arcsin.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

// arcsin 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_arcsin_hpp
#define __bt2il_fn_arcsin_hpp

#include "fn.hpp"
#include "pi.hpp"
#include "sin.hpp"

namespace btil
{
  namespace fn
  {
    template <typename x>
    struct arcsin;

    /*
    template <int n, typename x>
    struct __arcsin_item
    {
      typedef typename __arcsin_item<n-1, x>::b pb;
      typedef typename __arcsin_item<n-1, x>::e pe;

      static const double cos_s = pb::cos * pe::cos - pb::sin * pe::sin;

      struct cos_ss
      {
	static const double f_val = (1.0 - cos_s) / 2;
      };
      struct cos_sc
      {
	static const double f_val = (1.0 + cos_s) / 2;
      };
      struct pm
      {
	static const double f_val = (pb::f_val + pe::f_val) / 2;
	static const double __sin = sqrt<cos_ss>::value::f_val;
	static const double sin = (f_val > 0) ? __sin : -__sin;
	static const double cos = sqrt<cos_sc>::value::f_val;
      };

      static const bool less = pm::sin < x::f_val;

      struct b
      {
	static const double f_val = less ? pm::f_val : pb::f_val;
	static const double sin = less ? pm::sin : pb::sin;
	static const double cos = less ? pm::cos : pb::cos;
      };
      struct e
      {
	static const double f_val = less ? pe::f_val : pm::f_val;
	static const double sin = less ? pe::sin : pm::sin;
	static const double cos = less ? pe::cos : pm::cos;
      };
    };

    template <typename x>
    struct __arcsin_item<0, x>
    {
      struct b
      {
	static const double f_val = -pi::f_val / 2.0;
	static const double sin = -1.0;
	static const double cos = 0.0;
      };
      struct e
      {
	static const double f_val = pi::f_val / 2.0;
	static const double sin = 1.0;
	static const double cos = 0.0;
      };
    };

    template <typename x>
    struct arcsin
    {
      typedef typename __arcsin_item<58, x>::b value;
      typedef typename __arcsin_item<58, x>::e e;
    };
    */

    template <int n, typename x>
    struct __arcsin_item
    {
      static const double item = (__arcsin_item<n-1, x>::item
				  * (2*n-1) / (2*n) * x::f_val * x::f_val);
      static const double as_n = (__arcsin_item<n-1, x>::as_n
				  + item / (2*n+1));
    };

    template <typename x>
    struct __arcsin_item<0, x>
    {
      static const double item = x::f_val;
      static const double as_n = item;
    };

    template <typename x>
    struct arcsin
    {
      static const bool s = x::f_val < 0.0;
      static const double abs = s ? -x::f_val : x::f_val;

      static const bool big = abs > sin<angle<45>::value>::value::f_val;

      struct __xx
      {
	static const double f_val = big ? (1.0 - abs*abs) : (abs*abs);
      };
      struct __x
      {
	static const double f_val = sqrt<__xx>::value::f_val;
      };

      static const double v = __arcsin_item<60, __x>::as_n;
      static const double vv = big ? (pi::f_val / 2.0 - v) : v;

      struct value
      {
	static const double f_val = s ? -vv : vv;
      };
    };
  }
}

#endif