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fix recursion depth math functions.

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This commit is contained in:
bolero-MURAKAMI 2012-12-08 13:45:09 +09:00
parent 0754fd0fad
commit 74729ce14f
8 changed files with 80 additions and 115 deletions
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15
sprout/detail/pow.hpp
View file

@ -9,17 +9,26 @@ namespace sprout {
pow2(T const& x) {
return x * x;
}
template<typename T>
inline SPROUT_CONSTEXPR T
pow3(T const& x) {
return x * x * x;
}
template<typename T>
inline SPROUT_CONSTEXPR T
pow_n_impl(T const& x, int n) {
return n == 1 ? x
: n % 2 ? x * sprout::detail::pow2(sprout::detail::pow_n_impl(x, n / 2))
: sprout::detail::pow2(sprout::detail::pow_n_impl(x, n / 2))
;
}
template<typename T>
inline SPROUT_CONSTEXPR T
pow_n(T const& x, int n) {
return n == 1 ? x
: n % 2 ? x * sprout::detail::pow2(sprout::detail::pow_n(x, n / 2))
: sprout::detail::pow2(sprout::detail::pow_n(x, n / 2))
return n == 0 ? T(1)
: sprout::detail::pow_n_impl(x, n)
;
}
} // namespace detail

35
sprout/math/asin.hpp
View file

@ -5,6 +5,7 @@
#include <limits>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/detail/pow.hpp>
#include <sprout/math/detail/config.hpp>
#include <sprout/math/constants.hpp>
#include <sprout/math/factorial.hpp>
@ -16,37 +17,21 @@ namespace sprout {
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR T
asin_impl_2(T x, T tmp, std::size_t n, T x2n1, T _4n) {
return 2 * n > sprout::math::factorial_limit<T>() ? tmp
: sprout::math::detail::asin_impl_2(
x,
tmp + sprout::math::factorial<T>(2 * n)
/ _4n / sprout::math::factorial<T>(n) / sprout::math::factorial<T>(n) / (2 * n + 1)
* x2n1
,
n + 1,
x2n1 * x * x,
_4n * 4
)
asin_impl_1(T x, std::size_t n, std::size_t last) {
return last - n == 1
? sprout::math::factorial<T>(2 * n)
/ sprout::detail::pow_n(T(4), n) / sprout::detail::pow2(sprout::math::factorial<T>(n)) / (2 * n + 1)
* sprout::detail::pow_n(x, 2 * n + 1)
: sprout::math::detail::asin_impl_1(x, n, n + (last - n) / 2)
+ sprout::math::detail::asin_impl_1(x, n + (last - n) / 2, last)
;
}
template<typename T>
inline SPROUT_CONSTEXPR T
asin_impl_1(T x) {
return sprout::math::detail::asin_impl_2(
x,
x,
1,
x * x * x,
T(4)
);
}
template<typename T>
inline SPROUT_CONSTEXPR T
asin_impl(T x) {
return x > sprout::math::half_root_two<T>()
? sprout::math::half_pi<T>() - sprout::math::detail::asin_impl_1(sprout::math::sqrt(1 - x * x))
: sprout::math::detail::asin_impl_1(x)
? 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)
: x + sprout::math::detail::asin_impl_1(x, 1, sprout::math::factorial_limit<T>() / 2 + 1)
;
}

30
sprout/math/atan.hpp
View file

@ -4,6 +4,7 @@
#include <cstddef>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/detail/pow.hpp>
#include <sprout/math/detail/config.hpp>
#include <sprout/math/constants.hpp>
#include <sprout/math/factorial.hpp>
@ -14,34 +15,21 @@ namespace sprout {
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR T
atan_impl_2(T x, T tmp, std::size_t n, T x2n1) {
return n > sprout::math::factorial_limit<T>() ? tmp
: sprout::math::detail::atan_impl_2(
x,
tmp + (n % 2 ? -1 : 1) * x2n1 / (2 * n + 1),
n + 1,
x2n1 * x * x
)
atan_impl_1(T x, std::size_t n, std::size_t last) {
return last - n == 1
? (n % 2 ? -1 : 1) * sprout::detail::pow_n(x, 2 * n + 1) / (2 * n + 1)
: sprout::math::detail::atan_impl_1(x, n, n + (last - n) / 2)
+ sprout::math::detail::atan_impl_1(x, n + (last - n) / 2, last)
;
}
template<typename T>
inline SPROUT_CONSTEXPR T
atan_impl_1(T x) {
return sprout::math::detail::atan_impl_2(
x,
x,
1,
x * x * x
);
}
template<typename T>
inline SPROUT_CONSTEXPR T
atan_impl(T x) {
return x > sprout::math::root_two<T>() + 1
? sprout::math::half_pi<T>() - sprout::math::detail::atan_impl_1(1 / x)
? sprout::math::half_pi<T>() - sprout::math::detail::atan_impl_1(1 / x, 0, sprout::math::factorial_limit<T>() + 1)
: x > sprout::math::root_two<T>() - 1
? sprout::math::quarter_pi<T>() + sprout::math::detail::atan_impl_1((x - 1) / (x + 1))
: sprout::math::detail::atan_impl_1(x)
? sprout::math::quarter_pi<T>() + sprout::math::detail::atan_impl_1((x - 1) / (x + 1), 0, sprout::math::factorial_limit<T>() + 1)
: x + sprout::math::detail::atan_impl_1(x, 1, sprout::math::factorial_limit<T>() + 1)
;
}

10
sprout/math/cos.hpp
View file

@ -17,11 +17,11 @@ namespace sprout {
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR T
cos_impl_1(T x2, std::size_t first, std::size_t last) {
return last - first == 1
? (first % 2 ? -1 : 1) * sprout::detail::pow_n(x2, first) / sprout::math::factorial<T>(2 * first)
: sprout::math::detail::cos_impl_1(x2, first, first + (last - first) / 2)
+ sprout::math::detail::cos_impl_1(x2, first + (last - first) / 2, last)
cos_impl_1(T x2, std::size_t n, std::size_t last) {
return last - n == 1
? (n % 2 ? -1 : 1) * sprout::detail::pow_n(x2, n) / sprout::math::factorial<T>(2 * n)
: sprout::math::detail::cos_impl_1(x2, n, n + (last - n) / 2)
+ sprout::math::detail::cos_impl_1(x2, n + (last - n) / 2, last)
;
}
template<typename FloatType>

26
sprout/math/cosh.hpp
View file

@ -4,6 +4,7 @@
#include <cstddef>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/detail/pow.hpp>
#include <sprout/math/detail/config.hpp>
#include <sprout/math/factorial.hpp>
#include <sprout/type_traits/enabler_if.hpp>
@ -13,14 +14,11 @@ namespace sprout {
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR T
cosh_impl(T x, T tmp, std::size_t n, T x2n) {
return 2 * n > sprout::math::factorial_limit<T>() ? tmp
: sprout::math::detail::cosh_impl(
x,
tmp + x2n / sprout::math::factorial<T>(2 * n),
n + 1,
x2n * x * x
)
cosh_impl(T x2, std::size_t n, std::size_t last) {
return last - n == 1
? sprout::detail::pow_n(x2, n) / sprout::math::factorial<T>(2 * n)
: sprout::math::detail::cosh_impl(x2, n, n + (last - n) / 2)
+ sprout::math::detail::cosh_impl(x2, n + (last - n) / 2, last)
;
}
@ -31,12 +29,12 @@ namespace sprout {
inline SPROUT_CONSTEXPR FloatType
cosh(FloatType x) {
typedef double type;
return static_cast<FloatType>(sprout::math::detail::cosh_impl(
static_cast<type>(x),
type(1),
1,
static_cast<type>(x) * static_cast<type>(x)
));
return static_cast<FloatType>(
type(1) + sprout::math::detail::cosh_impl(
static_cast<type>(x) * static_cast<type>(x),
1, sprout::math::factorial_limit<type>() / 2 + 1
)
);
}
template<

26
sprout/math/exp.hpp
View file

@ -4,6 +4,7 @@
#include <cstddef>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/detail/pow.hpp>
#include <sprout/math/detail/config.hpp>
#include <sprout/math/factorial.hpp>
#include <sprout/type_traits/enabler_if.hpp>
@ -13,14 +14,11 @@ namespace sprout {
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR T
exp_impl(T x, T tmp, std::size_t n, T xn) {
return n > sprout::math::factorial_limit<T>() ? tmp
: sprout::math::detail::exp_impl(
x,
tmp + xn / sprout::math::factorial<T>(n),
n + 1,
xn * x
)
exp_impl(T x, std::size_t n, std::size_t last) {
return last - n == 1
? sprout::detail::pow_n(x, n) / sprout::math::factorial<T>(n)
: sprout::math::detail::exp_impl(x, n, n + (last - n) / 2)
+ sprout::math::detail::exp_impl(x, n + (last - n) / 2, last)
;
}
@ -31,12 +29,12 @@ namespace sprout {
inline SPROUT_CONSTEXPR FloatType
exp(FloatType x) {
typedef double type;
return static_cast<FloatType>(sprout::math::detail::exp_impl(
static_cast<type>(x),
type(1),
1,
static_cast<type>(x)
));
return static_cast<FloatType>(
type(1) + sprout::math::detail::exp_impl(
static_cast<type>(x),
1, sprout::math::factorial_limit<type>() + 1
)
);
}
template<

27
sprout/math/log.hpp
View file

@ -5,6 +5,7 @@
#include <limits>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/detail/pow.hpp>
#include <sprout/math/detail/config.hpp>
#include <sprout/math/constants.hpp>
#include <sprout/math/factorial.hpp>
@ -16,30 +17,18 @@ namespace sprout {
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR T
log_impl_2(T x, T tmp, std::size_t n, T xn) {
return n > sprout::math::factorial_limit<T>() ? tmp
: sprout::math::detail::log_impl_2(
x,
tmp + (n % 2 ? 1 : -1) * xn / n,
n + 1,
xn * x
)
log_impl_1(T x, std::size_t n, std::size_t last) {
return last - n == 1
? (n % 2 ? 1 : -1) * sprout::detail::pow_n(x, n) / n
: sprout::math::detail::log_impl_1(x, n, n + (last - n) / 2)
+ sprout::math::detail::log_impl_1(x, n + (last - n) / 2, last)
;
}
template<typename T>
inline SPROUT_CONSTEXPR T
log_impl_1(T x) {
return sprout::math::detail::log_impl_2(
x,
x,
2,
x * x
);
}
template<typename T>
inline SPROUT_CONSTEXPR T
log_impl(T x) {
return !(x > sprout::math::root_two<T>()) ? sprout::math::detail::log_impl_1(x - 1)
return !(x > sprout::math::root_two<T>())
? sprout::math::detail::log_impl_1(x - 1, 1, sprout::math::factorial_limit<T>() + 1)
: 2 * sprout::math::detail::log_impl(sprout::math::sqrt(x))
;
}

26
sprout/math/sinh.hpp
View file

@ -4,6 +4,7 @@
#include <cstddef>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/detail/pow.hpp>
#include <sprout/math/detail/config.hpp>
#include <sprout/math/factorial.hpp>
#include <sprout/type_traits/enabler_if.hpp>
@ -13,14 +14,11 @@ namespace sprout {
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR T
sinh_impl(T x, T tmp, std::size_t n, T x2n1) {
return 2 * n + 1 > sprout::math::factorial_limit<T>() ? tmp
: sprout::math::detail::sinh_impl(
x,
tmp + x2n1 / sprout::math::factorial<T>(2 * n + 1),
n + 1,
x2n1 * x * x
)
sinh_impl(T x, std::size_t n, std::size_t last) {
return last - n == 1
? sprout::detail::pow_n(x, 2 * n + 1) / sprout::math::factorial<T>(2 * n + 1)
: sprout::math::detail::sinh_impl(x, n, n + (last - n) / 2)
+ sprout::math::detail::sinh_impl(x, n + (last - n) / 2, last)
;
}
@ -31,12 +29,12 @@ namespace sprout {
inline SPROUT_CONSTEXPR FloatType
sinh(FloatType x) {
typedef double type;
return static_cast<FloatType>(sprout::math::detail::sinh_impl(
static_cast<type>(x),
static_cast<type>(x),
1,
static_cast<type>(x) * static_cast<type>(x) * static_cast<type>(x)
));
return static_cast<FloatType>(
static_cast<type>(x) + sprout::math::detail::sinh_impl(
static_cast<type>(x),
1, (sprout::math::factorial_limit<type>() - 1) / 2 + 1
)
);
}
template<