simd_complex_batch

template <class X>

class xsimd::simd_complex_batch

Base class for batch complex numbers.

The simd_complex_batch class is the base class for all classes representing a batch of complex numbers. Each type of batch (i.e. a class inheriting from simd_complex_batch) has its dedicated type of boolean batch (i.e. a class inheriting from simd_complex_batch_bool) for logical operations.

Internally, a batch of complex numbers holds two batches of real numbers, one for the real part and one for the imaginary part.

See

simd_complex_batch_bool

Template Parameters

• X: The derived type

Inherits from xsimd::simd_base< X >

Arithmetic computed assignment

X &operator+=(const X &rhs)

Adds the batch rhs to this.

Return

a reference to this.

Parameters

• rhs: the batch to add.

X &operator+=(const value_type &rhs)

Adds the scalar rhs to each value contained in this.

Return

a reference to this.

Parameters

• rhs: the scalar to add.

X &operator+=(const real_batch &rhs)

Adds the real batch rhs to this.

Return

a reference to this.

Parameters

• rhs: the real batch to add.

X &operator+=(const real_value_type &rhs)

Adds the real scalar rhs to each value contained in this.

Return

a reference to this.

Parameters

• rhs: the real scalar to add.

X &operator-=(const X &rhs)

Substracts the batch rhs to this.

Return

a reference to this.

Parameters

• rhs: the batch to substract.

X &operator-=(const value_type &rhs)

Substracts the scalar rhs to each value contained in this.

Return

a reference to this.

Parameters

• rhs: the scalar to substract.

X &operator-=(const real_batch &rhs)

Substracts the real batch rhs to this.

Return

a reference to this.

Parameters

• rhs: the batch to substract.

X &operator-=(const real_value_type &rhs)

Substracts the real scalar rhs to each value contained in this.

Return

a reference to this.

Parameters

• rhs: the real scalar to substract.

X &operator*=(const X &rhs)

Multiplies this with the batch rhs.

Return

a reference to this.

Parameters

• rhs: the batch involved in the multiplication.

X &operator*=(const value_type &rhs)

Multiplies each scalar contained in this with the scalar rhs.

Return

a reference to this.

Parameters

• rhs: the scalar involved in the multiplication.

X &operator*=(const real_batch &rhs)

Multiplies this with the real batch rhs.

Return

a reference to this.

Parameters

• rhs: the real batch involved in the multiplication.

X &operator*=(const real_value_type &rhs)

Multiplies each scalar contained in this with the real scalar rhs.

Return

a reference to this.

Parameters

• rhs: the real scalar involved in the multiplication.

X &operator/=(const X &rhs)

Divides this by the batch rhs.

Return

a reference to this.

Parameters

• rhs: the batch involved in the division.

X &operator/=(const value_type &rhs)

Divides each scalar contained in this by the scalar rhs.

Return

a reference to this.

Parameters

• rhs: the scalar involved in the division.

X &operator/=(const real_batch &rhs)

Divides this by the real batch rhs.

Return

a reference to this.

Parameters

• rhs: the real batch involved in the division.

X &operator/=(const real_value_type &rhs)

Divides each scalar contained in this by the real scalar rhs.

Return

a reference to this.

Parameters

• rhs: the real scalar involved in the division.

Load and store methods

template <class T>

X &load_aligned(const T *real_src, const T *imag_src)

Loads the N contiguous values pointed by real_src into the batch holding the real values, and N contiguous values pointed by imag_src into the batch holding the imaginary values.

real_src and imag_src must be aligned.

template <class T>

X &load_unaligned(const T *real_src, const T *imag_src)

Loads the N contiguous values pointed by real_src into the batch holding the real values, and N contiguous values pointed by imag_src into the batch holding the imaginary values.

real_src and imag_src are not required to be aligned.

template <class T>

void store_aligned(T *real_dst, T *imag_dst) const

Stores the N values of the batch holding the real values into a contiguous array pointed by real_dst., and the N values of the batch holding the imaginary values into a contiguous array pointer by imag_dst.

real_dst and imag_dst must be aligned.

template <class T>

void store_unaligned(T *real_dst, T *imag_dst) const

Stores the N values of the batch holding the real values into a contiguous array pointed by real_dst., and the N values of the batch holding the imaginary values into a contiguous array pointer by imag_dst.

real_dst and imag_dst are not required to be aligned.

template <class T>

std::enable_if<detail::is_complex<T>::value, X&>::type load_aligned(const T *src)

Loads the N contiguous values pointed by src into the batch.

src must be aligned.

template <class T>

std::enable_if<detail::is_complex<T>::value, X&>::type load_unaligned(const T *src)

Loads the N contiguous values pointed by src into the batch.

src is not required to be aligned.

template <class T>

void store_aligned(T *dst) const

Stores the N values of the batch into a contiguous array pointed by dst.

dst must be aligned.

template <class T>

void store_unaligned(T *dst) const

Stores the N values of the batch into a contiguous array pointed by dst.

dst is not required to be aligned.

Public Functions

simd_complex_batch(const value_type &v)

Initializes all the values of the batch to the complex value v.

simd_complex_batch(const real_value_type &v)

Initializes all the values of the batch to the real value v.

simd_complex_batch(const real_batch &re)

Initializes the values of the batch whith those of the real batch re.

Imaginary parts are set to 0.

simd_complex_batch(const real_batch &re, const real_batch &im)

Initializes the batch with two real batch, one for the real part and one for the inamginary part.

auto real()

Returns a batch for the real part.

auto imag()

Returns a batch for the imaginary part.

auto real() const

Returns a const batch for the real part.

auto imag() const

Returns a const batch for the imaginary part.

Arithmetic operators

template <class X>

X xsimd::operator-(const simd_complex_batch<X> &rhs)

Computes the opposite of the batch rhs.

Return

the opposite of rhs.

Template Parameters

• X: the actual type of batch.

Parameters

• rhs: batch involved in the operation.

template <class X>

X xsimd::operator+(const simd_complex_batch<X> &lhs, const simd_complex_batch<X> &rhs)

Computes the sum of the batches lhs and rhs.

Return

the result of the addition.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the addition.

• rhs: batch involved in the addition.

template <class X>

X xsimd::operator+(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::value_type &rhs)

Computes the sum of the batch lhs and the scalar rhs.

Equivalent to the sum of two batches where all the values of the second one are initialized to rhs.

Return

the result of the addition.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the addition.

• rhs: scalar involved in the addition.

template <class X>

X xsimd::operator+(const typename simd_batch_traits<X>::value_type &lhs, const simd_complex_batch<X> &rhs)

Computes the sum of the scalar lhs and the batch rhs.

Equivalent to the sum of two batches where all the values of the first one are initialized to rhs.

Return

the result of the addition.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: scalar involved in the addition.

• rhs: batch involved in the addition.

template <class X>

X xsimd::operator+(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::real_batch &rhs)

Computes the sum of the batches lhs and rhs.

Return

the result of the addition.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the addition.

• rhs: real batch involved in the addition.

template <class X>

X xsimd::operator+(const typename simd_batch_traits<X>::real_batch &lhs, const simd_complex_batch<X> &rhs)

Computes the sum of the batches lhs and rhs.

Return

the result of the addition.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: real batch involved in the addition.

• rhs: batch involved in the addition.

template <class X>

X xsimd::operator+(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::real_value_type &rhs)

Computes the sum of the batch lhs and the real scalar rhs.

Equivalent to the sum of two batches where all the values of the second one are initialized to rhs.

Return

the result of the addition.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the addition.

• rhs: real scalar involved in the addition.

template <class X>

X xsimd::operator+(const typename simd_batch_traits<X>::real_value_type &lhs, const simd_complex_batch<X> &rhs)

Computes the sum of the real scalar lhs and the batch rhs.

Equivalent to the sum of two batches where all the values of the first one are initialized to rhs.

Return

the result of the addition.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: real scalar involved in the addition.

• rhs: batch involved in the addition.

template <class X>

X xsimd::operator-(const simd_complex_batch<X> &lhs, const simd_complex_batch<X> &rhs)

Computes the difference of the batches lhs and rhs.

Return

the result of the difference.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the difference.

• rhs: batch involved in the difference.

template <class X>

X xsimd::operator-(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::value_type &rhs)

Computes the difference of the batch lhs and the scalar rhs.

Equivalent to the difference of two batches where all the values of the second one are initialized to rhs.

Return

the result of the difference.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the difference.

• rhs: scalar involved in the difference.

template <class X>

X xsimd::operator-(const typename simd_batch_traits<X>::value_type &lhs, const simd_complex_batch<X> &rhs)

Computes the difference of the scalar lhs and the batch rhs.

Equivalent to the difference of two batches where all the values of the first one are initialized to rhs.

Return

the result of the difference.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: scalar involved in the difference.

• rhs: batch involved in the difference.

template <class X>

X xsimd::operator-(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::real_batch &rhs)

Computes the difference of the batches lhs and rhs.

Return

the result of the difference.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the difference.

• rhs: real batch involved in the difference.

template <class X>

X xsimd::operator-(const typename simd_batch_traits<X>::real_batch &lhs, const simd_complex_batch<X> &rhs)

Computes the difference of the batches lhs and rhs.

Return

the result of the difference.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: real batch involved in the difference.

• rhs: batch involved in the difference.

template <class X>

X xsimd::operator-(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::real_value_type &rhs)

Computes the difference of the batch lhs and the real scalar rhs.

Equivalent to the difference of two batches where all the values of the second one are initialized to rhs.

Return

the result of the difference.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the difference.

• rhs: real scalar involved in the difference.

template <class X>

X xsimd::operator-(const typename simd_batch_traits<X>::real_value_type &lhs, const simd_complex_batch<X> &rhs)

Computes the difference of the real scalar lhs and the batch rhs.

Equivalent to the difference of two batches where all the values of the first one are initialized to rhs.

Return

the result of the difference.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: real scalar involved in the difference.

• rhs: batch involved in the difference.

template <class X>

X xsimd::operator*(const simd_complex_batch<X> &lhs, const simd_complex_batch<X> &rhs)

Computes the product of the batches lhs and rhs.

Return

the result of the product.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the product.

• rhs: batch involved in the product.

template <class X>

X xsimd::operator*(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::value_type &rhs)

Computes the product of the batch lhs and the scalar rhs.

Equivalent to the product of two batches where all the values of the second one are initialized to rhs.

Return

the result of the product.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the product.

• rhs: scalar involved in the product.

template <class X>

X xsimd::operator*(const typename simd_batch_traits<X>::value_type &lhs, const simd_complex_batch<X> &rhs)

Computes the product of the scalar lhs and the batch rhs.

Equivalent to the difference of two batches where all the values of the first one are initialized to rhs.

Return

the result of the product.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: scalar involved in the product.

• rhs: batch involved in the product.

template <class X>

X xsimd::operator*(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::real_batch &rhs)

Computes the product of the batches lhs and rhs.

Return

the result of the product.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the product.

• rhs: real batch involved in the product.

template <class X>

X xsimd::operator*(const typename simd_batch_traits<X>::real_batch &lhs, const simd_complex_batch<X> &rhs)

Computes the product of the batches lhs and rhs.

Return

the result of the product.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: real batch involved in the product.

• rhs: batch involved in the product.

template <class X>

X xsimd::operator*(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::real_value_type &rhs)

Computes the product of the batch lhs and the real scalar rhs.

Equivalent to the product of two batches where all the values of the second one are initialized to rhs.

Return

the result of the product.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the product.

• rhs: real scalar involved in the product.

template <class X>

X xsimd::operator*(const typename simd_batch_traits<X>::real_value_type &lhs, const simd_complex_batch<X> &rhs)

Computes the product of the real scalar lhs and the batch rhs.

Equivalent to the difference of two batches where all the values of the first one are initialized to rhs.

Return

the result of the product.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: real scalar involved in the product.

• rhs: batch involved in the product.

template <class X>

X xsimd::operator/(const simd_complex_batch<X> &lhs, const simd_complex_batch<X> &rhs)

Computes the division of the batch lhs by the batch rhs.

Return

the result of the division.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the division.

• rhs: batch involved in the division.

template <class X>

X xsimd::operator/(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::value_type &rhs)

Computes the division of the batch lhs by the scalar rhs.

Equivalent to the division of two batches where all the values of the second one are initialized to rhs.

Return

the result of the division.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the division.

• rhs: scalar involved in the division.

template <class X>

X xsimd::operator/(const typename simd_batch_traits<X>::value_type &lhs, const simd_complex_batch<X> &rhs)

Computes the division of the scalar lhs and the batch rhs.

Equivalent to the difference of two batches where all the values of the first one are initialized to rhs.

Return

the result of the division.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: scalar involved in the division.

• rhs: batch involved in the division.

template <class X>

X xsimd::operator/(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::real_batch &rhs)

Computes the division of the batch lhs by the batch rhs.

Return

the result of the division.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the division.

• rhs: real batch involved in the division.

template <class X>

X xsimd::operator/(const typename simd_batch_traits<X>::real_batch &lhs, const simd_complex_batch<X> &rhs)

Computes the division of the batch lhs by the batch rhs.

Return

the result of the division.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: real batch involved in the division.

• rhs: batch involved in the division.

template <class X>

X xsimd::operator/(const simd_complex_batch<X> &lhs, const typename simd_batch_traits<X>::real_value_type &rhs)

Computes the division of the batch lhs by the real scalar rhs.

Equivalent to the division of two batches where all the values of the second one are initialized to rhs.

Return

the result of the division.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: batch involved in the division.

• rhs: real scalar involved in the division.

template <class X>

X xsimd::operator/(const typename simd_batch_traits<X>::real_value_type &lhs, const simd_complex_batch<X> &rhs)

Computes the division of the real scalar lhs and the batch rhs.

Equivalent to the difference of two batches where all the values of the first one are initialized to rhs.

Return

the result of the division.

Template Parameters

• X: the actual type of batch.

Parameters

• lhs: real scalar involved in the division.

• rhs: batch involved in the division.

template <class X>

simd_batch_traits<X>::value_type xsimd::hadd(const simd_complex_batch<X> &rhs)

Adds all the scalars of the batch rhs.

Return

the result of the reduction.

Parameters

• rhs: batch involved in the reduction

template <class X>

X xsimd::select(const typename simd_batch_traits<X>::batch_bool_type &cond, const simd_complex_batch<X> &a, const simd_complex_batch<X> &b)

Ternary operator for batches: selects values from the batches a or b depending on the boolean values in cond.

Equivalent to

for(std::size_t i = 0; i < N; ++i)
    res[i] = cond[i] ? a[i] : b[i];

Return

the result of the selection.

Parameters

• cond: batch condition.

• a: batch values for truthy condition.

• b: batch value for falsy condition.

template <class X>

simd_batch_traits<X>::batch_bool_type xsimd::operator==(const simd_complex_batch<X> &lhs, const simd_complex_batch<X> &rhs)

Element-wise equality comparison of batches lhs and rhs.

Return

a boolean batch.

Parameters

• lhs: batch involved in the comparison.

• rhs: batch involved in the comparison.

template <class X>

simd_batch_traits<X>::batch_bool_type xsimd::operator!=(const simd_complex_batch<X> &lhs, const simd_complex_batch<X> &rhs)

Element-wise inequality comparison of batches lhs and rhs.

Return

a boolean batch.

Parameters

• lhs: batch involved in the comparison.

• rhs: batch involved in the comparison.

template <class X>

std::ostream &xsimd::operator<<(std::ostream &out, const simd_complex_batch<X> &rhs)

Insert the batch rhs into the stream out.

Return

the output stream.

Template Parameters

• X: the actual type of batch.

Parameters

• out: the output stream.

• rhs: the batch to output.

Comparison operators

template <class X>

simd_batch_traits<X>::batch_bool_type xsimd::operator==(const simd_complex_batch<X> &lhs, const simd_complex_batch<X> &rhs)

Element-wise equality comparison of batches lhs and rhs.

Return

a boolean batch.

Parameters

• lhs: batch involved in the comparison.

• rhs: batch involved in the comparison.

template <class X>

simd_batch_traits<X>::batch_bool_type xsimd::operator!=(const simd_complex_batch<X> &lhs, const simd_complex_batch<X> &rhs)

Element-wise inequality comparison of batches lhs and rhs.

Return

a boolean batch.

Parameters

• lhs: batch involved in the comparison.

• rhs: batch involved in the comparison.

Reducers

template <class X>

simd_batch_traits<X>::value_type xsimd::hadd(const simd_complex_batch<X> &rhs)

Adds all the scalars of the batch rhs.

Return

the result of the reduction.

Parameters

• rhs: batch involved in the reduction

Miscellaneous

template <class X>

X xsimd::select(const typename simd_batch_traits<X>::batch_bool_type &cond, const simd_complex_batch<X> &a, const simd_complex_batch<X> &b)

Ternary operator for batches: selects values from the batches a or b depending on the boolean values in cond.

Equivalent to

for(std::size_t i = 0; i < N; ++i)
    res[i] = cond[i] ? a[i] : b[i];

Return

the result of the selection.

Parameters

• cond: batch condition.

• a: batch values for truthy condition.

• b: batch value for falsy condition.

Other operators

template <class X>

std::ostream &xsimd::operator<<(std::ostream &out, const simd_complex_batch<X> &rhs)

Insert the batch rhs into the stream out.

Return

the output stream.

Template Parameters

• X: the actual type of batch.

Parameters

• out: the output stream.

• rhs: the batch to output.