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 ///////////////////////////////////////////////////////////////////////////////
 // Copyright Christopher Kormanyos 2014.
 // Copyright John Maddock 2014.
 // Copyright Paul Bristow 2014.
 // 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)
 //
 
 // Implement quadruple-precision I/O stream operations.
 
 #ifndef BOOST_MATH_CSTDFLOAT_IOSTREAM_2014_02_15_HPP_
   #define BOOST_MATH_CSTDFLOAT_IOSTREAM_2014_02_15_HPP_
 
   #include <boost/math/cstdfloat/cstdfloat_types.hpp>
   #include <boost/math/cstdfloat/cstdfloat_limits.hpp>
   #include <boost/math/cstdfloat/cstdfloat_cmath.hpp>
 
   #if defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_CMATH)
   #error You can not use <boost/math/cstdfloat/cstdfloat_iostream.hpp> with BOOST_CSTDFLOAT_NO_LIBQUADMATH_CMATH defined.
   #endif
 
   #if defined(BOOST_CSTDFLOAT_HAS_INTERNAL_FLOAT128_T) && defined(BOOST_MATH_USE_FLOAT128) && !defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT)
 
   #include <cstddef>
   #include <istream>
   #include <ostream>
   #include <sstream>
   #include <stdexcept>
   #include <string>
   #include <boost/math/tools/assert.hpp>
   #include <boost/math/tools/nothrow.hpp>
   #include <boost/math/tools/throw_exception.hpp>
 
 #if defined(__GNUC__) && !defined(BOOST_MATH_TEST_IO_AS_INTEL_QUAD)
 
   // Forward declarations of quadruple-precision string functions.
   extern "C" int quadmath_snprintf(char *str, size_t size, const char *format, ...) BOOST_MATH_NOTHROW;
   extern "C" boost::math::cstdfloat::detail::float_internal128_t strtoflt128(const char*, char **) BOOST_MATH_NOTHROW;
 
   namespace std
   {
     template<typename char_type, class traits_type>
     inline std::basic_ostream<char_type, traits_type>& operator<<(std::basic_ostream<char_type, traits_type>& os, const boost::math::cstdfloat::detail::float_internal128_t& x)
     {
       std::basic_ostringstream<char_type, traits_type> ostr;
       ostr.flags(os.flags());
       ostr.imbue(os.getloc());
       ostr.precision(os.precision());
 
       char my_buffer[64U];
 
       const int my_prec   = static_cast<int>(os.precision());
       const int my_digits = ((my_prec == 0) ? 36 : my_prec);
 
       const std::ios_base::fmtflags my_flags  = os.flags();
 
       char my_format_string[8U];
 
       std::size_t my_format_string_index = 0U;
 
       my_format_string[my_format_string_index] = '%';
       ++my_format_string_index;
 
       if(my_flags & std::ios_base::showpos)   { my_format_string[my_format_string_index] = '+'; ++my_format_string_index; }
       if(my_flags & std::ios_base::showpoint) { my_format_string[my_format_string_index] = '#'; ++my_format_string_index; }
 
       my_format_string[my_format_string_index + 0U] = '.';
       my_format_string[my_format_string_index + 1U] = '*';
       my_format_string[my_format_string_index + 2U] = 'Q';
 
       my_format_string_index += 3U;
 
       char the_notation_char;
 
       if     (my_flags & std::ios_base::scientific) { the_notation_char = 'e'; }
       else if(my_flags & std::ios_base::fixed)      { the_notation_char = 'f'; }
       else                                          { the_notation_char = 'g'; }
 
       my_format_string[my_format_string_index + 0U] = the_notation_char;
       my_format_string[my_format_string_index + 1U] = 0;
 
       const int v = ::quadmath_snprintf(my_buffer,
                                         static_cast<int>(sizeof(my_buffer)),
                                         my_format_string,
                                         my_digits,
                                         x);
 
       if(v < 0) { BOOST_MATH_THROW_EXCEPTION(std::runtime_error("Formatting of boost::float128_t failed internally in quadmath_snprintf().")); }
 
       if(v >= static_cast<int>(sizeof(my_buffer) - 1U))
       {
         // Evidently there is a really long floating-point string here,
         // such as a small decimal representation in non-scientific notation.
         // So we have to use dynamic memory allocation for the output
         // string buffer.
 
         char* my_buffer2 = nullptr;
 
 #ifndef BOOST_NO_EXCEPTIONS
         try
         {
 #endif
           my_buffer2 = new char[v + 3];
 #ifndef BOOST_NO_EXCEPTIONS
         }
         catch(const std::bad_alloc&)
         {
           BOOST_MATH_THROW_EXCEPTION(std::runtime_error("Formatting of boost::float128_t failed while allocating memory."));
         }
 #endif
         const int v2 = ::quadmath_snprintf(my_buffer2,
                                             v + 3,
                                             my_format_string,
                                             my_digits,
                                             x);
 
         if(v2 >= v + 3)
         {
           BOOST_MATH_THROW_EXCEPTION(std::runtime_error("Formatting of boost::float128_t failed."));
         }
 
         static_cast<void>(ostr << my_buffer2);
 
         delete [] my_buffer2;
       }
       else
       {
         static_cast<void>(ostr << my_buffer);
       }
 
       return (os << ostr.str());
     }
 
     template<typename char_type, class traits_type>
     inline std::basic_istream<char_type, traits_type>& operator>>(std::basic_istream<char_type, traits_type>& is, boost::math::cstdfloat::detail::float_internal128_t& x)
     {
       std::string str;
 
       static_cast<void>(is >> str);
 
       char* p_end;
 
       x = strtoflt128(str.c_str(), &p_end);
 
       if(static_cast<std::ptrdiff_t>(p_end - str.c_str()) != static_cast<std::ptrdiff_t>(str.length()))
       {
         for(std::string::const_reverse_iterator it = str.rbegin(); it != str.rend(); ++it)
         {
           static_cast<void>(is.putback(*it));
         }
 
         is.setstate(ios_base::failbit);
 
         BOOST_MATH_THROW_EXCEPTION(std::runtime_error("Unable to interpret input string as a boost::float128_t"));
       }
 
       return is;
     }
   }
 
 #elif defined(__INTEL_COMPILER) || defined(BOOST_MATH_TEST_IO_AS_INTEL_QUAD)
 
   // The section for I/O stream support for the ICC compiler is particularly
   // long, because these functions must be painstakingly synthesized from
   // manually-written routines (ICC does not support I/O stream operations
   // for its _Quad type).
 
   // The following string-extraction routines are based on the methodology
   // used in Boost.Multiprecision by John Maddock and Christopher Kormanyos.
   // This methodology has been slightly modified here for boost::float128_t.
 
 
   #include <cstring>
   #include <cctype>
   
   namespace boost { namespace math { namespace cstdfloat { namespace detail {
 
   template<class string_type>
   void format_float_string(string_type& str,
                             int my_exp,
                             int digits,
                             const std::ios_base::fmtflags f,
                             const bool iszero)
   {
     typedef typename string_type::size_type size_type;
 
     const bool scientific = ((f & std::ios_base::scientific) == std::ios_base::scientific);
     const bool fixed      = ((f & std::ios_base::fixed)      == std::ios_base::fixed);
     const bool showpoint  = ((f & std::ios_base::showpoint)  == std::ios_base::showpoint);
     const bool showpos    = ((f & std::ios_base::showpos)    == std::ios_base::showpos);
 
     const bool b_neg = ((str.size() != 0U) && (str[0] == '-'));
 
     if(b_neg)
     {
       str.erase(0, 1);
     }
 
     if(digits == 0)
     {
       digits = static_cast<int>((std::max)(str.size(), size_type(16)));
     }
 
     if(iszero || str.empty() || (str.find_first_not_of('0') == string_type::npos))
     {
       // We will be printing zero, even though the value might not
       // actually be zero (it just may have been rounded to zero).
       str = "0";
 
       if(scientific || fixed)
       {
         str.append(1, '.');
         str.append(size_type(digits), '0');
 
         if(scientific)
         {
           str.append("e+00");
         }
       }
       else
       {
         if(showpoint)
         {
           str.append(1, '.');
           if(digits > 1)
           {
             str.append(size_type(digits - 1), '0');
           }
         }
       }
 
       if(b_neg)
       {
         str.insert(0U, 1U, '-');
       }
       else if(showpos)
       {
         str.insert(0U, 1U, '+');
       }
 
       return;
     }
 
     if(!fixed && !scientific && !showpoint)
     {
       // Suppress trailing zeros.
       typename string_type::iterator pos = str.end();
 
       while(pos != str.begin() && *--pos == '0') { ; }
 
       if(pos != str.end())
       {
         ++pos;
       }
 
       str.erase(pos, str.end());
 
       if(str.empty())
       {
         str = '0';
       }
     }
     else if(!fixed || (my_exp >= 0))
     {
       // Pad out the end with zero's if we need to.
 
       std::ptrdiff_t chars = static_cast<std::ptrdiff_t>(str.size());
       chars = digits - chars;
 
       if(scientific)
       {
         ++chars;
       }
 
       if(chars > 0)
       {
         str.append(static_cast<size_type>(chars), '0');
       }
     }
 
     if(fixed || (!scientific && (my_exp >= -4) && (my_exp < digits)))
     {
       if((1 + my_exp) > static_cast<int>(str.size()))
       {
         // Just pad out the end with zeros.
         str.append(static_cast<size_type>((1 + my_exp) - static_cast<int>(str.size())), '0');
 
         if(showpoint || fixed)
         {
           str.append(".");
         }
       }
       else if(my_exp + 1 < static_cast<int>(str.size()))
       {
         if(my_exp < 0)
         {
           str.insert(0U, static_cast<size_type>(-1 - my_exp), '0');
           str.insert(0U, "0.");
         }
         else
         {
           // Insert the decimal point:
           str.insert(static_cast<size_type>(my_exp + 1), 1, '.');
         }
       }
       else if(showpoint || fixed) // we have exactly the digits we require to left of the point
       {
         str += ".";
       }
 
       if(fixed)
       {
         // We may need to add trailing zeros.
         int l = static_cast<int>(str.find('.') + 1U);
         l = digits - (static_cast<int>(str.size()) - l);
 
         if(l > 0)
         {
           str.append(size_type(l), '0');
         }
       }
     }
     else
     {
       // Scientific format:
       if(showpoint || (str.size() > 1))
       {
         str.insert(1U, 1U, '.');
       }
 
       str.append(1U, 'e');
 
       string_type e = std::to_string(std::abs(my_exp));
 
       if(e.size() < 2U)
       {
         e.insert(0U, 2U - e.size(), '0');
       }
 
       if(my_exp < 0)
       {
         e.insert(0U, 1U, '-');
       }
       else
       {
         e.insert(0U, 1U, '+');
       }
 
       str.append(e);
     }
 
     if(b_neg)
     {
       str.insert(0U, 1U, '-');
     }
     else if(showpos)
     {
       str.insert(0U, 1U, '+');
     }
   }
 
   template<class float_type, class type_a> inline void eval_convert_to(type_a* pa,    const float_type& cb)                        { *pa  = static_cast<type_a>(cb); }
   template<class float_type, class type_a> inline void eval_add       (float_type& b, const type_a& a)                             { b   += a; }
   template<class float_type, class type_a> inline void eval_subtract  (float_type& b, const type_a& a)                             { b   -= a; }
   template<class float_type, class type_a> inline void eval_multiply  (float_type& b, const type_a& a)                             { b   *= a; }
   template<class float_type>               inline void eval_multiply  (float_type& b, const float_type& cb, const float_type& cb2) { b    = (cb * cb2); }
   template<class float_type, class type_a> inline void eval_divide    (float_type& b, const type_a& a)                             { b   /= a; }
   template<class float_type>               inline void eval_log10     (float_type& b, const float_type& cb)                        { b    = std::log10(cb); }
   template<class float_type>               inline void eval_floor     (float_type& b, const float_type& cb)                        { b    = std::floor(cb); }
 
   inline void round_string_up_at(std::string& s, int pos, int& expon)
   {
     // This subroutine rounds up a string representation of a
     // number at the given position pos.
 
     if(pos < 0)
     {
       s.insert(0U, 1U, '1');
       s.erase(s.size() - 1U);
       ++expon;
     }
     else if(s[pos] == '9')
     {
       s[pos] = '0';
       round_string_up_at(s, pos - 1, expon);
     }
     else
     {
       if((pos == 0) && (s[pos] == '0') && (s.size() == 1))
       {
         ++expon;
       }
 
       ++s[pos];
     }
   }
 
   template<class float_type>
   std::string convert_to_string(float_type& x,
                                 std::streamsize digits,
                                 const std::ios_base::fmtflags f)
   {
     const bool isneg  = (x < 0);
     const bool iszero = ((!isneg) ? bool(+x < (std::numeric_limits<float_type>::min)())
                                   : bool(-x < (std::numeric_limits<float_type>::min)()));
     const bool isnan  = (x != x);
     const bool isinf  = ((!isneg) ? bool(+x > (std::numeric_limits<float_type>::max)())
                                   : bool(-x > (std::numeric_limits<float_type>::max)()));
 
     int expon = 0;
 
     if(digits <= 0) { digits = std::numeric_limits<float_type>::max_digits10; }
 
     const int org_digits = static_cast<int>(digits);
 
     std::string result;
 
     if(iszero)
     {
       result = "0";
     }
     else if(isinf)
     {
       if(x < 0)
       {
         return "-inf";
       }
       else
       {
         return ((f & std::ios_base::showpos) == std::ios_base::showpos) ? "+inf" : "inf";
       }
     }
     else if(isnan)
     {
       return "nan";
     }
     else
     {
       // Start by figuring out the base-10 exponent.
       if(isneg) { x = -x; }
 
       float_type t;
       constexpr float_type ten = 10;
 
       eval_log10(t, x);
       eval_floor(t, t);
       eval_convert_to(&expon, t);
 
       if(-expon > std::numeric_limits<float_type>::max_exponent10 - 3)
       {
         int e = -expon / 2;
 
         const float_type t2 = boost::math::cstdfloat::detail::pown(ten, e);
 
         eval_multiply(t, t2, x);
         eval_multiply(t, t2);
 
         if((expon & 1) != 0)
         {
           eval_multiply(t, ten);
         }
       }
       else
       {
         t = boost::math::cstdfloat::detail::pown(ten, -expon);
         eval_multiply(t, x);
       }
 
       // Make sure that the value lies between [1, 10), and adjust if not.
       if(t < 1)
       {
         eval_multiply(t, 10);
 
         --expon;
       }
       else if(t >= 10)
       {
         eval_divide(t, 10);
 
         ++expon;
       }
 
       float_type digit;
       int        cdigit;
 
       // Adjust the number of digits required based on formatting options.
       if(((f & std::ios_base::fixed) == std::ios_base::fixed) && (expon != -1))
       {
         digits += (expon + 1);
       }
 
       if((f & std::ios_base::scientific) == std::ios_base::scientific)
       {
         ++digits;
       }
 
       // Extract the base-10 digits one at a time.
       for(int i = 0; i < digits; ++i)
       {
         eval_floor(digit, t);
         eval_convert_to(&cdigit, digit);
 
         result += static_cast<char>('0' + cdigit);
 
         eval_subtract(t, digit);
         eval_multiply(t, ten);
       }
       if (result.size() == 0)
          result = "0";
 
       // Possibly round the result.
       if(digits >= 0)
       {
         eval_floor(digit, t);
         eval_convert_to(&cdigit, digit);
         eval_subtract(t, digit);
 
         if((cdigit == 5) && (t == 0))
         {
           // Use simple bankers rounding.
 
           if((static_cast<int>(*result.rbegin() - '0') & 1) != 0)
           {
             round_string_up_at(result, static_cast<int>(result.size() - 1U), expon);
             if (digits == 0) digits = 1;
           }
         }
         else if(cdigit >= 5)
         {
           round_string_up_at(result, static_cast<int>(result.size() - 1u), expon);
           if (digits == 0) digits = 1;
         }
       }
     }
 
     while((result.size() > static_cast<std::string::size_type>(digits)) && result.size())
     {
       // We may get here as a result of rounding.
 
       if(result.size() > 1U)
       {
         result.erase(result.size() - 1U);
       }
       else
       {
         if(expon > 0)
         {
           --expon; // so we put less padding in the result.
         }
         else
         {
           ++expon;
         }
 
         ++digits;
       }
     }
 
     if(isneg)
     {
       result.insert(0U, 1U, '-');
     }
 
     format_float_string(result, expon, org_digits, f, iszero);
 
     return result;
   }
 
   template <class float_type>
   bool convert_from_string(float_type& value, const char* p)
   {
     value = 0;
 
     if((p == nullptr) || (*p == '\0'))
     {
       return false;
     }
 
     bool is_neg       = false;
     bool is_neg_expon = false;
 
     constexpr int ten = 10;
 
     int expon       = 0;
     int digits_seen = 0;
 
     constexpr int max_digits = std::numeric_limits<float_type>::max_digits10 + 1;
 
     if(*p == '+')
     {
       ++p;
     }
     else if(*p == '-')
     {
       is_neg = true;
       ++p;
     }
 
     const bool isnan = ((std::strcmp(p, "nan") == 0) || (std::strcmp(p, "NaN") == 0) || (std::strcmp(p, "NAN") == 0));
 
     if(isnan)
     {
       eval_divide(value, 0);
 
       if(is_neg)
       {
         value = -value;
       }
 
       return true;
     }
 
     const bool isinf = ((std::strcmp(p, "inf") == 0) || (std::strcmp(p, "Inf") == 0) || (std::strcmp(p, "INF") == 0));
 
     if(isinf)
     {
       value = 1;
       eval_divide(value, 0);
 
       if(is_neg)
       {
         value = -value;
       }
 
       return true;
     }
 
     // Grab all the leading digits before the decimal point.
     while(std::isdigit(*p))
     {
       eval_multiply(value, ten);
       eval_add(value, static_cast<int>(*p - '0'));
       ++p;
       ++digits_seen;
     }
 
     if(*p == '.')
     {
       // Grab everything after the point, stop when we've seen
       // enough digits, even if there are actually more available.
 
       ++p;
 
       while(std::isdigit(*p))
       {
         eval_multiply(value, ten);
         eval_add(value, static_cast<int>(*p - '0'));
         ++p;
         --expon;
 
         if(++digits_seen > max_digits)
         {
           break;
         }
       }
 
       while(std::isdigit(*p))
       {
         ++p;
       }
     }
 
     // Parse the exponent.
     if((*p == 'e') || (*p == 'E'))
     {
       ++p;
 
       if(*p == '+')
       {
         ++p;
       }
       else if(*p == '-')
       {
         is_neg_expon = true;
         ++p;
       }
 
       int e2 = 0;
 
       while(std::isdigit(*p))
       {
         e2 *= 10;
         e2 += (*p - '0');
         ++p;
       }
 
       if(is_neg_expon)
       {
         e2 = -e2;
       }
 
       expon += e2;
     }
 
     if(expon)
     {
       // Scale by 10^expon. Note that 10^expon can be outside the range
       // of our number type, even though the result is within range.
       // If that looks likely, then split the calculation in two parts.
       float_type t;
       t = ten;
 
       if(expon > (std::numeric_limits<float_type>::min_exponent10 + 2))
       {
         t = boost::math::cstdfloat::detail::pown(t, expon);
         eval_multiply(value, t);
       }
       else
       {
         t = boost::math::cstdfloat::detail::pown(t, (expon + digits_seen + 1));
         eval_multiply(value, t);
         t = ten;
         t = boost::math::cstdfloat::detail::pown(t, (-digits_seen - 1));
         eval_multiply(value, t);
       }
     }
 
     if(is_neg)
     {
       value = -value;
     }
 
     return (*p == '\0');
   }
   } } } } // boost::math::cstdfloat::detail
 
   namespace std
   {
     template<typename char_type, class traits_type>
     inline std::basic_ostream<char_type, traits_type>& operator<<(std::basic_ostream<char_type, traits_type>& os, const boost::math::cstdfloat::detail::float_internal128_t& x)
     {
       boost::math::cstdfloat::detail::float_internal128_t non_const_x = x;
 
       const std::string str = boost::math::cstdfloat::detail::convert_to_string(non_const_x,
                                                                                 os.precision(),
                                                                                 os.flags());
 
       std::basic_ostringstream<char_type, traits_type> ostr;
       ostr.flags(os.flags());
       ostr.imbue(os.getloc());
       ostr.precision(os.precision());
 
       static_cast<void>(ostr << str);
 
       return (os << ostr.str());
     }
 
     template<typename char_type, class traits_type>
     inline std::basic_istream<char_type, traits_type>& operator>>(std::basic_istream<char_type, traits_type>& is, boost::math::cstdfloat::detail::float_internal128_t& x)
     {
       std::string str;
 
       static_cast<void>(is >> str);
 
       const bool conversion_is_ok = boost::math::cstdfloat::detail::convert_from_string(x, str.c_str());
 
       if(false == conversion_is_ok)
       {
         for(std::string::const_reverse_iterator it = str.rbegin(); it != str.rend(); ++it)
         {
           static_cast<void>(is.putback(*it));
         }
 
         is.setstate(ios_base::failbit);
 
         BOOST_MATH_THROW_EXCEPTION(std::runtime_error("Unable to interpret input string as a boost::float128_t"));
       }
 
       return is;
     }
   }
 
   #endif // Use __GNUC__ or __INTEL_COMPILER libquadmath
 
   #endif // Not BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT (i.e., the user would like to have libquadmath support)
 
 #endif // BOOST_MATH_CSTDFLOAT_IOSTREAM_2014_02_15_HPP_

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