FM / complex

/usr/include/boost/math/complex

Name	Size	Mode	Actions
acos.hpp	7614	0644	edit dl rm
acosh.hpp	1041	0644	edit dl rm
asin.hpp	7463	0644	edit dl rm
asinh.hpp	984	0644	edit dl rm
atan.hpp	1206	0644	edit dl rm
atanh.hpp	6103	0644	edit dl rm
details.hpp	2746	0644	edit dl rm
fabs.hpp	618	0644	edit dl rm

Edit: /usr/include/boost/math/complex/acos.hpp (7614B)

//  (C) Copyright John Maddock 2005.
//  Distributed under the Boost Software License, Version 1.0. (See accompanying
//  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_MATH_COMPLEX_ACOS_INCLUDED
#define BOOST_MATH_COMPLEX_ACOS_INCLUDED

#ifndef BOOST_MATH_COMPLEX_DETAILS_INCLUDED
#  include <boost/math/complex/details.hpp>
#endif
#ifndef BOOST_MATH_LOG1P_INCLUDED
#  include <boost/math/special_functions/log1p.hpp>
#endif
#include <boost/assert.hpp>

#ifdef BOOST_NO_STDC_NAMESPACE
namespace std{ using ::sqrt; using ::fabs; using ::acos; using ::asin; using ::atan; using ::atan2; }
#endif

namespace boost{ namespace math{

template<class T> 
std::complex<T> acos(const std::complex<T>& z)
{
   //
   // This implementation is a transcription of the pseudo-code in:
   //
   // "Implementing the Complex Arcsine and Arccosine Functions using Exception Handling."
   // T E Hull, Thomas F Fairgrieve and Ping Tak Peter Tang.
   // ACM Transactions on Mathematical Software, Vol 23, No 3, Sept 1997.
   //

//
   // These static constants should really be in a maths constants library,
   // note that we have tweaked a_crossover as per: https://svn.boost.org/trac/boost/ticket/7290
   //
   static const T one = static_cast<T>(1);
   //static const T two = static_cast<T>(2);
   static const T half = static_cast<T>(0.5L);
   static const T a_crossover = static_cast<T>(10);
   static const T b_crossover = static_cast<T>(0.6417L);
   static const T s_pi = boost::math::constants::pi<T>();
   static const T half_pi = s_pi / 2;
   static const T log_two = boost::math::constants::ln_two<T>();
   static const T quarter_pi = s_pi / 4;
   
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4127)
#endif
   //
   // Get real and imaginary parts, discard the signs as we can 
   // figure out the sign of the result later:
   //
   T x = std::fabs(z.real());
   T y = std::fabs(z.imag());

T real, imag; // these hold our result

// 
   // Handle special cases specified by the C99 standard,
   // many of these special cases aren't really needed here,
   // but doing it this way prevents overflow/underflow arithmetic
   // in the main body of the logic, which may trip up some machines:
   //
   if((boost::math::isinf)(x))
   {
      if((boost::math::isinf)(y))
      {
         real = quarter_pi;
         imag = std::numeric_limits<T>::infinity();
      }
      else if((boost::math::isnan)(y))
      {
         return std::complex<T>(y, -std::numeric_limits<T>::infinity());
      }
      else
      {
         // y is not infinity or nan:
         real = 0;
         imag = std::numeric_limits<T>::infinity();
      }
   }
   else if((boost::math::isnan)(x))
   {
      if((boost::math::isinf)(y))
         return std::complex<T>(x, ((boost::math::signbit)(z.imag())) ? std::numeric_limits<T>::infinity() :  -std::numeric_limits<T>::infinity());
      return std::complex<T>(x, x);
   }
   else if((boost::math::isinf)(y))
   {
      real = half_pi;
      imag = std::numeric_limits<T>::infinity();
   }
   else if((boost::math::isnan)(y))
   {
      return std::complex<T>((x == 0) ? half_pi : y, y);
   }
   else
   {
      //
      // What follows is the regular Hull et al code,
      // begin with the special case for real numbers:
      //
      if((y == 0) && (x <= one))
         return std::complex<T>((x == 0) ? half_pi : std::acos(z.real()), (boost::math::changesign)(z.imag()));
      //
      // Figure out if our input is within the "safe area" identified by Hull et al.
      // This would be more efficient with portable floating point exception handling;
      // fortunately the quantities M and u identified by Hull et al (figure 3), 
      // match with the max and min methods of numeric_limits<T>.
      //
      T safe_max = detail::safe_max(static_cast<T>(8));
      T safe_min = detail::safe_min(static_cast<T>(4));

T xp1 = one + x;
      T xm1 = x - one;

if((x < safe_max) && (x > safe_min) && (y < safe_max) && (y > safe_min))
      {
         T yy = y * y;
         T r = std::sqrt(xp1*xp1 + yy);
         T s = std::sqrt(xm1*xm1 + yy);
         T a = half * (r + s);
         T b = x / a;

if(b <= b_crossover)
         {
            real = std::acos(b);
         }
         else
         {
            T apx = a + x;
            if(x <= one)
            {
               real = std::atan(std::sqrt(half * apx * (yy /(r + xp1) + (s-xm1)))/x);
            }
            else
            {
               real = std::atan((y * std::sqrt(half * (apx/(r + xp1) + apx/(s+xm1))))/x);
            }
         }

if(a <= a_crossover)
         {
            T am1;
            if(x < one)
            {
               am1 = half * (yy/(r + xp1) + yy/(s - xm1));
            }
            else
            {
               am1 = half * (yy/(r + xp1) + (s + xm1));
            }
            imag = boost::math::log1p(am1 + std::sqrt(am1 * (a + one)));
         }
         else
         {
            imag = std::log(a + std::sqrt(a*a - one));
         }
      }
      else
      {
         //
         // This is the Hull et al exception handling code from Fig 6 of their paper:
         //
         if(y <= (std::numeric_limits<T>::epsilon() * std::fabs(xm1)))
         {
            if(x < one)
            {
               real = std::acos(x);
               imag = y / std::sqrt(xp1*(one-x));
            }
            else
            {
               // This deviates from Hull et al's paper as per https://svn.boost.org/trac/boost/ticket/7290
               if(((std::numeric_limits<T>::max)() / xp1) > xm1)
               {
                  // xp1 * xm1 won't overflow:
                  real = y / std::sqrt(xm1*xp1);
                  imag = boost::math::log1p(xm1 + std::sqrt(xp1*xm1));
               }
               else
               {
                  real = y / x;
                  imag = log_two + std::log(x);
               }
            }
         }
         else if(y <= safe_min)
         {
            // There is an assumption in Hull et al's analysis that
            // if we get here then x == 1.  This is true for all "good"
            // machines where :
            // 
            // E^2 > 8*sqrt(u); with:
            //
            // E =  std::numeric_limits<T>::epsilon()
            // u = (std::numeric_limits<T>::min)()
            //
            // Hull et al provide alternative code for "bad" machines
            // but we have no way to test that here, so for now just assert
            // on the assumption:
            //
            BOOST_ASSERT(x == 1);
            real = std::sqrt(y);
            imag = std::sqrt(y);
         }
         else if(std::numeric_limits<T>::epsilon() * y - one >= x)
         {
            real = half_pi;
            imag = log_two + std::log(y);
         }
         else if(x > one)
         {
            real = std::atan(y/x);
            T xoy = x/y;
            imag = log_two + std::log(y) + half * boost::math::log1p(xoy*xoy);
         }
         else
         {
            real = half_pi;
            T a = std::sqrt(one + y*y);
            imag = half * boost::math::log1p(static_cast<T>(2)*y*(y+a));
         }
      }
   }

//
   // Finish off by working out the sign of the result:
   //
   if((boost::math::signbit)(z.real()))
      real = s_pi - real;
   if(!(boost::math::signbit)(z.imag()))
      imag = (boost::math::changesign)(imag);

return std::complex<T>(real, imag);
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
}

} } // namespaces

#endif // BOOST_MATH_COMPLEX_ACOS_INCLUDED

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