AbaKus – a complex calculator
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#ifndef ABAKUS_NUMERICTYPES_H
#define ABAKUS_NUMERICTYPES_H
/*
* numerictypes.h - part of abakus
* Copyright (C) 2004, 2005 Michael Pyne <michael.pyne@kdemail.net>
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include <sstream>
#include <string>
#include <tqstring.h>
#include <tqstringlist.h>
#include <tqregexp.h>
#include "hmath.h"
#include "config.h"
#if HAVE_MPFR
#include <mpfr.h>
#endif
namespace Abakus
{
/* What trigonometric mode we're in. */
typedef enum { Degrees, Radians } TrigMode;
/* Shared application-wide */
extern TrigMode m_trigMode;
/* Precision to display at. */
extern int m_prec;
/**
* Representation of a number type. Includes the basic operators, along with
* built-in functions such as abs() and mod().
*
* You need to actually define it using template specializations though. You
* can add functions in a specialization, it may be worth it to have the
* functions declared here as well so that you get a compiler error if you
* forget to implement it.
*
* Note that since we're using a specialization, and then typedef'ing the
* new specialized class to number_t, that means we only support one type of
* number at a time, and the choice is made at compile-time.
*/
template <typename T>
class number
{
public:
/// Default ctor and set-and-assign ctor wrapped in one.
number(const T& t = T());
/// Copy constructor.
number(const number &other);
/// Create number from textual representation, useful for ginormously
/// precise numbers.
number(const char *str);
/// Convienience constructor to create a number from an integer.
explicit number(int i);
/// Assignment operator. Be sure to check for &other == this if necessary!
number<T> &operator =(const number<T> &other);
// You need to implement the suite of comparison operators as well, along
// with the negation operator. Sorry.
bool operator!=(const number<T> &other) const;
bool operator==(const number<T> &other) const;
bool operator<(const number<T> &other) const;
bool operator>(const number<T> &other) const;
bool operator<=(const number<T> &other) const;
bool operator>=(const number<T> &other) const;
number<T> operator -() const;
// These functions must be implemented by all specializations to be used.
// Note that when implementing these functions, the implicit value is the
// value that this object is wrapping. E.g. you'd call the function on
// a number object, kind of like 3.sin() if you were using Ruby.
// Trigonometric, must accept values in degrees.
number<T> sin() const;
number<T> cos() const;
number<T> tan() const;
// Inverse trigonometric, must return result in Degrees if necessary.
number<T> asin() const;
number<T> acos() const;
number<T> atan() const;
// Hyperbolic trigonometric (doesn't use Degrees).
number<T> sinh() const;
number<T> cosh() const;
number<T> tanh() const;
// Inverse hyperbolic trigonometric (doesn't use degrees).
number<T> asinh() const;
number<T> acosh() const;
number<T> atanh() const;
/// @return Number rounded to closest integer less than or equal to value.
number<T> floor() const;
/// @return Number rounded to closest integer greater than or equal to value.
number<T> ceil() const;
/// @return Number with only integer component of result.
number<T> integer() const;
/// @return Number with only fractional component of result.
number<T> frac() const;
/**
* @return Number rounded to nearest integer. What to do in 'strange'
* situations is specialization-dependant, I don't really care enough to
* mandate one or the other.
*/
number<T> round() const;
/// @return Absolute value of number.
number<T> abs() const;
/// @return Square root of number.
number<T> sqrt() const;
/// @return Natural-base logarithm of value.
number<T> ln() const;
/// @return base-10 logarithm of value.
number<T> log() const;
/// @return Natural base raised to the power given by our value.
number<T> exp() const;
/// @return Our value raised to the \p exponent power. Would be nice if
/// it supported even exponents on negative numbers correctly.
number<T> pow(const number<T> &exponent);
/// @return value rounded to double precision.
double asDouble() const;
/// @return Textual representation of the number, adjusted to the user's
/// current precision.
TQString toString() const;
/// @return Our value.
T value() const;
};
// You should also remember to overload the math operators for your
// specialization. These generic ones should work for templates wrapping a
// type that C++ already has operators for.
template<typename T>
inline number<T> operator+(const number<T> &l, const number<T> &r)
{
return number<T>(l.value() + r.value());
}
template<typename T>
inline number<T> operator-(const number<T> &l, const number<T> &r)
{
return number<T>(l.value() - r.value());
}
template<typename T>
inline number<T> operator*(const number<T> &l, const number<T> &r)
{
return number<T>(l.value() * r.value());
}
template<typename T>
inline number<T> operator/(const number<T> &l, const number<T> &r)
{
return number<T>(l.value() / r.value());
}
#if HAVE_MPFR
/**
* Utility function to convert a MPFR number to a string. This is declared
* this way so that when it changes we don't have to recompile all of Abakus.
*
* This function obeys the precision settings of the user. This means that if
* you change the precision between function calls, you may get different
* results, even on the same number!
*
* But, don't use this directly, you should be using
* number<mpfr_ptr>::toString() instead!
*
* @param number MPFR number to convert to string.
* @return The number converted to a string, in US Decimal format at this time.
* @see number<>::toString()
*/
TQString convertToString(const mpfr_ptr &number);
/**
* This is a specialization of the number<> template for the MPFR numeric type.
* It uses a weird hack in that it is declared as specializing mpfr_ptr instead
* of mpfr_t like is used everywhere in MPFR's public API.
*
* This is because mpfr_t does not seem to play well with C++ templates (it
* is implemented internally as a 1-length array to get pointer semantics
* while also allocating memory.
*
* What this means is that should you ever have to deal with allocating
* memory, you need to use allocate space for it (mpfr_ptr is a pointer to
* __mpfr_struct).
*
* I don't like using the internal API this way, but I have little choice.
*
* @author Michael Pyne <michael.pyne@kdemail.net>
*/
template<>
class number<mpfr_ptr>
{
public:
typedef mpfr_ptr value_type;
static const mp_rnd_t RoundDirection = GMP_RNDN;
number(const value_type& t)
{
m_t = (mpfr_ptr) new __mpfr_struct;
mpfr_init_set(m_t, t, RoundDirection);
}
number(const number<value_type> &other)
{
m_t = (mpfr_ptr) new __mpfr_struct;
mpfr_init_set(m_t, other.m_t, RoundDirection);
}
number(const char *str)
{
m_t = (mpfr_ptr) new __mpfr_struct;
mpfr_init_set_str (m_t, str, 10, RoundDirection);
}
explicit number(int i)
{
m_t = (mpfr_ptr) new __mpfr_struct;
mpfr_init_set_si(m_t, (signed long int) i, RoundDirection);
}
/// Construct a number with a value of NaN.
number()
{
m_t = (mpfr_ptr) new __mpfr_struct;
mpfr_init(m_t);
}
~number()
{
mpfr_clear(m_t);
delete (__mpfr_struct *) m_t;
}
number<value_type> &operator=(const number<value_type> &other)
{
if(&other == this)
return *this;
mpfr_clear (m_t);
mpfr_init_set (m_t, other.m_t, RoundDirection);
return *this;
}
bool operator!=(const number<value_type> &other) const
{
return mpfr_equal_p(m_t, other.m_t) == 0;
}
bool operator==(const number<value_type> &other) const
{
return mpfr_equal_p(m_t, other.m_t) != 0;
}
bool operator<(const number<value_type> &other) const
{
return mpfr_less_p(m_t, other.m_t) != 0;
}
bool operator>(const number<value_type> &other) const
{
return mpfr_greater_p(m_t, other.m_t) != 0;
}
bool operator<=(const number<value_type> &other) const
{
return mpfr_lessequal_p(m_t, other.m_t) != 0;
}
bool operator>=(const number<value_type> &other) const
{
return mpfr_greaterequal_p(m_t, other.m_t) != 0;
}
number<value_type> operator -() const
{
number<value_type> result(m_t);
mpfr_neg(result.m_t, result.m_t, RoundDirection);
return result;
}
// internal
number<value_type> asRadians() const
{
if(m_trigMode == Degrees)
{
number<value_type> result(m_t);
mpfr_t pi;
mpfr_init (pi);
mpfr_const_pi (pi, RoundDirection);
mpfr_mul (result.m_t, result.m_t, pi, RoundDirection);
mpfr_div_ui (result.m_t, result.m_t, 180, RoundDirection);
mpfr_clear (pi);
return result;
}
else
return m_t;
}
// internal
number<value_type> toTrig() const
{
// Assumes num is in radians.
if(m_trigMode == Degrees)
{
number<value_type> result(m_t);
mpfr_t pi;
mpfr_init (pi);
mpfr_const_pi (pi, RoundDirection);
mpfr_mul_ui (result.m_t, result.m_t, 180, RoundDirection);
mpfr_div (result.m_t, result.m_t, pi, RoundDirection);
mpfr_clear (pi);
return result;
}
else
return m_t;
}
/* There is a lot of boilerplate ahead, so define a macro to declare and
* define some functions for us to forward the call to MPFR.
*/
#define DECLARE_IMPL_BASE(name, func, in, out) number<value_type> name() const \
{ \
number<value_type> result = in; \
mpfr_##func (result.m_t, result.m_t, RoundDirection); \
\
return out; \
}
// Normal function, uses 2 rather than 3 params
#define DECLARE_NAMED_IMPL2(name, func) number<value_type> name() const \
{ \
number<value_type> result = m_t; \
mpfr_##func (result.m_t, result.m_t); \
\
return result; \
}
// Normal function, but MPFL uses a different name than abakus.
#define DECLARE_NAMED_IMPL(name, func) DECLARE_IMPL_BASE(name, func, m_t, result)
// Normal function, just routes call to MPFR.
#define DECLARE_IMPL(name) DECLARE_NAMED_IMPL(name, name)
// Trig function, degrees in
#define DECLARE_TRIG_IN_IMPL(name) DECLARE_IMPL_BASE(name, name, asRadians(), result)
// Trig function, degrees out
#define DECLARE_TRIG_OUT_IMPL(name) DECLARE_IMPL_BASE(name, name, m_t, result.toTrig())
// Now declare our functions.
DECLARE_TRIG_IN_IMPL(sin)
DECLARE_TRIG_IN_IMPL(cos)
DECLARE_TRIG_IN_IMPL(tan)
DECLARE_IMPL(sinh)
DECLARE_IMPL(cosh)
DECLARE_IMPL(tanh)
DECLARE_TRIG_OUT_IMPL(asin)
DECLARE_TRIG_OUT_IMPL(acos)
DECLARE_TRIG_OUT_IMPL(atan)
DECLARE_IMPL(asinh)
DECLARE_IMPL(acosh)
DECLARE_IMPL(atanh)
DECLARE_NAMED_IMPL2(floor, floor)
DECLARE_NAMED_IMPL2(ceil, ceil)
DECLARE_NAMED_IMPL(integer, rint)
DECLARE_IMPL(frac)
DECLARE_NAMED_IMPL2(round, round)
DECLARE_IMPL(abs)
DECLARE_IMPL(sqrt)
DECLARE_NAMED_IMPL(ln, log)
DECLARE_NAMED_IMPL(log, log10)
DECLARE_IMPL(exp)
// Can't use macro for this one, it's sorta weird.
number<value_type> pow(const number<value_type> &exponent)
{
number<value_type> result = m_t;
mpfr_pow(result.m_t, result.m_t, exponent.m_t, RoundDirection);
return result;
}
double asDouble() const
{
return mpfr_get_d(m_t, RoundDirection);
}
// Note that this can be used dangerously, be careful.
value_type value() const { return m_t; }
TQString toString() const
{
// Move this to .cpp to avoid recompiling as I fix it.
return convertToString(m_t);
}
static number<value_type> nan()
{
// Doesn't apply, but the default value when initialized happens
// to be nan.
return number<value_type>();
}
static const value_type PI;
static const value_type E;
private:
mpfr_ptr m_t;
};
// Specializations of math operators for mpfr.
template<>
inline number<mpfr_ptr> operator+(const number<mpfr_ptr> &l, const number<mpfr_ptr> &r)
{
number<mpfr_ptr> result;
mpfr_add(result.value(), l.value(), r.value(), GMP_RNDN);
return result;
}
template<>
inline number<mpfr_ptr> operator-(const number<mpfr_ptr> &l, const number<mpfr_ptr> &r)
{
number<mpfr_ptr> result;
mpfr_sub(result.value(), l.value(), r.value(), GMP_RNDN);
return result;
}
template<>
inline number<mpfr_ptr> operator*(const number<mpfr_ptr> &l, const number<mpfr_ptr> &r)
{
number<mpfr_ptr> result;
mpfr_mul(result.value(), l.value(), r.value(), GMP_RNDN);
return result;
}
template<>
inline number<mpfr_ptr> operator/(const number<mpfr_ptr> &l, const number<mpfr_ptr> &r)
{
number<mpfr_ptr> result;
mpfr_div(result.value(), l.value(), r.value(), GMP_RNDN);
return result;
}
// Abakus namespace continues.
typedef number<mpfr_ptr> number_t;
#else
// Defined in numerictypes.cpp for ease of reimplementation.
TQString convertToString(const HNumber &num);
/**
* Specialization for internal HMath library, used if MPFR isn't usable.
*
* @author Michael Pyne <michael.pyne@kdemail.net>
*/
template<>
class number<HNumber>
{
public:
typedef HNumber value_type;
number(const HNumber& t = HNumber()) : m_t(t)
{
}
explicit number(int i) : m_t(i) { }
number(const number<HNumber> &other) : m_t(other.m_t) { }
number(const char *s) : m_t(s) { }
bool operator!=(const number<HNumber> &other) const
{
return m_t != other.m_t;
}
bool operator==(const number<HNumber> &other) const
{
return m_t == other.m_t;
}
bool operator<(const number<HNumber> &other) const
{
return m_t < other.m_t;
}
bool operator>(const number<HNumber> &other) const
{
return m_t > other.m_t;
}
bool operator<=(const number<HNumber> &other) const
{
return m_t <= other.m_t;
}
bool operator>=(const number<HNumber> &other) const
{
return m_t >= other.m_t;
}
number<HNumber> &operator=(const number<HNumber> &other)
{
m_t = other.m_t;
return *this;
}
HNumber asRadians() const
{
if(m_trigMode == Degrees)
return m_t * PI / HNumber("180.0");
else
return m_t;
}
HNumber toTrig(const HNumber &num) const
{
// Assumes num is in radians.
if(m_trigMode == Degrees)
return num * HNumber("180.0") / PI;
else
return num;
}
number<HNumber> sin() const
{
return HMath::sin(asRadians());
}
number<HNumber> cos() const
{
return HMath::cos(asRadians());
}
number<HNumber> tan() const
{
return HMath::tan(asRadians());
}
number<HNumber> asin() const
{
return toTrig(HMath::asin(m_t));
}
number<HNumber> acos() const
{
return toTrig(HMath::acos(m_t));
}
number<HNumber> atan() const
{
return toTrig(HMath::atan(m_t));
}
number<HNumber> floor() const
{
if(HMath::frac(m_t) == HNumber("0.0"))
return integer();
if(HMath::integer(m_t) < HNumber("0.0"))
return HMath::integer(m_t) - 1;
return integer();
}
number<HNumber> ceil() const
{
return floor().value() + HNumber(1);
}
/* There is a lot of boilerplate ahead, so define a macro to declare and
* define some functions for us to forward the call to HMath.
*/
#define DECLARE_IMPL(name) number<value_type> name() const \
{ return HMath::name(m_t); }
DECLARE_IMPL(frac)
DECLARE_IMPL(integer)
DECLARE_IMPL(round)
DECLARE_IMPL(abs)
DECLARE_IMPL(sqrt)
DECLARE_IMPL(ln)
DECLARE_IMPL(log)
DECLARE_IMPL(exp)
DECLARE_IMPL(sinh)
DECLARE_IMPL(cosh)
DECLARE_IMPL(tanh)
DECLARE_IMPL(asinh)
DECLARE_IMPL(acosh)
DECLARE_IMPL(atanh)
HNumber value() const { return m_t; }
double asDouble() const { return toString().toDouble(); }
number<HNumber> operator-() const { return HMath::negate(m_t); }
// TODO: I believe this doesn't work for negative numbers with even
// exponents. Which breaks simple stuff like (-2)^2. :(
number<HNumber> pow(const number<HNumber> &exponent)
{
return HMath::raise(m_t, exponent.m_t);
}
TQString toString() const
{
return convertToString(m_t);
}
static number<HNumber> nan()
{
return HNumber::nan();
}
static const HNumber PI;
static const HNumber E;
private:
HNumber m_t;
};
// Abakus namespace continues.
typedef number<HNumber> number_t;
#endif /* HAVE_MPFR */
}; // namespace Abakus
#endif /* ABAKUS_NUMERICTYPES_H */
// vim: set et ts=8 sw=4: