constexpr inline T sin(T x)
{
x = x - trunc(x / c_pi<T, 2>) * c_pi<T, 2>;
constexpr T c2 = -0.16665853559970855712890625;
constexpr T c4 = +8.31427983939647674560546875e-3;
constexpr T c6 = -1.85423981747590005397796630859375e-4;
x -= c_pi<T>;
T y = abs(x);
y = select(y > c_pi<T, 1, 2>, c_pi<T> - y, y);
y = mulsign(y, -x);
const T y2 = y * y;
T formula = c6;
const T y3 = y2 * y;
formula = fmadd(formula, y2, c4);
formula = fmadd(formula, y2, c2);
formula = formula * y3 + y;
return formula;
}
constexpr CMT_INLINE common_type<T1, T2, T3, Ts...> horner_odd(const T1& x, const T2& c1, const T3& c3,
const Ts&... values)
{
const T1 x2 = x * x;
return fmadd(horner(x2, c3, values...), x2, c1) * x;
}
constexpr CMT_INLINE common_type<T1, T2, T3, Ts...> horner_even(const T1& x, const T2& c0, const T3& c2,
const Ts&... values)
{
const T1 x2 = x * x;
return fmadd(horner(x2, c2, values...), x2, c0);
}
constexpr CMT_INLINE common_type<T1, T2, T3, Ts...> horner(const T1& x, const T2& c0, const T3& c1,
const Ts&... values)
{
return fmadd(horner(x, c1, values...), x, c0);
}
KFR_INTRIN constexpr common_type<T1, T2, T3> mixs(const T1& c, const T2& x, const T3& y)
{
return mix(fmadd(c, 0.5, 0.5), x, y);
}
KFR_INTRIN constexpr common_type<T1, T2, T3> mix(const T1& c, const T2& x, const T3& y)
{
return fmadd(c, y - x, x);
}