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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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> XSIMD_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