complex.h

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#pragma once

#include <cuComplex.h>
#include <cstdint>

#include "cutlass/cutlass.h"
#include "cutlass/half.h"
#include "cutlass/real.h"

#if !defined(__CUDACC_RTC__)
#include <iosfwd>
#endif

namespace cutlass {


enum class ComplexTransform {
  kNone,
  kConjugate
};


//
// Accessors for CUDA complex types
//

CUTLASS_HOST_DEVICE
float const &real(cuFloatComplex const &z) { return z.x; }

CUTLASS_HOST_DEVICE
float &real(cuFloatComplex &z) { return z.x; }

CUTLASS_HOST_DEVICE
double const &real(cuDoubleComplex const &z) { return z.x; }

CUTLASS_HOST_DEVICE
double &real(cuDoubleComplex &z) { return z.x; }

CUTLASS_HOST_DEVICE
float const &imag(cuFloatComplex const &z) { return z.y; }

CUTLASS_HOST_DEVICE
float &imag(cuFloatComplex &z) { return z.y; }

CUTLASS_HOST_DEVICE
double const &imag(cuDoubleComplex const &z) { return z.y; }

CUTLASS_HOST_DEVICE
double &imag(cuDoubleComplex &z) { return z.y; }



template <typename T>
class complex
{
 public:

 private:
  //
  // Data members
  //

  T _real;

  T _imag;

 public:

//
// Methods
//

  CUTLASS_HOST_DEVICE
  complex(T r = T(0)) : _real(r), _imag(T(0)) {}

  CUTLASS_HOST_DEVICE
  complex(T r, T i) : _real(r), _imag(i) {}
  //
  template<typename A>
  CUTLASS_HOST_DEVICE
  complex(complex<A> const &z) : _real(static_cast<T>(z.real())), _imag(static_cast<T>(z.imag())) {}

  CUTLASS_HOST_DEVICE
  complex(cuFloatComplex const &z) : _real(static_cast<T>(cuCrealf(z))), _imag(static_cast<T>(cuCimagf(z))) {}

  CUTLASS_HOST_DEVICE
  complex(cuDoubleComplex const &z) : _real(static_cast<T>(cuCreal(z))), _imag(static_cast<T>(cuCimag(z))) {}

  template<typename A>
  CUTLASS_HOST_DEVICE
  complex<T>& operator=(complex<A> const &z)
  {
    _real = static_cast<T>(z.real());
    _imag = static_cast<T>(z.imag());
    return *this;
  }

  CUTLASS_HOST_DEVICE bool operator==(complex<T> const &rhs) const {
    return this->real() == rhs.real() && this->imag() == rhs.imag();
  }

  CUTLASS_HOST_DEVICE bool operator!=(complex<T> const &rhs) const {
    return !(*this == rhs);
  }

    template <typename A>
  CUTLASS_HOST_DEVICE complex<T> operator+(complex<A> const &rhs) const {
    return complex<T>(this->real() + rhs.real(), this->imag() + rhs.imag());
  }

    template <typename A>
  CUTLASS_HOST_DEVICE complex<T> operator-(complex<A> const &rhs) const {
    return complex<T>(this->real() - rhs.real(), this->imag() - rhs.imag());
  }

    template <typename A>
  CUTLASS_HOST_DEVICE complex<T> operator*(complex<A> const &rhs) const {
    return complex<T>(this->real() * rhs.real() - this->imag() * rhs.imag(),
                      this->real() * rhs.imag() + this->imag() * rhs.real());
  }

    template <typename A>
  CUTLASS_HOST_DEVICE complex<T> operator*(A const &s) const {
    return complex<T>(this->real() * s, this->imag() * s);
  }

    template <typename A>
  CUTLASS_HOST_DEVICE complex<T> operator/(complex<A> const &rhs) const {
    T d = (rhs.real() * (rhs) + rhs.imag() * rhs.imag());

    return complex<T>((this->real() * (rhs) + this->imag() * rhs.imag()) / d,
                      (this->imag() * (rhs)-this->real() * rhs.imag()) / d);
  }

    template <typename A>
  CUTLASS_HOST_DEVICE complex<T> operator/(A const &s) const {
    return complex<T>(this->real() / s, this->imag() / s);
  }

    template <typename A>
  CUTLASS_HOST_DEVICE complex<T> &operator+=(complex<A> const &rhs) {
      *this = *this + rhs;
      return *this;
  }

  template <typename A>
  CUTLASS_HOST_DEVICE complex<T> &operator-=(complex<A> const &rhs) {
      *this = *this - rhs;
      return *this;
  }

  template <typename A>
  CUTLASS_HOST_DEVICE complex<T> &operator*=(complex<A> const &rhs) {
      *this = *this * rhs;
      return *this;
  }

  template <typename A>
  CUTLASS_HOST_DEVICE complex<T> &operator*=(A s) {
      *this = *this * s;
      return *this;
  }

  template <typename A>
  CUTLASS_HOST_DEVICE complex<T> &operator/=(complex<A> const &rhs) {
      *this = *this / rhs;
      return *this;
  }

  CUTLASS_HOST_DEVICE
  T const &real() const { return _real; }

  CUTLASS_HOST_DEVICE
  T &real() { return _real; }

  CUTLASS_HOST_DEVICE
  T const &imag() const { return _imag; }

  CUTLASS_HOST_DEVICE
  T &imag() { return _imag; }

  CUTLASS_HOST_DEVICE
  explicit operator cuFloatComplex() const { return make_cuFloatComplex(float(real()), float(imag())); }

  CUTLASS_HOST_DEVICE
  explicit operator cuDoubleComplex() const { return make_cuDoubleComplex(real(), imag()); }
};


//
// Accessors for complex template
//

template <typename T>
CUTLASS_HOST_DEVICE T const &real(complex<T> const &z) {
  return z.real();
}

template <typename T>
CUTLASS_HOST_DEVICE T &real(complex<T> &z) {
  return z.real();
}

template <typename T>
CUTLASS_HOST_DEVICE T const &imag(complex<T> const &z) {
  return z.imag();
}

template <typename T>
CUTLASS_HOST_DEVICE T &imag(complex<T> &z) {
  return z.imag();
}

//
// Output operators
//

#if !defined(__CUDACC_RTC__)
template <typename T>
std::ostream &operator<<(std::ostream &out, complex<T> const &z) {
  T _r = real(z);
  T _i = imag(z);

  if (bool(_i)) {
    return out << _r << "+i" << _i;
  }
  return out << _r;
}
#endif

//
// Non-member operators defined for complex types
//


//
// Non-member functions defined for complex numbers
//

template <typename T>
CUTLASS_HOST_DEVICE T abs(complex<T> const &z) {
  return sqrt(norm(z));
}

template <typename T>
CUTLASS_HOST_DEVICE T arg(complex<T> const &z) {
  return atan2(imag(z), real(z));
}

template <typename T>
CUTLASS_HOST_DEVICE T norm(T const &z) {
    return z * z;
}

template <>
CUTLASS_HOST_DEVICE int8_t norm(int8_t const &z) {
    return static_cast<int8_t>(z * z);
}

template <typename T>
CUTLASS_HOST_DEVICE double norm(complex<T> const &z) {
  return real(z) * real(z) + imag(z) * imag(z);
}

template <typename T, typename R>
CUTLASS_HOST_DEVICE R norm_accumulate(T const &x, R const & accumulator) {
  return accumulator + static_cast<R>(x) * static_cast<R>(x);
}

template <typename T, typename R>
CUTLASS_HOST_DEVICE R norm_accumulate(complex<T> const &z, R const &accumulator) {
  return accumulator + static_cast<R>(real(z)) * static_cast<R>(real(z)) + 
    static_cast<R>(imag(z)) * static_cast<R>(imag(z));
}

template <typename T>
CUTLASS_HOST_DEVICE complex<T> conj(complex<T> const &z) {
  return complex<T>(real(z), -imag(z));
}

template <typename T>
CUTLASS_HOST_DEVICE complex<T> proj(complex<T> const &z) {
  T d = real(z) * real(z) + imag(z) * imag(z) + T(1);
  return complex<T>((T(2) * real(z)) / d, (T(2) * imag(z)) / d);
}

template <typename T>
CUTLASS_HOST_DEVICE complex<T> polar(T const &r, T const &theta = T()) {
  return complex<T>(r * cos(theta), r * sin(theta));
}

template <typename T>
CUTLASS_HOST_DEVICE complex<T> exp(complex<T> const &z) {
  return complex<T>(real(z) * cos(imag(z)), real(z) * sin(imag(z)));
}

template <typename T>
CUTLASS_HOST_DEVICE complex<T> log(complex<T> const &z) {
  return complex<T>(log(abs(z)), arg(z));
}

template <typename T>
CUTLASS_HOST_DEVICE complex<T> log10(complex<T> const &z) {
  return log(z) / T(log(T(10)));
}

template <typename T>
CUTLASS_HOST_DEVICE complex<T> sqrt(complex<T> const &z) {
  return sqrt(T(2)) / T(2) *
         complex<T>(sqrt(sqrt(norm(z)) + real(z)),
                    (imag(z) < 0 ? T(-1) : T(1)) * sqrt(sqrt(norm(z)) - real(z)));
}

template <typename T>
CUTLASS_HOST_DEVICE complex<T> cos(complex<T> const &z) {
  return (exp(z) + exp(-z)) / T(2);
}

template <typename T>
CUTLASS_HOST_DEVICE complex<T> sin(complex<T> const &z) {
  return (exp(-z) - exp(z)) * complex<T>(T(0), T(1) / T(2));
}


template <typename T>
struct RealType< complex<T> > {
  using Type = T;
};


template <>
CUTLASS_HOST_DEVICE
cutlass::complex<half_t> from_real<cutlass::complex<half_t> >(double r) {
  return cutlass::complex<half_t>(half_t(r));
}

template <>
CUTLASS_HOST_DEVICE
cutlass::complex<float> from_real<cutlass::complex<float> >(double r) {
  return cutlass::complex<float>(float(r));
}

template <>
CUTLASS_HOST_DEVICE
cutlass::complex<double> from_real<cutlass::complex<double> >(double r) {
  return cutlass::complex<double>(r);
}


}  // namespace cutlass