Fixed precision floating point and locale facets

[Roger Leigh]

Hello,

I'm writing a fixed-precision floating point class, based on the ideas
in the example fixed_pt class in the "Practical C++ Programming" book
by Steve Oualline (O' Reilly). This uses a long int to store the
value, and the precision (number of decimal points) is variable (it's
a templated class):

template <size_t _decimal_places = 4>
class FixedFloat {
private:
/// The integer value.
long int m_value;
[...]
};

double is not allowed due to precision loss.). The conversion between
long int and string forms is done in the latter functions.

To output a number, I was manually splitting up the number into whole
and fractional parts and processing them separately, using '.' as the
decimal point symbol. However, I've just discovered the existence of
std::locale::numeric and std::locale::monetary locale facets, and the
num_put() and num_get() methods. Ideally, I'd like to use these
functions for the the conversions (FixedFloat -> std::string).
However, their support for the standard numeric types (int, long,
float, double) is hard-coded into the class. I can't risk conversion
to a supported type such as double, due to loss of precision (0.60
would becomes 0.59 on my i686-pc-linux-gnu arch), and they will be
used to process financial data!

Is it possible to extend these to support my FixedFloat class?

Is it reasonable to derive from std::num_put in this case? I had a
look into the GNU libstdc++ headers to see if it was possible, but
they were hideously complex, and I'm not keen on using the internals
such as num_put<>::do_put and __convert_from_v(), since these are
presumably non-portable.

Lastly, are there any standard classes that do this sort of thing?


Many thanks!
Roger

 

[P.J. Plauger]

To output a number, I was manually splitting up the number into whole
and fractional parts and processing them separately, using '.' as the
decimal point symbol. However, I've just discovered the existence of
std::locale::numeric and std::locale::monetary locale facets, and the
num_put() and num_get() methods. Ideally, I'd like to use these
functions for the the conversions (FixedFloat -> std::string).
However, their support for the standard numeric types (int, long,
float, double) is hard-coded into the class. I can't risk conversion
to a supported type such as double, due to loss of precision (0.60
would becomes 0.59 on my i686-pc-linux-gnu arch), and they will be
used to process financial data!

Is it possible to extend these to support my FixedFloat class?

It's possible, but probably not a rewarding exercise.

Is it reasonable to derive from std::num_put in this case? I had a
look into the GNU libstdc++ headers to see if it was possible, but
they were hideously complex, and I'm not keen on using the internals
such as num_put<>::do_put and __convert_from_v(), since these are
presumably non-portable.

The do_put part is portable, the other isn't. But you're right to
observe that they're hideously complex.

Lastly, are there any standard classes that do this sort of thing?

You can pervert money_put and moneypunct to output a digit sequence
stored in a string, with a specified number of decimal places, commas
between thousands groups, etc.

P.J. Plauger
Dinkumware, Ltd.
http://www.dinkumware.com

 

[Roger Leigh]

It's possible, but probably not a rewarding exercise.

If I'm correct here, I would have to add my own custom locale facet(s)
to allow this, but I'd need to do this manually for each locale I want
to use, which would be a pain.

[do_put() and __convert_from_v()]

The do_put part is portable, the other isn't. But you're right to
observe that they're hideously complex.
OK.


You can pervert money_put and moneypunct to output a digit sequence
stored in a string, with a specified number of decimal places, commas
between thousands groups, etc.

This looks like what I'll do. I'll derive a "Money" class from
FixedFloat and do that in there, overriding the standard ostream<< and
istream>> operators.

I've attached a copy of the working class, and a small driver program
to show it in action (sorry it's so long). I have a few questions
about this:

1. Is the header file OK style-wise? Is there anything wrong that I
should not be doing?

2. I've noticed that the modulus (operator%) member and friend
functions can be out by a small factor e.g. 0.0001 in a 4
d.p. precision class. With fixed-point arithmetic, should I be
doing anything to correct this? Is it actually incorrect? For
some reason, I couldn't get the "real" % operator to work, so had
to resort to the hack that actually gets used (subtracting the
result of division and subsequent multiplication from the original
value).

3. Looking at the compiled binary, the FixedFloat symbols have weak,
rather than vague linkage. I thought that /all/ templated class
methods and functions would be vague. This is with GCC 3.3.2, GNU
ld 2.14.90.0.6 and binutils 2.14.90.0.6-5 on i686-pc-linux-gnu
using ELF binary format (this is probably OT).

4. In the stream output and extraction friend classes, is the use of
locales correct? I've not used locales (in C++) before, and I've
done this using the Josuttis Standard Library book.


Many thanks for your time,
Roger


----begin main.cc----
#include <iostream>

#include "fixedfloat.h"

int main()
{
std::locale::global(std::locale(""));
std::cout.imbue(std::locale());

FixedFloat<4> f1("4.1246");
FixedFloat<4> f2("2.3443");

std::cout << f1 << std::endl;
std::cout << f2 << std::endl;

FixedFloat<4> n(f1);
FixedFloat<4> o;
o = f2;

std::cout << n << std::endl;
std::cout << o << std::endl;

std::cout << "Signedness\n";
std::cout << +f1 << std::endl;
std::cout << -f1 << std::endl;

std::cout << "Binary arithmetic\n";
std::cout << f1 << "-" << f2 << "=" << f1-f2 << "\n";
std::cout << f1 << "+" << f2 << "=" << f1+f2 << "\n";
std::cout << f1 << "*" << f2 << "=" << f1*f2 << "\n";
std::cout << f1 << "/" << f2 << "=" << f1/f2 << "\n";
std::cout << f1 << "%" << f2 << "=" << f1%f2 << "\n";
std::cout << -f1 << "/" << f2 << "=" << (-f1)/f2 << "\n";
std::cout << -f1 << "%" << f2 << "=" << (-f1)%f2 << "\n";

std::cout << "Logic\n";
std::cout << f1 << "==" << f1 << "=" << (f1==f1) << "\n";
std::cout << f1 << "==" << f2 << "=" << (f1==f2) << "\n";
std::cout << f1 << "!=" << f1 << "=" << (f1!=f1) << "\n";
std::cout << f1 << "!=" << f2 << "=" << (f1!=f2) << "\n";

std::cout << "Unary arithmetic\n";
FixedFloat<4> f3 = f1;
f3 += FixedFloat<4>("2.3430");
std::cout << f1 << "+=2.3430" << "=" << f3 << "\n";

f3 = f1;
f3 -= FixedFloat<4>("2.3430");
std::cout << f1 << "-=2.3430" << "=" << f3 << "\n";

f3 = f1;
f3 *= FixedFloat<4>("2.3430");
std::cout << f1 << "*=2.3430" << "=" << f3 << "\n";

f3 = f1;
f3 /= FixedFloat<4>("2.3430");
std::cout << f1 << "/=2.3430" << "=" << f3 << "\n";

f3 = f1;
f3 %= FixedFloat<4>("2.3430");
std::cout << f1 << "%=2.3430" << "=" << f3 << "\n";

f3 = f1;
++f3;
std::cout << "++" << f1 << "=" << f3 << "\n";

f3 = f1;
std::cout << f1 << "++" << "=" << f3++ << " (before)\n";
std::cout << f1 << "++" << "=" << f3 << " (after)\n";

f3 = f1;
--f3;
std::cout << "--" << f1 << "=" << f3 << "\n";

f3 = f1;
std::cout << f1 << "--" << "=" << f3-- << " (before)\n";
std::cout << f1 << "--" << "=" << f3 << " (after)\n";

return 1;
}
----end main.cc----

----begin fixedfloat.h----
// fixed floating point class -*- C++ -*-
// $Id: template.cc,v 1.1 2003/09/14 21:56:55 roger Exp $
//
// Copyright (C) 2003 Roger Leigh.
//
// Authors: Roger Leigh <[email protected]>

#include <iomanip>
#include <istream>
#include <locale>
#include <ostream>
#include <sstream>

/**
* A class to represent fixed floating point numbers with high
* accuracy.
* The float and double data types to not offer enough accuracy when
* dealing with some types of data, for example currency values, since
* they cannot garuantee that a particular value is representable in
* their floating-point binary format. This class will garuantee
* accuracy, with the restriction that there is a fixed number of
* decimal places after the decimal point. Internally, the value is
* held as a long integer.
*
* Conversion to and from the double data type is not implicit--this
* must be done using the methods provided. However, conversion to
* and from std::string is possible.
*/
template <size_t _decimal_places = 2>
class FixedFloat {
public:
/// The type used internally to hold fixed floating point values.
typedef long int value_type;

private:
/// The integer value.
value_type m_value;
/// The correction factor.
value_type m_correction;

/**
* Compute the correction factor.
* The correction value is used to correct multiplication and
* division of fixed point numbers.
*/
void compute_correction()
{
m_correction = 1;
for (int i = 0; i < _decimal_places; ++i)
m_correction *= 10;
}

/**
* The constructor.
* The initial value is set to the value provided.
* @param value the initial value.
*/
FixedFloat(value_type value):
m_value(value)
{
compute_correction();
}

public:
/**
* The constructor.
* The initial value is set to 0.
*/
FixedFloat():
m_value(0)
{
compute_correction();
}

/**
* The constructor.
* The initial value is set to the value provided. If there are too
* many numbers after the decimal place, they will be rounded to the
* nearest representable value (0 to 4 are rounded down, 5 to 9 are
* rounded up.
* @param value the initial value.
*/
FixedFloat(const std::string& value)
{
compute_correction();

std::istringstream input(value);
input >> *this;
}

/**
* The copy constructor.
*/
FixedFloat(const FixedFloat& original):
m_value(original.m_value),
m_correction(original.m_correction)
{}

/// The destructor.
~FixedFloat()
{}


FixedFloat& operator = (const FixedFloat& rhs)
{
m_value = rhs.m_value;
return *this;
}

FixedFloat& operator += (const FixedFloat& rhs)
{
m_value += rhs.m_value;
return *this;
}

FixedFloat& operator -= (const FixedFloat& rhs)
{
m_value -= rhs.m_value;
return *this;
}

FixedFloat& operator *= (const FixedFloat& rhs)
{
m_value *= rhs.m_value;
m_value /= m_correction;
return *this;
}

FixedFloat& operator /= (const FixedFloat& rhs)
{
m_value *= m_correction;
m_value /= rhs.m_value;
return *this;
}

FixedFloat& operator %= (const FixedFloat& rhs)
{
*this = (*this - ((*this / rhs) * rhs));
return *this;
}

FixedFloat& operator ++ ()
{
m_value += m_correction;
return *this;
}

FixedFloat operator ++ (int)
{
FixedFloat ret(*this);
m_value += m_correction;
return ret;
}

FixedFloat& operator -- ()
{
m_value -= m_correction;
return *this;
}

FixedFloat operator -- (int)
{
FixedFloat ret(*this);
m_value -= m_correction;
return ret;
}

friend FixedFloat<_decimal_places> operator +<> (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs);

friend FixedFloat<_decimal_places> operator -<> (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs);

friend FixedFloat<_decimal_places> operator *<> (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs);

friend FixedFloat<_decimal_places> operator /<> (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs);

friend FixedFloat<_decimal_places> operator %<> (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs);

friend bool operator ==<> (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs);

friend bool operator !=<> (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs);

friend FixedFloat<_decimal_places> operator -<> (const FixedFloat<_decimal_places>& rhs);

friend FixedFloat<_decimal_places> operator +<> (const FixedFloat<_decimal_places>& rhs);

friend std:stream& operator <<<> (std:stream& output_stream,
const FixedFloat<_decimal_places>& rhs);

friend std::istream& operator >><> (std::istream& input_stream,
FixedFloat<_decimal_places>& rhs);

}; // class FixedFloat<>


// Friend functions.

template <size_t _decimal_places>
inline FixedFloat<_decimal_places> operator + (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs)
{
return FixedFloat<_decimal_places>(lhs.m_value + rhs.m_value);
}

template <size_t _decimal_places>
inline FixedFloat<_decimal_places> operator - (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs)
{
return FixedFloat<_decimal_places>(lhs.m_value - rhs.m_value);
}

template <size_t _decimal_places>
inline FixedFloat<_decimal_places> operator * (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs)
{
return FixedFloat<_decimal_places>((lhs.m_value * rhs.m_value) / lhs.m_correction);
}

template <size_t _decimal_places>
inline FixedFloat<_decimal_places> operator / (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs)
{
return FixedFloat<_decimal_places>((lhs.m_value * lhs.m_correction) / rhs.m_value);
}

template <size_t _decimal_places>
inline FixedFloat<_decimal_places> operator % (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs)
{
return FixedFloat<_decimal_places>(lhs - ((lhs / rhs) * rhs));
}

template <size_t _decimal_places>
inline bool operator == (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs)
{
return lhs.m_value == rhs.m_value;
}

template <size_t _decimal_places>
inline bool operator != (const FixedFloat<_decimal_places>& lhs,
const FixedFloat<_decimal_places>& rhs)
{
return lhs.m_value != rhs.m_value;
}

template <size_t _decimal_places>
inline FixedFloat<_decimal_places> operator - (const FixedFloat<_decimal_places>& rhs)
{
return FixedFloat<_decimal_places>(-rhs.m_value);
}

template <size_t _decimal_places>
inline FixedFloat<_decimal_places> operator + (const FixedFloat<_decimal_places>& rhs)
{
return FixedFloat<_decimal_places>(rhs.m_value);
}

template <size_t _decimal_places>
inline std:stream& operator << (std:stream& output_stream,
const FixedFloat<_decimal_places>& rhs)
{
bool negative = false;
if (rhs.m_value < 0)
negative = true;

typename FixedFloat<_decimal_places>::value_type whole_part
= rhs.m_value / rhs.m_correction;
typename FixedFloat<_decimal_places>::value_type fractional_part
= rhs.m_value - (whole_part * rhs.m_correction);

if (whole_part < 0) // turn into a positive number
whole_part = -whole_part;
if (fractional_part < 0) // turn into a positive number
fractional_part = -fractional_part;

std:stringstream s;
s.copyfmt(output_stream);
s.width(0);

if (negative == true)
s << '-'; // output sign, if needed
s << whole_part; // output the whole part
if (_decimal_places > 0) // output the fractional part, including decimal point
{
std:stringstream fractional_string;
fractional_string.imbue(std::locale::classic()); // "plain" numbers
fractional_string << fractional_part;

s << std::use_facet<std::numpunct<char> >(s.getloc()).decimal_point()
<< std::setw(_decimal_places) << std::setfill('0')
<< fractional_string.str();
}
output_stream << s.str();

return output_stream;
}

template <size_t _decimal_places>
inline std::istream& operator >> (std::istream& input_stream,
FixedFloat<_decimal_places>& rhs)
{
bool negative = false;
typename FixedFloat<_decimal_places>::value_type whole_part = 0;
char decimal_point;
typename FixedFloat<_decimal_places>::value_type fractional_part = 0;

std::istream::sentry stream_sentry(input_stream, true);

if (stream_sentry)
{
// Get the whole part of the number
if (input_stream.bad())
return input_stream;

// Check signedness (would be lost if value is < 1, since -0 == 0)
if (input_stream.peek() == '+')
negative = false;
else if (input_stream.peek() == '-')
negative = true;

input_stream >> whole_part;
whole_part *= rhs.m_correction;
if (whole_part < 0) // turn into a positive number
whole_part = -whole_part;
if (_decimal_places > 0)
{
// Get the decimal point.
if (input_stream.bad())
return input_stream;

input_stream >> decimal_point;
// Check that the decimal point was the correct type for this locale
if (decimal_point != std::use_facet<std::numpunct<char> >(input_stream.getloc()).decimal_point())
{
rhs.m_value = 0;
input_stream.setstate(std::ios::failbit);
}

// Get the fractional part of the number
fractional_part = 0;
for (size_t i = _decimal_places; i > 0; --i)
{
if (input_stream.bad())
return input_stream;

char decimal_char = '0';
input_stream >> decimal_char;
if (decimal_char < '0' || decimal_char > '9')
{
rhs.m_value = 0;
input_stream.setstate(std::ios::failbit);
return input_stream;
}
size_t decimal_number = decimal_char - '0';

size_t multiply_factor = 1;
for (int j = 1; j < i; ++j)
multiply_factor *= 10;

fractional_part += (decimal_number * multiply_factor);
}
}
if (negative == false)
rhs.m_value = whole_part + fractional_part;
else
rhs.m_value = - (whole_part + fractional_part);
}
else
input_stream.setstate(std::ios::failbit);

return input_stream;
}
----end fixedfloat.h----

 

[P.J. Plauger]

This looks like what I'll do. I'll derive a "Money" class from
FixedFloat and do that in there, overriding the standard ostream<< and
istream>> operators.

I've attached a copy of the working class, and a small driver program
to show it in action (sorry it's so long). I have a few questions
about this:

1. Is the header file OK style-wise? Is there anything wrong that I
should not be doing?

Sorry, I don't have time to critique what you've done in detail.
Instead I supply below a sample use of money_put and moneypunct
I published in The C/C++ Users Journal (April 1998), for comparative
anatomy studies.

2. I've noticed that the modulus (operator%) member and friend
functions can be out by a small factor e.g. 0.0001 in a 4
d.p. precision class. With fixed-point arithmetic, should I be
doing anything to correct this? Is it actually incorrect? For
some reason, I couldn't get the "real" % operator to work, so had
to resort to the hack that actually gets used (subtracting the
result of division and subsequent multiplication from the original
value).

Not such a hack, since it's built on the basic definition. It's very
hard to avoid 1 or even 2 ulp errors with this sort of math. That's
why people are reconsidering decimal floating point these days.

3. Looking at the compiled binary, the FixedFloat symbols have weak,
rather than vague linkage. I thought that /all/ templated class
methods and functions would be vague. This is with GCC 3.3.2, GNU
ld 2.14.90.0.6 and binutils 2.14.90.0.6-5 on i686-pc-linux-gnu
using ELF binary format (this is probably OT).

I don't know anything about these forms of linkage. But I think
"vague linkage" is a wonderfully surreal term, FWIW.

4. In the stream output and extraction friend classes, is the use of
locales correct? I've not used locales (in C++) before, and I've
done this using the Josuttis Standard Library book.

If it works... The example below uses our magic locale macros to
deal with VC++ V6.0 compiler limitations.

P.J. Plauger
Dinkumware, Ltd.
http://www.dinkumware.com


--------------

#include <iomanip>
#include <iostream>
#include <locale>
using namespace std;

// MONETARY TYPES
typedef long double MoneyVal;

class Money {
public:
Money(MoneyVal v)
: value(v) {}
operator MoneyVal() const
{return (value); }
private:
MoneyVal value;
};

// Money INSERTER
template<class _E, class _Tr> inline
basic_ostream<_E, _Tr>& operator<<(
basic_ostream<_E, _Tr>& _O, Money _Y)
{typedef ostreambuf_iterator<_E, _Tr> _Iter;
typedef money_put<_E, _Iter> _Mput;

ios_base::iostate _St = ios_base::goodbit;
const typename basic_ostream<_E, _Tr>::sentry _Ok(_O);
if (_Ok)
{try
{const _Mput& _Fac =
_USEFAC(_O.getloc(), _Mput);
if (_Fac.put(_Iter(_O.rdbuf()),
(_O.flags() & ios_base::showpos) != 0,
_O, _O.fill(), _Y).failed())
_St |= ios_base::badbit; }
catch (...)
{_O.setstate(ios_base::badbit, true); }}
_O.setstate(_St);
return (_O); }

// moneypunct FOR USA LOCALE
money_base:attern mon_fmt = {
money_base::symbol, money_base::space,
money_base::sign, money_base::value};

class Mymoneypunct
: public moneypunct<char, false> {
protected:
virtual char do_decimal_point() const
{return ('.'); }
virtual char do_thousands_sep() const
{return (','); }
virtual string do_grouping() const
{return (string("\3")); }
virtual string do_curr_symbol() const
{return (string("$")); }
virtual string do_positive_sign() const
{return (string("")); }
virtual string do_negative_sign() const
{return (string("-")); }
virtual int do_frac_digits() const
{return (2); }
virtual pattern do_pos_format() const
{return (mon_fmt); }
virtual pattern do_neg_format() const
{return (mon_fmt); }
};

int main()
{locale loc = _ADDFAC(locale::classic(), new Mymoneypunct);
cout.imbue(loc);

cout << showbase << setw(20) << internal << setfill('*')
<< Money(123456789.0) << endl;
return (0); }

 

[Roger Leigh]

Not such a hack, since it's built on the basic definition. It's very
hard to avoid 1 or even 2 ulp errors with this sort of math. That's
why people are reconsidering decimal floating point these days.

I noticed your post in the thread about this in comp.lang.c.moderated.
This looks quite exciting, and I look forward to using this in the
future, when it's implemented. Are there any C++ classes implementing
this yet?

I've got hold of the specs from the IBM Hursley site, and also some
docs about BCD arithmetic. If it's not too hairy, I might be able to
knock out a C++ class for this myself, but I'm not a mathematician and
worry about the subtleties I might get wrong when dealing with
financial stuff.

For the time being, I've been looking for other classes and libraries
out there. GNU MP (libgmp) looks like a decent choice, since it can
do arbitrary-precision computation, and it has a C++ binding. I
wouldn't have to worry about overflow or underflow if I used this.
However, the values still have to be stored in a fixed-precision
backend database (PostgreSQL numeric type), so having a
fixed-precision class to directly represent the database types would
be highly advantageous.

I don't know anything about these forms of linkage. But I think
"vague linkage" is a wonderfully surreal term, FWIW.

With weak linkage, if the same symbol is present in multiple
translation units, only one will be resolved by the runtime linker.
In contrast, vague linkage means that additional copies are thrown
away by the linker at link time, e.g. multiple template instantiations
emitted for every translation unit (I believe this is called COMDAT on
some platforms). I expected the latter behaviour, but didn't get it
with my own templates (although I see it for all the Standard Library

If it works... The example below uses our magic locale macros to
deal with VC++ V6.0 compiler limitations.

Thanks, that was quite informative. I'll be using GCC and GNU
libstdc++5 on all our target platforms, including Windows, so I won't
have to deal with VC++, at least initially. It would merit further
investigation if it provided a POSIX/SUSv3 layer like Cygwin or MinGW.
I require the Gtkmm and PostgreSQL client libraries for my current
project, though.