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newton-riemann/src/dual.cu
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/* | |
Class for dual numbers. | |
Dual numbers exhibit the following property for any analytic function f: | |
f(dual(x, 1)) = dual(f(x), f'(x)) | |
This makes them useful for calculating the value and derivative of a function. | |
*/ | |
template <typename T> | |
class dual { | |
public: | |
T a, b; | |
typedef T value_type; | |
inline __host__ __device__ | |
dual(const T & _a = T(), const T & _b = T()) { | |
a = _a; | |
b = _b; | |
} | |
inline __host__ __device__ | |
dual<T> operator+(const dual<T> that) const { | |
dual<T> out; | |
out.a = a + that.a; | |
out.b = b + that.b; | |
return out; | |
} | |
inline __host__ __device__ | |
dual<T> operator-() const { | |
dual<T> out; | |
out.a = -a; | |
out.b = -b; | |
return out; | |
} | |
inline __host__ __device__ | |
dual<T> operator-(const dual<T> that) const { | |
return operator+(-that); | |
} | |
inline __host__ __device__ | |
dual<T> operator*(const dual<T> that) const { | |
dual<T> out; | |
out.a = a * that.a; | |
out.b = a * that.b + b * that.a; | |
return out; | |
} | |
inline __host__ __device__ | |
dual<T> inverse() const { | |
dual<T> out; | |
out.a = T(1)/a; | |
out.b = -b / (a*a); | |
return out; | |
} | |
inline __host__ __device__ | |
dual<T> operator/(const dual<T> that) const { | |
return operator*(that.inverse()); | |
} | |
}; | |
template <typename T> | |
inline __host__ __device__ | |
dual<T> dpow(dual<T> a, dual<T> b) { | |
T one = T(1); | |
T zero = T(); | |
dual<T> out; | |
out.a = thrust::pow(a.a, b.a); | |
out.b = b.a * a.b * thrust::pow(a.a, b.a-one); | |
if (b.b != zero) out.b += b.b * out.a * thrust::log(a.a); | |
return out; | |
} | |
template <typename T> | |
inline __host__ __device__ | |
dual<T> dpown(dual<T> a, unsigned int n) { | |
if (n == 0) return T(1); | |
if (n == 1) return a; | |
if (n % 2 == 0) return dpown(a*a, n / 2); | |
return a * dpown(a*a, (n-1) / 2); | |
} | |
template <typename T> | |
inline __host__ __device__ | |
dual<T> dlog(dual<T> x) { | |
dual<T> out; | |
out.a = thrust::log(x.a); | |
out.b = x.b / x.a; | |
return out; | |
} | |
template <typename T> | |
inline __host__ __device__ | |
dual<T> dexp(dual<T> x) { | |
dual<T> out; | |
out.a = thrust::exp(x.a); | |
out.b = x.b * out.a; | |
return out; | |
} | |
template <typename T> | |
inline __host__ __device__ | |
dual<T> dsin(dual<T> x) { | |
dual<T> out; | |
out.a = thrust::sin(x.a); | |
out.b = x.b * thrust::cos(x.a); | |
return out; | |
} | |
template <typename T> | |
inline __host__ __device__ | |
dual<T> dcos(dual<T> x) { | |
dual<T> out; | |
out.a = thrust::cos(x.a); | |
out.b = -x.b * thrust::sin(x.a); | |
return out; | |
} | |
template <typename T> | |
inline __host__ __device__ | |
dual<T> dtan(dual<T> x) { | |
T one = T(1); | |
T two = T(2); | |
dual<T> out; | |
out.a = thrust::tan(x.a); | |
out.b = x.b * two / (cos(two*x.a)+one); | |
return out; | |
} | |