Function tan

include/half.hpp:3591–3618

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

	/// \exception FE_INVALID for signaling NaN or infinity
	/// \exception FE_OVERFLOW, ...UNDERFLOW, ...INEXACT according to rounding
	inline half tan(half arg)
	{
	#ifdef HALF_ARITHMETIC_TYPE
		return half(detail::binary, detail::float2half<half::round_style>(std::tan(detail::half2float<detail::internal_t>(arg.data_))));
	#else
		int abs = arg.data_ & 0x7FFF, exp = 13, k;
		if(!abs)
			return arg;
		if(abs >= 0x7C00)
			return half(detail::binary, (abs==0x7C00) ? detail::invalid() : detail::signal(arg.data_));
		if(abs < 0x2700)
			return half(detail::binary, detail::rounded<half::round_style,true>(arg.data_, 0, 1));
		if(half::round_style != std::round_to_nearest)
			switch(abs)
			{
				case 0x658C: return half(detail::binary, detail::rounded<half::round_style,true>((arg.data_&0x8000)|0x07E6, 1, 1));
				case 0x7330: return half(detail::binary, detail::rounded<half::round_style,true>((~arg.data_&0x8000)|0x4B62, 1, 1));
			}
		std::pair<detail::uint32,detail::uint32> sc = detail::sincos(detail::angle_arg(abs, k), 30);
		if(k & 1)
			sc = std::make_pair(-sc.second, sc.first);
		detail::uint32 signy = detail::sign_mask(sc.first), signx = detail::sign_mask(sc.second);
		detail::uint32 my = (sc.first^signy) - signy, mx = (sc.second^signx) - signx;
		for(; my<0x80000000; my<<=1,--exp) ;
		for(; mx<0x80000000; mx<<=1,++exp) ;
		return half(detail::binary, detail::tangent_post<half::round_style>(my, mx, exp, (signy^signx^arg.data_)&0x8000));
	#endif
	}

	/// Arc sine.
	/// This function is exact to rounding for all rounding modes.