Trigonometric

Detailed Description

These functions allows performing trigonometric computations

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

• for example eve::cos[eve::rad], eve::cos[eve::deg], eve::cos[eve::radpi]. (eve::cos is equivalent to eve::cos[eve::rad])

• The main avantage of using eve::cos[eve::radpi](x) instead of eve::cos(eve::pi(as(x)* x)) (as well as the other radpi decorated 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::cosradpi is 0 (as 0.5 is exact).

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

• 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.

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::cot = functor<cot_t>
	elementwise_callable object computing the cotangent of the input.
constexpr auto	eve::csc = functor<csc_t>
	elementwise_callable object computing the cosecant of the input.
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::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::sinpic = functor<sinpic_t>
	elementwise_callable object computing the normalized cardinal sine.
constexpr auto	eve::tan = functor<tan_t>
	elementwise_callable object computing the tangent.