Arithmetic operators

Binary operations:

add()

per slot addition

sub()

per slot subtraction

mul()

per slot multiply

div()

per slot division

mod()

per slot modulo

Unary operations:

neg()

per slot negate

pos()

per slot positive

reciprocal()

per slot reciprocal

decr()

per slot decrement

decr_if()

per slot decrement, based on a mask

incr()

per slot increment

incr_if()

per slot increment, based on a mask

Saturated arithmetic:

sadd()

per slot saturated addition

ssub()

per slot saturated subtraction

Fused operations:

fma()

fused multiply add

fms()

fused multiply sub

fnma()

fused negate multiply add

fnms()

fused negate multiply sub

Average computation:

avg()

per slot average

avgr()

per slot rounded average
template<class T, class A>
inline auto add(batch<T, A> const &x, batch<T, A> const &y) noexcept -> decltype(x + y)

Computes the sum of the batches x and y.

Parameters:

  • x – batch or scalar involved in the addition.

  • y – batch or scalar involved in the addition.

Returns:

the sum of x and y

template<class T, class A>
inline batch<T, A> decr(batch<T, A> const &x) noexcept

Subtract 1 to batch x.

Parameters:

x – batch involved in the decrement.

Returns:

the subtraction of x and 1.

template<class T, class A, class Mask>
inline batch<T, A> decr_if(batch<T, A> const &x, Mask const &mask) noexcept

Subtract 1 to batch x for each element where mask is true.

Parameters:

  • x – batch involved in the increment.

  • mask – whether to perform the increment or not. Can be a batch_bool or a batch_bool_constant.

Returns:

the subtraction of x and 1 when mask is true.

template<class T, class A>
inline auto div(batch<T, A> const &x, batch<T, A> const &y) noexcept -> decltype(x / y)

Computes the division of the batch x by the batch y.

Parameters:

  • x – scalar or batch of scalars

  • y – scalar or batch of scalars

Returns:

the result of the division.

template<class T, class A>
inline batch<T, A> fma(batch<T, A> const &x, batch<T, A> const &y, batch<T, A> const &z) noexcept

Computes (x*y) + z in a single instruction when possible.

Parameters:

  • x – a batch of integer or floating point values.

  • y – a batch of integer or floating point values.

  • z – a batch of integer or floating point values.

Returns:

the result of the fused multiply-add operation.

template<class T, class A>
inline batch<T, A> fms(batch<T, A> const &x, batch<T, A> const &y, batch<T, A> const &z) noexcept

Computes (x*y) - z in a single instruction when possible.

Parameters:

  • x – a batch of integer or floating point values.

  • y – a batch of integer or floating point values.

  • z – a batch of integer or floating point values.

Returns:

the result of the fused multiply-sub operation.

template<class T, class A>
inline batch<T, A> fnma(batch<T, A> const &x, batch<T, A> const &y, batch<T, A> const &z) noexcept

Computes -(x*y) + z in a single instruction when possible.

Parameters:

  • x – a batch of integer or floating point values.

  • y – a batch of integer or floating point values.

  • z – a batch of integer or floating point values.

Returns:

the result of the fused negated multiply-add operation.

template<class T, class A>
inline batch<T, A> fnms(batch<T, A> const &x, batch<T, A> const &y, batch<T, A> const &z) noexcept

Computes -(x*y) - z in a single instruction when possible.

Parameters:

  • x – a batch of integer or floating point values.

  • y – a batch of integer or floating point values.

  • z – a batch of integer or floating point values.

Returns:

the result of the fused negated multiply-sub operation.

template<class T, class A>
inline batch<T, A> incr(batch<T, A> const &x) noexcept

Add 1 to batch x.

Parameters:

x – batch involved in the increment.

Returns:

the sum of x and 1.

template<class T, class A, class Mask>
inline batch<T, A> incr_if(batch<T, A> const &x, Mask const &mask) noexcept

Add 1 to batch x for each element where mask is true.

Parameters:

  • x – batch involved in the increment.

  • mask – whether to perform the increment or not. Can be a batch_bool or a batch_bool_constant.

Returns:

the sum of x and 1 when mask is true.

template<class T, class A>
inline auto mod(batch<T, A> const &x, batch<T, A> const &y) noexcept -> decltype(x % y)

Computes the integer modulo of the batch x by the batch y.

Parameters:

  • x – batch involved in the modulo.

  • y – batch involved in the modulo.

Returns:

the result of the modulo.

template<class T, class A>
inline auto mul(batch<T, A> const &x, batch<T, A> const &y) noexcept -> decltype(x * y)

Computes the product of the batches x and y.

Template Parameters:

X – the actual type of batch.

Parameters:

  • x – batch involved in the product.

  • y – batch involved in the product.

Returns:

the result of the product.

template<class T, class A>
inline batch<T, A> neg(batch<T, A> const &x) noexcept

Computes the opposite of the batch x.

Parameters:

x – batch involved in the operation.

Returns:

the opposite of x.

template<class T, class A>
inline batch<T, A> pos(batch<T, A> const &x) noexcept

No-op on x.

Parameters:

x – batch involved in the operation.

Returns:

x.

template<class T, class A, class = typename std::enable_if<std::is_floating_point<T>::value, void>::type>
inline batch<T, A> reciprocal(batch<T, A> const &x) noexcept

Computes the approximate reciprocal of the batch x.

The maximum relative error for this approximation is less than 1.5*2^-12.

Parameters:

x – batch of floating point numbers.

Returns:

the reciprocal.

template<class T, class A>
inline batch<T, A> sadd(batch<T, A> const &x, batch<T, A> const &y) noexcept

Computes the saturate sum of the batch x and the batch y.

Template Parameters:

X – the actual type of batch.

Parameters:

  • x – batch involved in the saturated addition.

  • y – batch involved in the saturated addition.

Returns:

the result of the saturated addition.

template<class T, class A>
inline batch<T, A> ssub(batch<T, A> const &x, batch<T, A> const &y) noexcept

Computes the saturate difference of the batch x and the batch y.

Template Parameters:

X – the actual type of batch.

Parameters:

  • x – batch involved in the saturated difference.

  • y – batch involved in the saturated difference.

Returns:

the result of the saturated difference.

template<class T, class A>
inline auto sub(batch<T, A> const &x, batch<T, A> const &y) noexcept -> decltype(x - y)

Computes the difference between x and y.

Template Parameters:

X – the actual type of batch.

Parameters:

  • x – scalar or batch of scalars

  • y – scalar or batch of scalars

Returns:

the difference between x and y