Function sinh

include/half.hpp:3767–3785

Hyperbolic sine. This function is exact to rounding for all rounding modes. See also:** Documentation for [std::sinh](https://en.cppreference.com/w/cpp/numeric/math/sinh). \param arg function argument \return hyperbolic sine value of \a arg \exception FE_INVALID for signaling NaN \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding

	/// \exception FE_INVALID for signaling NaN
	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
	inline half sinh(half arg)
	{
	#ifdef HALF_ARITHMETIC_TYPE
		return half(detail::binary, detail::float2half<half::round_style>(std::sinh(detail::half2float<detail::internal_t>(arg.data_))));
	#else
		int abs = arg.data_ & 0x7FFF, exp;
		if(!abs || abs >= 0x7C00)
			return (abs>0x7C00) ? half(detail::binary, detail::signal(arg.data_)) : arg;
		if(abs <= 0x2900)
			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));
		std::pair<detail::uint32,detail::uint32> mm = detail::hyperbolic_args(abs, exp, (half::round_style==std::round_to_nearest) ? 29 : 27);
		detail::uint32 m = mm.first - mm.second;
		for(exp+=13; m<0x80000000 && exp; m<<=1,--exp) ;
		unsigned int sign = arg.data_ & 0x8000;
		if(exp > 29)
			return half(detail::binary, detail::overflow<half::round_style>(sign));
		return half(detail::binary, detail::fixed2half<half::round_style,31,false,false,true>(m, exp, sign));
	#endif
	}

	/// Hyperbolic cosine.
	/// This function is exact to rounding for all rounding modes.