compute pi using c++ MPL

pi.h

/* ///////////////////////////////////////////////////////////////////////
* File: pi.h
*
* Created: 08.09.27
* Updated: 08.09.27
*
* Brief: Caculate pi = 3.14159265358979
*
* [<Home>]
* Copyright (c) 2008-2020, Waruqi All rights reserved.
* //////////////////////////////////////////////////////////////////// */
#ifndef EXTL_MPL_MATH_PI_H
#define EXTL_MPL_MATH_PI_H

/*!\file pi.h
* \brief Caculate pi = 3.14159265358979
*
*/
#ifndef EXTL_MPL_MATH_PI_SUPPORT
# error extl::pi is not supported by current compiler.
#endif

/* ///////////////////////////////////////////////////////////////////////
* Includes
*/
#include "math.h"
#include "pow.h"
#include "../int_.h"

/* ///////////////////////////////////////////////////////////////////////
* Macros
*/
#define EXTL_PI_TRAITS_MAX_BITCOUNT (15)
#define EXTL_PI_TRAITS_MAX_BITWIDTH (1)

/* ///////////////////////////////////////////////////////////////////////
* ::extl::mpl namespace
*/
EXTL_MPL_BEGIN_WHOLE_NAMESPACE

/* ///////////////////////////////////////////////////////////////////////
* Compatibility
*/
#ifdef EXTL_MPL_SUPPORT

/*!\brief: pi class
*
* \param N bit count of pi
*
* \ingroup extl_group_mpl
*
* formula:\n
* <pre>
* 1 2 3 k
* pi = 2 + --- * (2 + --- * (2 + --- * (2 + ... (2 + ------- * (2 + ... ))...)))
* 3 5 7 2k + 1
*
* </pre>
*
* algorithm:\n
* \code
int count = 2800, error = 0, error_array[2801] = {0};
int deta_value = 2000 * 10000;
while (count != 0)
{
int value = 0;
for (int i = count; i > 0; i--)
{
int next = value + error_array[i] * 10000;
error_array[i] = next % (2 * i + 1);
value = (next / (2 * i + 1)) * i + deta_value;
}
count = count - 14;
printf("%.4d", error + value / 10000);
error = value % 10000;

deta_value = 0;
}
* \endcode
*/
template<e_umax_int_t N>
struct pi
{
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, count = pi<N - 1>::count - 14 );
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, base = pow_10<EXTL_PI_TRAITS_MAX_BITWIDTH>::value );

template<e_umax_int_t I>
struct pi_impl
{
#if defined(EXTL_COMPILER_IS_INTEL)
typedef pi<N - 1>::template_qual_k pi_impl<I> prev_pi_impl;
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, next = pi_impl<I + 1>::value + base * (prev_pi_impl::error) );
#else
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, next = pi_impl<I + 1>::value + base * (pi<N - 1>::template_qual_k pi_impl<I>::error) );
#endif

EXTL_STATIC_MEMBER_CONST(e_umax_int_t, value = (next / (2 * I + 1)) * I );
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, error = (next % (2 * I + 1)) );
};

EXTL_TEMPLATE_SPECIALISATION
struct pi_impl<count>
{
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, value = 0 );
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, error = 0 );
};

EXTL_STATIC_MEMBER_CONST(e_umax_int_t, value = pi<N - 1>::error + pi_impl<1>::value / base );
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, error = pi_impl<1>::value % base );

~pi()
{
EXTL_STATIC_ASSERT(EXTL_PI_TRAITS_MAX_BITWIDTH < 5);
}

/*static void make()
{
pi<N - 1>::make();
printf("%.1d", value);
}*/
};

EXTL_TEMPLATE_SPECIALISATION
struct pi<0>
{
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, count = (14 * (EXTL_PI_TRAITS_MAX_BITCOUNT + 1)) );
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, base = pow_10<EXTL_PI_TRAITS_MAX_BITWIDTH>::value );

template<e_umax_int_t I>
struct pi_impl
{
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, next = pi_impl<I + 1>::value );
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, value = ((next) / (2 * I + 1)) * I + 2 * base );
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, error = (next % (2 * I + 1)) );
};

EXTL_TEMPLATE_SPECIALISATION
struct pi_impl<count>
{
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, value = 2 * base );
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, error = 0 );
};

EXTL_STATIC_MEMBER_CONST(e_umax_int_t, value = pi_impl<1>::value / base );
EXTL_STATIC_MEMBER_CONST(e_umax_int_t, error = pi_impl<1>::value % base );

~pi()
{
EXTL_STATIC_ASSERT(EXTL_PI_TRAITS_MAX_BITWIDTH < 5);
}

/*static void make()
{
printf("%.1d.", value);
}*/
};

/* ///////////////////////////////////////////////////////////////////////
* Unit testing
*/
#if defined(EXTL_MPL_MATH_PI_TEST_ENABLE) && \
defined(EXTL_MPL_MATH_PI_SUPPORT)
# include "unit_test/pi_test.h"
#endif

/* //////////////////////////////////////////////////////////////////// */
#endif /* EXTL_MPL_SUPPORT */
/* //////////////////////////////////////////////////////////////////// */

/* ///////////////////////////////////////////////////////////////////////
* ::extl::mpl namespace
*/
EXTL_MPL_END_WHOLE_NAMESPACE

/* //////////////////////////////////////////////////////////////////// */
#endif /* EXTL_MPL_MATH_PI_H */
/* //////////////////////////////////////////////////////////////////// */

useage:

int main()
{
pi<7>:make();
}

compiler output: 3.1415926