fnem.hpp~

浮点数基本运算 浮点数的基本运算主要有四则运算、符号处理、大小比较

// Float Number exp implementation -*- C++ -*-

// Copyright (C) 2005 Ben T. Bear
//
// This file is part of the BTB's Template<Integer> Library.  This
// library 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, or (at your option)
// any later version.

// This library 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 library; see the file COPYING.  If not, write to
// the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
// MA 02111-1307, USA.

// As a special exception, you may use this file as part of a free
// software library without restriction.  Specifically, if other files
// instantiate templates or use macros or inline functions from this
// file, or you compile this file and link it with other files to
// produce an executable, this file does not by itself cause the
// resulting executable to be covered by the GNU General Public
// License.  This exception does not however invalidate any other
// reasons why the executable file might be covered by the GNU General
// Public License.

#ifndef __bt2il_fn_fnem_hpp
#define __bt2il_fn_fnem_hpp

namespace btil
{
  namespace fn
  {
    template <typename f, int k = 10>
    struct fn2em;
    
    template <int n, int k>
    struct __em_exp;

    
    template <int n, int k>
    struct ____em_exp_p              // n > 0
    {
      static const double __e = ____em_exp_p<n/2, k>::f_val;
      static const double __b = (n % 2 == 0) ? 1.0 : k;
      static const double f_val = __e * __e * __b;
    };
    
    template <int k>
    struct ____em_exp_p<0, k>
    {
      static const double f_val = 1.0;
    };

    template <int t, int n, int k>
    struct ____em_exp;
    
    template <int n, int k>
    struct ____em_exp<-1, n, k>
    {
      static const double f_val = 1.0 / ____em_exp_p<-n, k>::f_val;
    };
    
    template <int n, int k>
    struct ____em_exp<0, n, k>
    {
      static const double f_val = ____em_exp_p<n, k>::f_val;
    };
    
    template <int n, int k>
    struct __em_exp
    {
      static const int __s = (n < 0) ? -1 : 0;
      struct value
      {
        static const double f_val = ____em_exp<__s, n, k>::f_val;
      };
    };



    template <int t, typename f, int k>
    struct __fn2em;
    
    
    template <typename f, int k>
    struct fn2em
    {
      static const double __f = f::f_val;
      static const int sign = (__f < 0.0) ? -1 : (__f != 0.0);

      static const double __x = (sign == -1) ? -__f : __f;
      static const int __t = ((__x == 0.0) ? 0
			      : ((__x < 1.0) ? 1
				 : ((__x < k) ? 2 : 3)));
      struct x
      {
	static const double f_val = __x;
      };
      static const int e = __fn2em<__t, x, k>::e;
      typedef typename __fn2em<__t, x, k>::m m;
    };
    
    template <typename f, int k>
    struct __fn2em<0, f, k>           // less than 1
    {
      static const int e = 0;
      struct m
      {
	static const double f_val = 0.0;
      };
    };
    
    template <typename f, int k>
    struct __fn2em<2, f, k>          // [1.0, k)
    {
      static const int e = 0;
      typedef f m;
    };
    
    template <typename f, int k>
    struct __fn2em_s;		// small than 1.0

    template <typename f, int k>
    struct __fn2em<1, f, k>	// (0.0, 1.0)
    {
      static const int e = __fn2em_s<f, k>::e;
      typedef typename __fn2em_s<f, k>::m m;
    };
    
    template <typename f, int k>
    struct __fn2em_b;		// big & equal than k

    template <typename f, int k>
    struct __fn2em<3, f, k>	// [k, .....
    {
      static const int e = __fn2em_b<f, k>::e;
      typedef typename __fn2em_b<f, k>::m m;
    };
    
    template <int n, typename f, int k>
    struct __fn2em_s_n;          // get __em_exp<2n> < f
    
    template <int n, typename f, int k>
    struct __fn2em_s_e;
    
    template <typename f, int k>
    struct __fn2em_s                 // small
    {
      static const int __n = __fn2em_s_n<1, f, k>::value;
      
      static const int e = -__fn2em_s_e<__n, f, k>::e-1;
      //typedef typename __fn2em_s_e<__n, f, k>::m m;
      struct m
      {
	static const double __m =  __fn2em_s_e<__n, f, k>::m::f_val * k;
	static const double f_val = (__m < 1.0) ? 1.0 : __m;
      };
    };
    
    template <bool b, int n, typename f, int k>
    struct __fn2em_s_n_bool;
    
    template <int n, typename f, int k>
    struct __fn2em_s_n
    {
      static const double __en = __em_exp<-n, k>::value::f_val;
      static const double __h = f::f_val / __en;
      static const bool __b = __h >= __en;

      static const int value = __fn2em_s_n_bool<__b, n, f, k>::value;
    };
    
    template <int n, typename f, int k>
    struct __fn2em_s_n_bool<true, n, f, k>
    {
      static const int value = n;
    };
    
    template <int n, typename f, int k>
    struct __fn2em_s_n_bool<false, n, f, k>
    {
      static const int value = __fn2em_s_n<2*n, f, k>::value;
    };
    
    template <int n, typename f, int k>
    struct __fn2em_s_e
    {
      static const double __f = f::f_val;
      static const double __en = __em_exp<-n, k>::value::f_val;
      static const bool __s = __en > __f;
      struct __h
      {
	static const double f_val = __s ? __f / __en : __f;
      };
      
      static const int e = __fn2em_s_e<n/2, __h, k>::e + (__s ? n : 0);
      typedef typename __fn2em_s_e<n/2, __h, k>::m m;
    };
    
    template <typename f, int k>
    struct __fn2em_s_e<0, f, k>
    {
      static const int e = 0;
      typedef f m;
    };
    
    template <int n, typename f, int k>
    struct __fn2em_b_n;
    template <int n, typename f, int k>
    struct __fn2em_b_e;
    
    template <typename f, int k>
    struct __fn2em_b
    {
      static const int __n = __fn2em_b_n<1, f, k>::value;
      
      static const int e = __fn2em_b_e<__n, f, k>::e;
      typedef typename __fn2em_b_e<__n, f, k>::m m;
    };
    
    template <bool b, int n, typename f, int k>
    struct __fn2em_b_n_bool;
    
    template <int n, typename f, int k>
    struct __fn2em_b_n
    {
      static const double __en = __em_exp<n, k>::value::f_val;
      static const double __h = f::f_val / __en;
      static const bool __b = __h < __en;
      
      static const int value = __fn2em_b_n_bool<__b, n, f, k>::value;
    };
    
    template <int n, typename f, int k>
    struct __fn2em_b_n_bool<true, n, f, k>
    {
      static const int value = n;
    };
    
    template <int n, typename f, int k>
    struct __fn2em_b_n_bool<false, n, f, k>
    {
      static const int value = __fn2em_b_n<2*n, f, k>::value;
    };
    
    template <int n, typename f, int k>
    struct __fn2em_b_e
    {
      static const double __f = f::f_val;
      static const double __en = __em_exp<n, k>::value::f_val;
      static const bool __s = __f >= __en;
      
      struct __h
      {
        static const double f_val = __s ? __f / __en : __f;
      };
      static const int e = __fn2em_b_e<n/2, __h, k>::e + (__s ? n : 0);
      typedef typename __fn2em_b_e<n/2, __h, k>::m m;
    };
    
    template <typename f, int k>
    struct __fn2em_b_e<0, f, k>
    {
      static const int e = 0;
      typedef f m;
    };
  }
}

#endif