williamr@2: //  (C) Copyright John Maddock 2005.
williamr@2: //  Use, modification and distribution are subject to the
williamr@2: //  Boost Software License, Version 1.0. (See accompanying file
williamr@2: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
williamr@2: 
williamr@2: #ifndef BOOST_MATH_HYPOT_INCLUDED
williamr@2: #define BOOST_MATH_HYPOT_INCLUDED
williamr@2: 
williamr@2: #include <cmath>
williamr@2: #include <boost/limits.hpp>
williamr@2: #include <algorithm> // swap
williamr@2: 
williamr@2: #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
williamr@2: #  include <boost/static_assert.hpp>
williamr@2: #else
williamr@2: #  include <boost/assert.hpp>
williamr@2: #endif
williamr@2: 
williamr@2: #ifdef BOOST_NO_STDC_NAMESPACE
williamr@2: namespace std{ using ::sqrt; using ::fabs; }
williamr@2: #endif
williamr@2: 
williamr@2: 
williamr@2: namespace boost{ namespace math{
williamr@2: 
williamr@2: template <class T>
williamr@2: T hypot(T x, T y)
williamr@2: {
williamr@2: #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
williamr@2:    BOOST_STATIC_ASSERT(::std::numeric_limits<T>::is_specialized);
williamr@2: #else
williamr@2:    BOOST_ASSERT(std::numeric_limits<T>::is_specialized);
williamr@2: #endif
williamr@2: 
williamr@2:    //
williamr@2:    // normalize x and y, so that both are positive and x >= y:
williamr@2:    //
williamr@2:    x = (std::fabs)(x);
williamr@2:    y = (std::fabs)(y);
williamr@2: 
williamr@2:    // special case, see C99 Annex F:
williamr@2:    if(std::numeric_limits<T>::has_infinity
williamr@2:       && ((x == std::numeric_limits<T>::infinity())
williamr@2:       || (y == std::numeric_limits<T>::infinity())))
williamr@2:       return std::numeric_limits<T>::infinity();
williamr@2: 
williamr@2:    if(y > x) 
williamr@2:       (std::swap)(x, y);
williamr@2:    //
williamr@2:    // figure out overflow and underflow limits:
williamr@2:    //
williamr@2:    T safe_upper = (std::sqrt)((std::numeric_limits<T>::max)()) / 2;
williamr@2:    T safe_lower = (std::sqrt)((std::numeric_limits<T>::min)());
williamr@2:    static const T one = 1;
williamr@2:    //
williamr@2:    // Now handle special cases:
williamr@2:    //
williamr@2:    if(x >= safe_upper)
williamr@2:    {
williamr@2:       if(y <= one)
williamr@2:       {
williamr@2:          // y is neligible:
williamr@2:          return x;
williamr@2:       }
williamr@2:       return (std::sqrt)(x) * (std::sqrt)(y) * (std::sqrt)(x/y + y/x);
williamr@2:    }
williamr@2:    else if(y <= safe_lower)
williamr@2:    {
williamr@2:       if((x >= one) || (y == 0))
williamr@2:       {
williamr@2:          // y is negligible:
williamr@2:          return x;
williamr@2:       }
williamr@2:       return (std::sqrt)(x) * (std::sqrt)(y) * (std::sqrt)(x/y + y/x);
williamr@2:    }
williamr@2:    //
williamr@2:    // If we get here then x^2+y^2 will not overflow or underflow:
williamr@2:    //
williamr@2:    return (std::sqrt)(x*x + y*y);
williamr@2: }
williamr@2: 
williamr@2: } } // namespaces
williamr@2: 
williamr@2: #endif // BOOST_MATH_HYPOT_INCLUDED