mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
synced 2024-11-14 10:39:05 +00:00
fix recursion depth math functions.
This commit is contained in:
bolero-MURAKAMI
parent
0754fd0fad
commit
74729ce14f
8 changed files with 80 additions and 115 deletions
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@ -9,17 +9,26 @@ namespace sprout {
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pow2(T const& x) {
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return x * x;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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pow3(T const& x) {
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return x * x * x;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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pow_n_impl(T const& x, int n) {
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return n == 1 ? x
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: n % 2 ? x * sprout::detail::pow2(sprout::detail::pow_n_impl(x, n / 2))
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: sprout::detail::pow2(sprout::detail::pow_n_impl(x, n / 2))
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;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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pow_n(T const& x, int n) {
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return n == 1 ? x
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: n % 2 ? x * sprout::detail::pow2(sprout::detail::pow_n(x, n / 2))
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: sprout::detail::pow2(sprout::detail::pow_n(x, n / 2))
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return n == 0 ? T(1)
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: sprout::detail::pow_n_impl(x, n)
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;
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}
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} // namespace detail
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@ -5,6 +5,7 @@
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#include <limits>
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/detail/pow.hpp>
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#include <sprout/math/detail/config.hpp>
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#include <sprout/math/constants.hpp>
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#include <sprout/math/factorial.hpp>
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@ -16,37 +17,21 @@ namespace sprout {
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR T
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asin_impl_2(T x, T tmp, std::size_t n, T x2n1, T _4n) {
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return 2 * n > sprout::math::factorial_limit<T>() ? tmp
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: sprout::math::detail::asin_impl_2(
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x,
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tmp + sprout::math::factorial<T>(2 * n)
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/ _4n / sprout::math::factorial<T>(n) / sprout::math::factorial<T>(n) / (2 * n + 1)
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* x2n1
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,
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n + 1,
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x2n1 * x * x,
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_4n * 4
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)
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asin_impl_1(T x, std::size_t n, std::size_t last) {
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return last - n == 1
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? sprout::math::factorial<T>(2 * n)
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/ sprout::detail::pow_n(T(4), n) / sprout::detail::pow2(sprout::math::factorial<T>(n)) / (2 * n + 1)
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* sprout::detail::pow_n(x, 2 * n + 1)
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: sprout::math::detail::asin_impl_1(x, n, n + (last - n) / 2)
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+ sprout::math::detail::asin_impl_1(x, n + (last - n) / 2, last)
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;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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asin_impl_1(T x) {
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return sprout::math::detail::asin_impl_2(
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x,
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x,
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1,
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x * x * x,
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T(4)
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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asin_impl(T x) {
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return x > sprout::math::half_root_two<T>()
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? sprout::math::half_pi<T>() - sprout::math::detail::asin_impl_1(sprout::math::sqrt(1 - x * x))
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: sprout::math::detail::asin_impl_1(x)
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? sprout::math::half_pi<T>() - sprout::math::detail::asin_impl_1(sprout::math::sqrt(1 - x * x), 0, sprout::math::factorial_limit<T>() / 2 + 1)
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: x + sprout::math::detail::asin_impl_1(x, 1, sprout::math::factorial_limit<T>() / 2 + 1)
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;
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}
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@ -4,6 +4,7 @@
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#include <cstddef>
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/detail/pow.hpp>
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#include <sprout/math/detail/config.hpp>
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#include <sprout/math/constants.hpp>
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#include <sprout/math/factorial.hpp>
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@ -14,34 +15,21 @@ namespace sprout {
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR T
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atan_impl_2(T x, T tmp, std::size_t n, T x2n1) {
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return n > sprout::math::factorial_limit<T>() ? tmp
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: sprout::math::detail::atan_impl_2(
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x,
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tmp + (n % 2 ? -1 : 1) * x2n1 / (2 * n + 1),
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n + 1,
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x2n1 * x * x
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)
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atan_impl_1(T x, std::size_t n, std::size_t last) {
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return last - n == 1
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? (n % 2 ? -1 : 1) * sprout::detail::pow_n(x, 2 * n + 1) / (2 * n + 1)
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: sprout::math::detail::atan_impl_1(x, n, n + (last - n) / 2)
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+ sprout::math::detail::atan_impl_1(x, n + (last - n) / 2, last)
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;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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atan_impl_1(T x) {
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return sprout::math::detail::atan_impl_2(
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x,
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x,
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1,
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x * x * x
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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atan_impl(T x) {
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return x > sprout::math::root_two<T>() + 1
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? sprout::math::half_pi<T>() - sprout::math::detail::atan_impl_1(1 / x)
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? sprout::math::half_pi<T>() - sprout::math::detail::atan_impl_1(1 / x, 0, sprout::math::factorial_limit<T>() + 1)
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: x > sprout::math::root_two<T>() - 1
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? sprout::math::quarter_pi<T>() + sprout::math::detail::atan_impl_1((x - 1) / (x + 1))
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: sprout::math::detail::atan_impl_1(x)
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? sprout::math::quarter_pi<T>() + sprout::math::detail::atan_impl_1((x - 1) / (x + 1), 0, sprout::math::factorial_limit<T>() + 1)
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: x + sprout::math::detail::atan_impl_1(x, 1, sprout::math::factorial_limit<T>() + 1)
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;
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}
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@ -17,11 +17,11 @@ namespace sprout {
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR T
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cos_impl_1(T x2, std::size_t first, std::size_t last) {
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return last - first == 1
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? (first % 2 ? -1 : 1) * sprout::detail::pow_n(x2, first) / sprout::math::factorial<T>(2 * first)
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: sprout::math::detail::cos_impl_1(x2, first, first + (last - first) / 2)
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+ sprout::math::detail::cos_impl_1(x2, first + (last - first) / 2, last)
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cos_impl_1(T x2, std::size_t n, std::size_t last) {
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return last - n == 1
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? (n % 2 ? -1 : 1) * sprout::detail::pow_n(x2, n) / sprout::math::factorial<T>(2 * n)
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: sprout::math::detail::cos_impl_1(x2, n, n + (last - n) / 2)
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+ sprout::math::detail::cos_impl_1(x2, n + (last - n) / 2, last)
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;
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}
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template<typename FloatType>
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@ -4,6 +4,7 @@
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#include <cstddef>
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/detail/pow.hpp>
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#include <sprout/math/detail/config.hpp>
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#include <sprout/math/factorial.hpp>
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#include <sprout/type_traits/enabler_if.hpp>
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@ -13,14 +14,11 @@ namespace sprout {
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR T
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cosh_impl(T x, T tmp, std::size_t n, T x2n) {
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return 2 * n > sprout::math::factorial_limit<T>() ? tmp
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: sprout::math::detail::cosh_impl(
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x,
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tmp + x2n / sprout::math::factorial<T>(2 * n),
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n + 1,
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x2n * x * x
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)
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cosh_impl(T x2, std::size_t n, std::size_t last) {
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return last - n == 1
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? sprout::detail::pow_n(x2, n) / sprout::math::factorial<T>(2 * n)
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: sprout::math::detail::cosh_impl(x2, n, n + (last - n) / 2)
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+ sprout::math::detail::cosh_impl(x2, n + (last - n) / 2, last)
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;
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}
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@ -31,12 +29,12 @@ namespace sprout {
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inline SPROUT_CONSTEXPR FloatType
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cosh(FloatType x) {
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typedef double type;
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return static_cast<FloatType>(sprout::math::detail::cosh_impl(
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static_cast<type>(x),
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type(1),
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1,
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static_cast<type>(x) * static_cast<type>(x)
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));
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return static_cast<FloatType>(
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type(1) + sprout::math::detail::cosh_impl(
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static_cast<type>(x) * static_cast<type>(x),
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1, sprout::math::factorial_limit<type>() / 2 + 1
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)
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);
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}
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template<
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@ -4,6 +4,7 @@
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#include <cstddef>
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/detail/pow.hpp>
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#include <sprout/math/detail/config.hpp>
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#include <sprout/math/factorial.hpp>
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#include <sprout/type_traits/enabler_if.hpp>
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@ -13,14 +14,11 @@ namespace sprout {
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR T
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exp_impl(T x, T tmp, std::size_t n, T xn) {
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return n > sprout::math::factorial_limit<T>() ? tmp
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: sprout::math::detail::exp_impl(
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x,
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tmp + xn / sprout::math::factorial<T>(n),
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n + 1,
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xn * x
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)
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exp_impl(T x, std::size_t n, std::size_t last) {
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return last - n == 1
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? sprout::detail::pow_n(x, n) / sprout::math::factorial<T>(n)
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: sprout::math::detail::exp_impl(x, n, n + (last - n) / 2)
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+ sprout::math::detail::exp_impl(x, n + (last - n) / 2, last)
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;
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}
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@ -31,12 +29,12 @@ namespace sprout {
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inline SPROUT_CONSTEXPR FloatType
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exp(FloatType x) {
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typedef double type;
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return static_cast<FloatType>(sprout::math::detail::exp_impl(
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static_cast<type>(x),
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type(1),
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1,
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static_cast<type>(x)
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));
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return static_cast<FloatType>(
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type(1) + sprout::math::detail::exp_impl(
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static_cast<type>(x),
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1, sprout::math::factorial_limit<type>() + 1
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)
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);
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}
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template<
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@ -5,6 +5,7 @@
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#include <limits>
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/detail/pow.hpp>
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#include <sprout/math/detail/config.hpp>
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#include <sprout/math/constants.hpp>
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#include <sprout/math/factorial.hpp>
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@ -16,30 +17,18 @@ namespace sprout {
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR T
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log_impl_2(T x, T tmp, std::size_t n, T xn) {
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return n > sprout::math::factorial_limit<T>() ? tmp
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: sprout::math::detail::log_impl_2(
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x,
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tmp + (n % 2 ? 1 : -1) * xn / n,
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n + 1,
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xn * x
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)
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log_impl_1(T x, std::size_t n, std::size_t last) {
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return last - n == 1
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? (n % 2 ? 1 : -1) * sprout::detail::pow_n(x, n) / n
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: sprout::math::detail::log_impl_1(x, n, n + (last - n) / 2)
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+ sprout::math::detail::log_impl_1(x, n + (last - n) / 2, last)
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;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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log_impl_1(T x) {
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return sprout::math::detail::log_impl_2(
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x,
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x,
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2,
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x * x
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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log_impl(T x) {
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return !(x > sprout::math::root_two<T>()) ? sprout::math::detail::log_impl_1(x - 1)
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return !(x > sprout::math::root_two<T>())
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? sprout::math::detail::log_impl_1(x - 1, 1, sprout::math::factorial_limit<T>() + 1)
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: 2 * sprout::math::detail::log_impl(sprout::math::sqrt(x))
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;
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}
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@ -4,6 +4,7 @@
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#include <cstddef>
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/detail/pow.hpp>
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#include <sprout/math/detail/config.hpp>
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#include <sprout/math/factorial.hpp>
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#include <sprout/type_traits/enabler_if.hpp>
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@ -13,14 +14,11 @@ namespace sprout {
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR T
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sinh_impl(T x, T tmp, std::size_t n, T x2n1) {
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return 2 * n + 1 > sprout::math::factorial_limit<T>() ? tmp
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: sprout::math::detail::sinh_impl(
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x,
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tmp + x2n1 / sprout::math::factorial<T>(2 * n + 1),
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n + 1,
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x2n1 * x * x
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)
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sinh_impl(T x, std::size_t n, std::size_t last) {
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return last - n == 1
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? sprout::detail::pow_n(x, 2 * n + 1) / sprout::math::factorial<T>(2 * n + 1)
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: sprout::math::detail::sinh_impl(x, n, n + (last - n) / 2)
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+ sprout::math::detail::sinh_impl(x, n + (last - n) / 2, last)
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;
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}
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@ -31,12 +29,12 @@ namespace sprout {
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inline SPROUT_CONSTEXPR FloatType
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sinh(FloatType x) {
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typedef double type;
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return static_cast<FloatType>(sprout::math::detail::sinh_impl(
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static_cast<type>(x),
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static_cast<type>(x),
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1,
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static_cast<type>(x) * static_cast<type>(x) * static_cast<type>(x)
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));
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return static_cast<FloatType>(
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static_cast<type>(x) + sprout::math::detail::sinh_impl(
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static_cast<type>(x),
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1, (sprout::math::factorial_limit<type>() - 1) / 2 + 1
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)
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);
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}
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template<
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