Function hypot

include/half.hpp:3290–3324

Hypotenuse function. This function is exact to rounding for all rounding modes. See also:** Documentation for [std::hypot](https://en.cppreference.com/w/cpp/numeric/math/hypot). \param x first argument \param y second argument \return square root of sum of squares without internal over- or underflows \exception FE_INVALID if \a x or \a y is signaling NaN \exception FE_OVERFLOW, ...UNDERFLOW, ...I

	/// \exception FE_INVALID if \a x or \a y is signaling NaN
	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding of the final square root
	inline half hypot(half x, half y)
	{
	#ifdef HALF_ARITHMETIC_TYPE
		detail::internal_t fx = detail::half2float<detail::internal_t>(x.data_), fy = detail::half2float<detail::internal_t>(y.data_);
		#if HALF_ENABLE_CPP11_CMATH
			return half(detail::binary, detail::float2half<half::round_style>(std::hypot(fx, fy)));
		#else
			return half(detail::binary, detail::float2half<half::round_style>(std::sqrt(fx*fx+fy*fy)));
		#endif
	#else
		int absx = x.data_ & 0x7FFF, absy = y.data_ & 0x7FFF, expx = 0, expy = 0;
		if(absx >= 0x7C00 || absy >= 0x7C00)
			return half(detail::binary,	(absx==0x7C00) ? detail::select(0x7C00, y.data_) :
				(absy==0x7C00) ? detail::select(0x7C00, x.data_) : detail::signal(x.data_, y.data_));
		if(!absx)
			return half(detail::binary, absy ? detail::check_underflow(absy) : 0);
		if(!absy)
			return half(detail::binary, detail::check_underflow(absx));
		if(absy > absx)
			std::swap(absx, absy);
		for(; absx<0x400; absx<<=1,--expx) ;
		for(; absy<0x400; absy<<=1,--expy) ;
		detail::uint32 mx = (absx&0x3FF) | 0x400, my = (absy&0x3FF) | 0x400;
		mx *= mx;
		my *= my;
		int ix = mx >> 21, iy = my >> 21;
		expx = 2*(expx+(absx>>10)) - 15 + ix;
		expy = 2*(expy+(absy>>10)) - 15 + iy;
		mx <<= 10 - ix;
		my <<= 10 - iy;
		int d = expx - expy;
		my = (d<30) ? ((my>>d)|((my&((static_cast<detail::uint32>(1)<<d)-1))!=0)) : 1;
		return half(detail::binary, detail::hypot_post<half::round_style>(mx+my, expx));
	#endif
	}

	/// Hypotenuse function.
	/// This function is exact to rounding for all rounding modes.