
<!-- common text for workgroup functions, section 6.13.15 -->

    <para>
        This built-in function must be encountered by 
        all work-items in a 
        work-group executing the kernel. We use the 
        generic type name gentype to indicate the 
        built-in data types <type>half</type> (if the
        <citerefentry><refentrytitle>cl_khr_fp16</refentrytitle></citerefentry>
        extension is supported),
        <type>int</type>, <type>uint</type>, <type>long</type>, 
        <type>ulong</type>, <type>float</type> or <type>double</type> 
        (if double precision is supported) as the type 
        for the arguments.
    </para>

    <para>
        The <emphasis>&lt;op></emphasis> in 
        <function>work_group_reduce_<emphasis>&lt;op></emphasis></function>, 
        <function>work_group_scan_exclusive_<emphasis>&lt;op></emphasis></function> and 
        <function>work_group_scan_inclusive_<emphasis>&lt;op></emphasis></function> 
        defines the operator and can be <code>add</code>, <code>min</code> or <code>max</code>.
    </para>

    <para>
        The inclusive scan operation takes a binary operator <code>op</code> 
        with an identity <code>I</code> and <code>n</code> (where 
        <code>n</code> is the size of the work-group) elements 
        <code>[a0, a1, ... an-1]</code> and returns 
        <code>[a0, (a0 <emphasis>op</emphasis> a1), ... (a0 <emphasis>op</emphasis> a1 
        <emphasis>op</emphasis> ... <emphasis>op</emphasis> an-1)]</code>. 
        If &lt;<code>op</code>&gt; = <code>add</code>, the identity 
        <code>I</code> is 0. If &lt;<code>op</code>&gt; = <code>min</code>, 
        the identity <code>I</code> is <constant>INT_MAX</constant>, 
        <constant>UINT_MAX</constant>, <constant>LONG_MAX</constant>, 
        <constant>ULONG_MAX</constant>, for <type>int</type>, 
        <type>uint</type>, <type>long</type>, <type>ulong</type> types 
        and is <code>+INF</code> for floating-point types. Similarly 
        if &lt;<code>op</code>&gt; = max, the identity <code>I</code> is 
        <constant>INT_MIN</constant>, 0, <constant>LONG_MIN</constant>, 
        0 and <code>-INF</code>.
    </para>

    <para>
        Consider the following example:
    </para>

    <para>
<literallayout><code>
void foo(int *p)
{
    ... 
    int prefix_sum_val = work_group_scan_inclusive_add(
              p[get_local_id(0)]);
}</code></literallayout>
    </para>

    <para>
        For the example above, let's assume that the work-group 
        size is 8 and p points to the following 
        elements [3 1 7 0 4 1 6 3]. Work-item 0 calls 
        <function>work_group_scan_inclusive_add</function> 
        with 3 and returns 3. Work-item 1 calls 
        <function>work_group_scan_inclusive_add</function> with 1 and 
        returns 4. The full set of values returned by 
        <function>work_group_scan_inclusive_add</function> 
        for work-items 0 ... 7 are [3 4 11 11 14 16 22 25].
    </para>

    <para>
        The exclusive scan operation takes a binary 
        associative operator <varname>op</varname> with an 
        identity <code>I</code> and <code>n</code>
        (where <code>n</code> is the size of the work-group) 
        elements <code>[a0, a1, ... an-1]</code> and returns <code>[I, a0, 
        (a0 <emphasis>op</emphasis> a1), ... (a0 <emphasis>op</emphasis> a1 
        <emphasis>op</emphasis> ... <emphasis>op</emphasis> an-2)]</code>. For the 
        example above, the exclusive scan 
        add operation on the ordered set [3 1 7 0 4 1 6 3]
        would return [0 3 4 11 11 14 16 22].
    </para>

    <para>
        NOTE: The order of floating-point operations is not guaranteed for the
        <function>work_group_reduce_<emphasis>&lt;op></emphasis></function>, 
        <function>work_group_scan_inclusive_<emphasis>&lt;op></emphasis></function> and 
        <function>work_group_scan_exclusive_<emphasis>&lt;op></emphasis></function> 
        built-in functions that operate on <type>half</type>, <type>float</type> and 
        <type>double</type> data types.
        The order of these floating-point operations is also non-deterministic 
        for a given workgroup.
    </para>

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