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{*AI12-0242-1*}
{*AI12-0262-1*}
Reduction expressions
provide a way to map or transform a collection of values into a new set
of values, and then summarize the values produced by applying an operation
to reduce the set to a single value result. A reduction expression is
represented as an attribute_reference
of the reduction attributes Reduce or Parallel_Reduce.

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{*AI12-0262-1*}
reduction_attribute_reference ::=

value_sequence'reduction_attribute_designator

| prefix'reduction_attribute_designator

value_sequence'reduction_attribute_designator

| prefix'reduction_attribute_designator

{*AI12-0262-1*}
value_sequence ::=

'[' [**parallel**[(chunk_specification)]] iterated_element_association ']'

'[' [

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{*AI12-0262-1*}
The iterated_element_association
of a value_sequence
shall not have a *key_*expression,
nor shall it have a loop_parameter_specification
that has the reserved word **reverse**.

{*AI12-0262-1*}
The chunk_specification,
if any, of a value_sequence
shall be an *integer_*simple_expression.

{*AI12-0262-1*}
The expected type for a reduction_attribute_reference
shall be a single nonlimited type.

{*AI12-0262-1*}
In the remainder of this subclause, we will refer
to nonlimited subtypes *Value_Type* and *Accum_Type* of a reduction_attribute_reference.
These subtypes and interpretations of the names
and expressions
of a reduction_attribute_reference
are determined by the following rules:

{*AI12-0262-1*}
*Accum_Type* is a subtype of the expected
type of the reduction_attribute_reference.

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A *reducer subprogram*
is either subtype conformant with the following specification:

or
is subtype conformant with the following specification:

{*AI12-0262-1*}
A *combiner subprogram*
is a reducer subprogram where the Value parameter is of subtype *Accum_Type*
rather than subtype *Value_Type*.

{*AI12-0262-1*}
The *reducer_*name
of a reduction_specification
denotes a reducer subprogram.

{*AI12-0262-1*}
The *combiner_*name,
if any, of a reduction_specification
denotes a combiner subprogram.

{*AI12-0262-1*}
The expected type of an *initial_value_*expression
of a reduction_specification
is that of subtype *Accum_Type*.

{*AI12-0250-1*}
{*AI12-0262-1*}
The expected type of the expression
of the iterated_element_association
of a value_sequence
is that of subtype *Value_Type*.

{*AI12-0262-1*}
The *combiner_*name
of a reduction_specification
shall be specified if the subtypes of the parameters of the subprogram
denoted by the *reducer_*name
of the reduction_specification
do not statically match each other and the reduction_attribute_reference
has a value_sequence
with the reserved word **parallel**.

{*AI12-0262-1*}
If the identifier
of a reduction_attribute_designator
is Parallel_Reduce then the *combiner_*name
of the reduction_specification
shall be specified if the subtypes of all the parameters of the subprogram
denoted by the *reducer_*name
of the reduction_specification
do not statically match.

{*AI12-0262-1*}
A reduction_attribute_reference
denotes a value, with nominal subtype being the subtype of the first
parameter of the subprogram denoted by the *reducer_*name.

{*AI12-0262-1*}
For a reduction_attribute_reference
that has a value_sequence
with the reserved word **parallel**, if the *combiner_*name
is not specified, then the subprogram denoted by the *reducer_*name
also implicitly denotes the combiner subprogram.

{*AI12-0262-1*}
For a reduction_attribute_reference
where the identifier
of the reduction_attribute_designator
is Parallel_Reduce, if the *combiner_*name
is not specified, then the subprogram denoted by the *reducer_*name
also implicitly denotes the combiner subprogram.

{*AI12-0250-1*}
{*AI12-0262-1*}
{*AI12-0327-1*}
For the evaluation of a value_sequence,
the iterated_element_association
is elaborated, then an iteration is performed, and for each value conditionally
produced by the iteration (see 5.5 and 5.5.2),
the associated expression
is evaluated with the loop parameter having this value, to produce a
result that is converted to Value_Type, and used to define the next value
in the sequence.

{*AI12-0262-1*}
If the value_sequence
does not have the reserved word **parallel**, it is produced as a
single sequence of values by a single logical thread of control. If the
reserved word **parallel** is present in the value_sequence,
the enclosing reduction_attribute_reference
is a parallel construct, and the sequence of values is generated by a
parallel iteration (as defined in 5.5, 5.5.1,
and 5.5.2), as a set of non-empty, non-overlapping
contiguous chunks (*subsequences*) with one
logical thread of control (see clause 9) associated
with each subsequence. If there is a chunk_specification,
it determines the maximum number of chunks, as defined in 5.5;
otherwise the maximum number of chunks is implementation defined.

{*AI12-0262-1*}
For a value_sequence
V, the following attribute is defined:

V'Reduce(Reducer,
Initial_Value[, Combiner])

{

{*AI12-0262-1*}
The evaluation of a use of
this attribute begins by evaluating the parts of the reduction_attribute_designator
(the *reducer_*name
Reducer, the *initial_value_*expression
Initial_Value, and the *combiner_*name
Combiner, if any), in an arbitrary order. It then
initializes the *accumulator* of the reduction expression to the
value of the *initial_value_*expression
(the *initial value*).
The value_sequence
V is then evaluated.

{*AI12-0262-1*}
If the value_sequence
does not have the reserved word **parallel**, each value of the value_sequence
is passed, in order, as the second (Value) parameter to a call on Reducer,
with the first (Accumulator) parameter being the prior value of the accumulator,
saving the result as the new value of the accumulator. The reduction
expression yields the final value of the accumulator. Combiner, if specified,
is ignored for such a (sequential) reduction expression.

{*AI12-0262-1*}
If the reserved word **parallel** is present
in a value_sequence,
then the (parallel) reduction expression is a parallel construct and
the sequence has been partitioned into one or more subsequences (see
above) each with its own separate logical thread of control.

{*AI12-0262-1*}
Each logical thread of control creates a local
accumulator for processing its subsequence. If there is a separate Combiner
subprogram specified, then the accumulator for each subsequence is initialized
to the initial value, and Reducer is called in sequence order with each
value of the subsequence as the second (Value) parameter, and with this
local accumulator as the first (Accumulator) parameter, saving the result
back into this local accumulator. If there is no separate combiner specified,
then the accumulator for a subsequence is initialized to the first value
of the subsequence, and calls on Reducer start with the second value
of the subsequence (if any). In either case, the result for the subsequence
is the final value of its local accumulator.

{*AI12-0262-1*}
After all logical threads of control of a parallel
reduction expression have completed, Combiner (or Reducer, if Combiner
is not specified) is called for each subsequence, in the original sequence
order, passing the local accumulator for that subsequence as the second
(Value) parameter, and the overall accumulator [(initialized above to
the initial value)] as the first (Accumulator) parameter, with the result
saved back in the overall accumulator. The parallel reduction expression
yields the final value of the overall accumulator.

{*AI12-0262-1*}
If the evaluation of the value_sequence
yields an empty sequence of values, the reduction expression yields the
initial value.

{*AI12-0262-1*}
If an exception is propagated by one of the calls
on Reducer or Combiner, that exception is propagated from the reduction
expression. If different exceptions are propagated in different logical
threads of control, one is chosen arbitrarily to be propagated from the
reduction expression as a whole.

{*AI12-0242-1*}
For a prefix
X of an array type[ (after any implicit dereference)], or that denotes
an iterable container object (see 5.5.1),
the following attributes are defined:

X'Reduce(Reducer,
Initial_Value[, Combiner])

{

[**for** Item **of** X => Item]

X'Parallel_Reduce(Reducer,
Initial_Value[, Combiner])

{

[**parallel for** Item **of** X => Item]

{*AI12-0262-1*}
If a parallel reduction expression
has a combiner subprogram specified, then it is a bounded error if the
initial value is not the (left) identity of the combiner subprogram.
That is, the result of calling the combiner subprogram with the Accumulator
being the initial value and the Value being any arbitrary value of subtype
*Accum_Type* should produce a result equal to the Value parameter.
The possible consequences are Program_Error, or a result that does not
match the equivalent sequential reduction expression due to multiple
uses of the non-identity initial value in the overall reduction.

{*AI12-0262-1*}
An expression function that returns its result
as a Reduction Expression:

([

{*AI12-0262-1*}
An expression function that computes the Sin of
X using Taylor expansion:

([

'Reduce("+", 0.0));

{*AI12-0262-1*}
A reduction expression that outputs the sum of
squares:

Put_Line ("Sum of Squares is" &

Integer'Image([**for** I **in** 1 .. 10 => I**2]'Reduce("+", 0));

Integer'Image([

{*AI12-0262-1*}
An expression function to compute the value of
Pi:

-- *See 3.5.7.*

**function** Pi (Number_Of_Steps : Natural := 10_000) **return** Real **is**

(1.0 / Number_Of_Steps *

[**for** I **in** 1 .. Number_Of_Steps =>

(4.0 / (1.0 + ((Real (I) - 0.5) * (1.0 / Number_Of_Steps))**2))]

'Reduce("+", 0.0));

(1.0 / Number_Of_Steps *

[

(4.0 / (1.0 + ((Real (I) - 0.5) * (1.0 / Number_Of_Steps))**2))]

'Reduce("+", 0.0));

{*AI12-0242-1*}
Calculate the sum of elements of an array of integers:

A'Reduce("+",0) -- *See 4.3.3.*

{*AI12-0242-1*}
Determine if all elements in a two dimensional
array of booleans are set to true:

Grid'Reduce("and", True) -- *See 3.6.*

{*AI12-0242-1*}
Calculate the minimum value of an array of integers
in parallel:

A'Parallel_Reduce(Integer'Min, Integer'Last)

{*AI12-0262-1*}
Reduction expressions attributes
are new.

Ada 2005 and 2012 Editions sponsored in part by **Ada-Europe**