mirror/Sprout
1
0
Fork 0
mirror of https://github.com/bolero-MURAKAMI/Sprout.git synced 2025-07-04 14:14:09 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions

add sprout/math/comparison.hpp

Browse source
This commit is contained in:
bolero-MURAKAMI 2012-07-06 23:10:49 +09:00
parent d51bd06eda
commit 1c65d59971
20 changed files with 379 additions and 109 deletions
Download patch file Download diff file Expand all files Collapse all files

78
sprout/complex.hpp
View file

@ -290,13 +290,11 @@ namespace sprout {
}
template<typename T>
SPROUT_CONSTEXPR T abs(sprout::complex<T> const& x) {
using sprout::sqrt;
return sqrt(sprout::norm(x));
return sprout::sqrt(sprout::norm(x));
}
template<typename T>
SPROUT_CONSTEXPR T arg(sprout::complex<T> const& x) {
using sprout::atan2;
return atan2(x.imag(), x.real());
return sprout::atan2(x.imag(), x.real());
}
template<typename T>
SPROUT_CONSTEXPR T norm(sprout::complex<T> const& x) {
@ -324,9 +322,7 @@ namespace sprout {
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> polar(T const& rho, T const& theta = 0) {
using sprout::cos;
using sprout::sin;
return sprout::complex<T>(rho * cos(theta), rho * sin(theta));
return sprout::complex<T>(rho * sprout::cos(theta), rho * sprout::sin(theta));
}
// 26.4.8, transcendentals:
template<typename T>
@ -397,11 +393,9 @@ namespace sprout {
T const& den
)
{
using sprout::atan2;
using sprout::log;
return sprout::complex<T>(
T(0.5) * atan2(T(2) * x.real(), z),
T(0.25) * log((r2 + num * num) / (r2 + den * den))
T(0.5) * sprout::atan2(T(2) * x.real(), z),
T(0.25) * sprout::log((r2 + num * num) / (r2 + den * den))
);
}
template<typename T>
@ -449,11 +443,9 @@ namespace sprout {
T const& den
)
{
using sprout::atan2;
using sprout::log;
return sprout::complex<T>(
T(0.25) * (log(i2 + num * num) - log(i2 + den * den)),
T(0.5) * atan2(T(2) * x.imag(), z)
T(0.25) * (sprout::log(i2 + num * num) - sprout::log(i2 + den * den)),
T(0.5) * sprout::atan2(T(2) * x.imag(), z)
);
}
template<typename T>
@ -477,30 +469,21 @@ namespace sprout {
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> cos(sprout::complex<T> const& x) {
using sprout::cos;
using sprout::sin;
using sprout::cosh;
using sprout::sinh;
return sprout::complex<T>(
cos(x.real()) * cosh(x.imag()),
-(sin(x.real()) * sinh(x.imag()))
sprout::cos(x.real()) * sprout::cosh(x.imag()),
-(sprout::sin(x.real()) * sprout::sinh(x.imag()))
);
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> cosh(sprout::complex<T> const& x) {
using sprout::cos;
using sprout::sin;
using sprout::cosh;
using sprout::sinh;
return sprout::complex<T>(
cosh(x.real()) * cos(x.imag()),
sinh(x.real()) * sin(x.imag())
sprout::cosh(x.real()) * sprout::cos(x.imag()),
sprout::sinh(x.real()) * sprout::sin(x.imag())
);
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> exp(sprout::complex<T> const& x) {
using sprout::exp;
return sprout::polar(exp(x.real()), x.imag());
return sprout::polar(sprout::exp(x.real()), x.imag());
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> log(sprout::complex<T> const& x) {
@ -508,21 +491,18 @@ namespace sprout {
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> log10(sprout::complex<T> const& x) {
using sprout::log;
return sprout::log(x) / log(T(10));
return sprout::log(x) / sprout::log(T(10));
}
namespace detail {
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> pow_impl(sprout::complex<T> const& t, T const& y) {
using sprout::exp;
return sprout::polar(exp(y * t.real()), y * t.imag());
return sprout::polar(sprout::exp(y * t.real()), y * t.imag());
}
} // namespace detail
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> pow(sprout::complex<T> const& x, T const& y) {
using sprout::pow;
return x == T() ? T()
: x.imag() == T() && x.real() > T() ? pow(x.real(), y)
: x.imag() == T() && x.real() > T() ? sprout::pow(x.real(), y)
: sprout::detail::pow_impl(sprout::log(x), y)
;
}
@ -534,31 +514,22 @@ namespace sprout {
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> pow(T const& x, sprout::complex<T> const& y) {
using sprout::log;
return x > T() ? sprout::polar(sprout::pow(x, y.real()), y.imag() * log(x))
return x > T() ? sprout::polar(sprout::pow(x, y.real()), y.imag() * sprout::log(x))
: sprout::pow(sprout::complex<T>(x), y)
;
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> sin(sprout::complex<T> const& x) {
using sprout::cos;
using sprout::sin;
using sprout::cosh;
using sprout::sinh;
return sprout::complex<T>(
sin(x.real()) * cosh(x.imag()),
cos(x.real()) * sinh(x.imag())
sprout::sin(x.real()) * sprout::cosh(x.imag()),
sprout::cos(x.real()) * sprout::sinh(x.imag())
);
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> sinh(sprout::complex<T> const& x) {
using sprout::cos;
using sprout::sin;
using sprout::cosh;
using sprout::sinh;
return sprout::complex<T>(
sinh(x.real()) * cos(x.imag()),
cosh(x.real()) * sin(x.imag())
sprout::sinh(x.real()) * sprout::cos(x.imag()),
sprout::cosh(x.real()) * sprout::sin(x.imag())
);
}
namespace detail {
@ -568,9 +539,8 @@ namespace sprout {
}
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> sqrt_impl_2_1(sprout::complex<T> const& x, T const& t, T const& u) {
using sprout::abs;
return x.real() > T() ? sprout::complex<T>(u, x.imag() / t)
: sprout::complex<T>(abs(x.imag()) / t, x.imag() < T() ? -u : u)
: sprout::complex<T>(sprout::abs(x.imag()) / t, x.imag() < T() ? -u : u)
;
}
template<typename T>
@ -580,10 +550,8 @@ namespace sprout {
} // namespace detail
template<typename T>
SPROUT_CONSTEXPR sprout::complex<T> sqrt(sprout::complex<T> const& x) {
using sprout::sqrt;
using sprout::abs;
return x.real() == T() ? sprout::detail::sqrt_impl_1(x, sqrt(abs(x.imag()) / 2))
: sprout::detail::sqrt_impl_2(x, sqrt(2 * (sprout::abs(x) + abs(x.real()))))
return x.real() == T() ? sprout::detail::sqrt_impl_1(x, sprout::sqrt(abs(x.imag()) / 2))
: sprout::detail::sqrt_impl_2(x, sprout::sqrt(2 * (sprout::abs(x) + sprout::abs(x.real()))))
;
}
template<typename T>