Trigonometric

Detailed Description

These functions allows performing trigonometric computations

All trigonometric functions exists in three flavors for parameters being radian, degrees or \(\pi\) multiples.

• for example eve::cos, eve::cosd, eve::cospi.

• The main avantage of using eve::cospi(x) instead of eve::cos(eve::pi(as(x)* x)) (as well as the other pi ended functions) is that if x is exactly representable the multiplication by the floating \(\pi\) multiplier is not.

  For example eve::cos(eve::pio_2(as<double>()))) is 6.1232e-17 (as pio_2 is not exact), but eve::cospi(0.5) is 0 (as 0.5 is exact).

Moreover each function can be decorated with eve::quarter_circle, eve:half_circle, eve::full_circle, eve::medium, eve::big.

• eve::quarter_circle provides accurate result for the corresponding radian angle in \(]-\pi/4,\pi/4[\), Nan outside
• eve::half_circle provides accurate result for the corresponding radian angle in \(]-\pi/2,\pi/2[\), Nan outside
• eve::full_circle provides accurate result for the corresponding radian angle in \(]-\pi,\pi[\), Nan outside
• regular call (not decorated) choose the best call and is valid on the full range.

Warning

Note that these decorator only work for floating real values.

Variables
constexpr auto	eve::arg = functor<arg_t>
	elementwise_callable object computing the phase angle (in radians).
constexpr auto	eve::cos = functor<cos_t>
	elementwise_callable object computing the cosine.
constexpr auto	eve::cosd = functor<cosd_t>
	elementwise_callable object object computing cosine from an input in degrees.
constexpr auto	eve::cospi = functor<cospi_t>
	elementwise_callable object computing the cosine from an input in \(\pi\) multiples.
constexpr auto	eve::cot = functor<cot_t>
	elementwise_callable object computing the cotangent of the input.
constexpr auto	eve::cotd = functor<cotd_t>
	elementwise_callable object computing the cotangent from an input in degrees.
constexpr auto	eve::cotpi = functor<cotpi_t>
	elementwise_callable object computing the cotangent from an input in \(\pi\) multiples.
constexpr auto	eve::csc = functor<csc_t>
	elementwise_callable object computing the cosecant of the input.
constexpr auto	eve::cscd = functor<cscd_t>
	elementwise_callable object computing the cosecant from an input in degree.
constexpr auto	eve::cscpi = functor<cscpi_t>
	elementwise_callable object computing the cosecant in \(\pi\) multiples.
constexpr auto	eve::deginrad = functor<deginrad_t>
	elementwise_callable object computing the product of the input by \(\pi/180\).
constexpr auto	eve::div_180 = functor<div_180_t>
	elementwise_callable object computing the product of the input by \(1/180\).
constexpr auto	eve::quadrant = functor<quadrant_t>
	Callable object computing the quadrant value.
constexpr auto	eve::radindeg = functor<radindeg_t>
	elementwise_callable object multiplying the input by \(180/\pi\).
constexpr auto	eve::radinpi = functor<radinpi_t>
	elementwise_callable object multiplying the input by \(1/\pi\).
constexpr auto	eve::rempio2 = functor<rempio2_t>
	elementwise_callable object computing the remainder of the division by \(\pi/2\).
constexpr auto	eve::sec = functor<sec_t>
	elementwise_callable object computing the secant of the input.
constexpr auto	eve::secd = functor<secd_t>
	elementwise_callable object computing the secant from an input in degree.
constexpr auto	eve::secpi = functor<secpi_t>
	elementwise_callable object computing secant from an input in \(\pi\) multiples.
constexpr auto	eve::sin = functor<sin_t>
	elementwise_callable object computing the sine.
constexpr auto	eve::sinc = functor<sinc_t>
	elementwise_callable object computing the sine cardinal.
constexpr auto	eve::sincos = functor<sincos_t>
	elementwise_callable object computing the simultaneous computation of sine an cosine.
constexpr auto	eve::sind = functor<sind_t>
	elementwise_callable object computing the sine from an input in degrees.
constexpr auto	eve::sindcosd = functor<sindcosd_t>
	elementwise_callable object computing the simultaneous computation of sine an cosine from an argument in degrees.
constexpr auto	eve::sinpi = functor<sinpi_t>
	elementwise_callable object computing the sine from an input in \(\pi\) multiples.
constexpr auto	eve::sinpic = functor<sinpic_t>
	elementwise_callable object computing the normalized cardinal sine.
constexpr auto	eve::sinpicospi = functor<sinpicospi_t>
	elementwise_callable object computing the simultaneous computation of sin an cos from an argument in \(\pi\) multiples.
constexpr auto	eve::tan = functor<tan_t>
	elementwise_callable object computing the tangent.
constexpr auto	eve::tand = functor<tand_t>
	elementwise_callable object computing the tangent from an input in degrees.
constexpr auto	eve::tanpi = functor<tanpi_t>
	elementwise_callable object computing the tangent from an input in \(\pi\) multiples.
constexpr full_circle_type const	eve::full_circle = {}
	Higher-order Callable Object imbuing a limited range semantic onto other Callable Objects.
constexpr quarter_circle_type const	eve::quarter_circle = {}
	Higher-order Callable Object imbuing a limited range semantic onto other Callable Objects.
constexpr half_circle_type const	eve::half_circle = {}
	Higher-order Callable Object imbuing a limited range standard semantic onto other Callable Objects.