inline SPROUT_CONSTEXPR T
triangle_value_impl(T const& t) {
typedef double elem_type;
using sprout::sin;
using sprout::asin;
return T(sprout::math::two_div_pi<elem_type>()) * asin(sin(T(sprout::math::two_pi<elem_type>()) * t));
}
inline SPROUT_CONSTEXPR typename std::iterator_traits<RandomAccessIterator>::value_type
dft_element_gen_impl_ra(
RandomAccessIterator first, RandomAccessIterator last,
typename std::iterator_traits<RandomAccessIterator>::value_type::value_type arg,
typename std::iterator_traits<RandomAccessIterator>::difference_type pivot,
typename std::iterator_traits<RandomAccessIterator>::difference_type k = 0
)
{
typedef typename std::iterator_traits<RandomAccessIterator>::value_type value_type;
using sprout::cos;
using sprout::sin;
return pivot == 0 ? *first * value_type(cos(arg * k), sin(arg * k))
: sprout::detail::dft_element_gen_impl_ra(
first, sprout::next(first, pivot), arg, pivot / 2, k
)
+ sprout::detail::dft_element_gen_impl_ra(
sprout::next(first, pivot), last, arg, (sprout::distance(first, last) - pivot) / 2, k + pivot
)
;
}
inline SPROUT_CONSTEXPR typename sprout::fixed::result_of::algorithm<Result>::type
phase_spectrum_impl(
InputIterator first, InputIterator last, Result const& result,
sprout::index_tuple<Indexes...>,
typename sprout::container_traits<Result>::difference_type offset,
typename sprout::container_traits<Result>::size_type size,
typename sprout::container_traits<Result>::size_type input_size
)
{
using sprout::real;
using sprout::imag;
return sprout::remake<Result>(
result,
size,
(Indexes >= offset && Indexes < offset + size && Indexes < offset + input_size
? sprout::atan2(
sprout::llround(imag(*sprout::next(first, Indexes))),
sprout::llround(real(*sprout::next(first, Indexes)))
)
: *sprout::next(sprout::internal_begin(result), Indexes)
)...
);
}
inline SPROUT_CONSTEXPR typename std::iterator_traits<InputIterator>::value_type
dft_element_gen_impl_1(
InputIterator first, InputIterator last,
typename std::iterator_traits<InputIterator>::value_type::value_type arg,
typename std::iterator_traits<InputIterator>::difference_type k = 0,
typename std::iterator_traits<InputIterator>::value_type value
= typename std::iterator_traits<InputIterator>::value_type(),
typename std::iterator_traits<InputIterator>::value_type::value_type theta
= typename std::iterator_traits<InputIterator>::value_type::value_type()
)
{
typedef typename std::iterator_traits<InputIterator>::value_type value_type;
using sprout::cos;
using sprout::sin;
return first == last ? value
: value + sprout::detail::dft_element_gen_impl_1(
sprout::next(first), last,
arg,
k + 1,
*first * value_type(cos(theta), sin(theta)),
arg * (k + 1)
)
;
}
inline SPROUT_CONSTEXPR typename sprout::fixed::result_of::algorithm<Container>::type
sinusoid_impl(
Container const& cont,
typename sprout::container_traits<Container>::value_type const& d,
typename sprout::container_traits<Container>::value_type const& amplitude,
typename sprout::container_traits<Container>::value_type const& phase,
sprout::index_tuple<Indexes...>,
typename sprout::container_traits<Container>::difference_type offset,
typename sprout::container_traits<Container>::size_type size
)
{
typedef typename sprout::container_traits<Container>::value_type value_type;
using sprout::sin;
return sprout::remake<Container>(
cont, size,
(Indexes >= offset && Indexes < offset + size
? amplitude * sin(d * value_type(Indexes) + phase)
: *sprout::next(sprout::internal_begin(cont), Indexes)
)...
);
}
inline SPROUT_CONSTEXPR typename T::value_type
phase_spectrum_value(T const& x) {
using sprout::real;
using sprout::imag;
return sprout::atan2(sprout::llround(imag(x)), sprout::llround(real(x)));
}
inline SPROUT_CONSTEXPR typename T::value_type
amplitude_spectrum_value(T const& x) {
using sprout::real;
using sprout::imag;
return sprout::sqrt(real(x) * real(x) + imag(x) * imag(x));
}
inline SPROUT_CONSTEXPR std::size_t
to_hash(T&& v) {
using sprout::hash_value;
using sprout_adl::hash_value;
return hash_value(SPROUT_FORWARD(T, v));
}
inline SPROUT_CONSTEXPR T
sinusoid_value(T const& amplitude, T const& phase, T const& d, Index i) {
using sprout::sin;
return amplitude * sin(d * T(i) + phase);
}
SPROUT_CONSTEXPR typename sprout::float_promote<ArithmeticType1, ArithmeticType2>::type
equal_temperament_value(ArithmeticType1 i, ArithmeticType2 div) {
typedef typename sprout::float_promote<ArithmeticType1, ArithmeticType2>::type type;
using sprout::pow;
return pow(type(2), type(i) / type(div));
}
inline SPROUT_CONSTEXPR std::size_t
to_hash(T&& v) {
using sprout::hash_value;
using sprout_adl::hash_value;
return hash_value(sprout::forward<T>(v));
}
inline SPROUT_CONSTEXPR std::size_t
call_hash_value(T const& v) {
using sprout::hash_value;
using sprout_adl::hash_value;
return hash_value(v);
}
inline SPROUT_CONSTEXPR T
sawtooth_value_impl(T const& t) {
using sprout::floor;
return 2 * (t - floor(t + T(0.5)));
}
