safe_num<T> a_class)
        {
                divide(a_class);

                return(*this);
        }

        /** Arithmetic operator */
        safe_num<T>& operator%=(safe_num<T> a_class)
        {
                m_num %= a_class.value();

                return(*this);
        }

private:
        T m_num;
};

/** Arithmetic operator */
template<typename T>
safe_num<T> operator+(safe_num<T> a_class1, safe_num<T> a_class2)
{
        safe_num<T> result;

        result.assign(a_class1);
        result.add(a_class2);

        return(result);
}

/** Arithmetic operator */
template<typename T>
safe_num<T> operator-(safe_num<T> a_class1, safe_num<T> a_class2)
{
        safe_num<T> result;

        result.assign(a_class1);
        result.subtract(a_class2);
        
        return(result);
}

/** Arithmetic operator */
template<typename T>
safe_num<T> operator*(safe_num<T> a_class1, safe_num<T> a_class2)
{
        safe_num<T> result;

        result.assign(a_class1);
        result.multiply(a_class2);

        return(result);
}

/** Arithmetic operator */
template<typename T>
safe_num<T> operator/(safe_num<T> a_class1, safe_num<T> a_class2)
{
        safe_num<T> result;

        result.assign(a_class1);
        result.divide(a_class2);

        return(result);
}

/** Arithmetic operator */
template<typename T>
safe_num<T> operator%(safe_num<T> a_class1, safe_num<T> a_class2)
{
        safe_num<T> result;

        result.assign(a_class1.value() % a_class2.value());

        return(result);
}

/** Arithmetic operator */
template<typename T>
safe_num<T>& operator++(safe_num<T>& a_class)
{
        a_class.add(static_cast<T>(1));

        return(a_class);
}

/** Arithmetic operator */
template<typename T>
safe_num<T> operator++(safe_num<T>& a_class, int)
{
        safe_num<T> result;

        result.assign(a_class);
        a_class.add(static_cast<T>(1));

        return(result);
}

/** Arithmetic operator */
template<typename T>
safe_num<T>& operator--(safe_num<T>& a_class)
{
        a_class.subtract(static_cast<T>(1));

        return(a_class);
}

/** Arithmetic operator */
template<typename T>
safe_num<T> operator--(safe_num<T>& a_class, int)
{
        safe_num<T> result;

        result.assign(a_class);
        a_class.subtract(static_cast<T>(1));

        return(result);
}

/** Arithmetic operator */
template<typename T>
std::ostream& operator<<(std::ostream& a_out, safe_num<T> a_class)
{
        a_out << a_class.value();

        return(a_out);
}

/** Arithmetic operator */
template<typename T>
std::istream& operator>>(std::istream& a_in, safe_num<T>& a_class)
{
        T num;

        a_in >> num;
        a_class = num;

        return(a_in);
}

// ---------------------------------------------------------------------------

#endif