J3/05-246 To: J3 From: Dan Nagle Subject: Adding some HPF Intrinsics Date 2005 August 4 At Delft (N1637), it was decided to add some HPF intrinsics, specifically, a subset of the *_prefix() and *_suffix() ones. This paper is an attempt to do so. The functions are placed in Section 13 in alphabetical order. N1637 omits the COPY_*(), COUNT_*(), MINVAL_*() and MAXVAL_*(), this paper includes them because it is easy to do and we may decide to include them. They easily may be omitted if desired. IALL(), IANY(), IPARITY(), PARITY() were agreed at Delft to be part of the BITS proposal so they are not included here. However, they may be included here or in a separate paper if that measure fails. It will help the reader's understanding of these procedures to understand Section 7.4.5 starting on page 93 of the HPF 2.0 standard document. That language is largely, but not completely, reproduced here as the edit at [282:18+]. The edits following are largely based upon Section 7.7 of the HPF 2.0 standard document, with some changes to fit the language and format of 04-007. I omit some HPF examples. I listed these intrinsics in a new 13.5.19, because no existing category seemed to be a very good fit. Otherwise, perhaps 13.5.12 or 13.5.13 are good places. In the descriptions, they are listed as Transformational functions. Edits: [292:18+] Add section "13.2.3 Array Prefix and Suffix Procedures In a scan of a vector each element of the result is a function of the elements of the vector that precede it (for a prex scan) or that follow it (for a suffix scan). These functions provide scan operations on arrays and subarrays. The functions have the general form XXX_PREFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) XXX_SUFFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) except in the special cases noted below. The allowed values of XXX are ALL, ANY, COPY, COUNT, IALL, IANY, IPARITY, MAXVAL, MINVAL, PARITY, PRODUCT, and SUM. When comments below apply to both prexfix and suffix forms of the routines, we will refer to them as YYYFIX functions. The arguments DIM, MASK, SEGMENT, and EXCLUSIVE are optional The COPY_YYYFIX functions do not have MASK or EXCLUSIVE arguments The ALL_YYYFIX, ANY_YYYFIX, COUNT_YYYFIX, and PARITY_YYYFIX functions do not have MASK arguments. Their ARRAY argument shall be of type logical, it is denoted MASK in their specications in Section. The arguments MASK and SEGMENT shall be of type logical. SEGMENT shall have the same shape as ARRAY. MASK shall be conformable with ARRAY. EXCLUSIVE is a logical scalar. DIM is a scalar integer between one and the rank of ARRAY. Result Value The result has the same shape as ARRAY, and, with the exception of COUNT_YYYFIX, the same type and kind type parameter as ARRAY. The result of COUNT_YYYFIX is default integer. In every case, every element of the result is determined by the values of certain selected elements of ARRAY in a way that is specific to the particular function and is described in its specication. The optional arguments affect the selection of elements of ARRAY for each element of the result, the selected elements of ARRAY are said to contribute to the result element. This section describes fully which elements of ARRAY contribute to a given element of the result. If no elements of ARRAY are selected for a given element of the result, that result element is set to a default value that is specific to the particular function and is described in its specication For any given element r of the result, let a be the corresponding element of ARRAY. Every element of ARRAY contributes to r unless disqualied by one of the following rules. If the function is XXX_PREFIX, no element that follows a in the array element ordering of ARRAY contributes to r. If the function is XXX_SUFFIX, no element that precedes a in the array element ordering of ARRAY contributes to r If the DIM argument is provided, an element z of ARRAY does not contribute to r unless all its indices, excepting only the index for dimension DIM, are the same as the corresponding indices of a. It follows that if the DIM argument is omitted, then ARRAY, MASK, and SEGMENT are processed in array element order as if temporarily regarded as rank-one arrays. If the DIM argument is present, then a family of completely independent scan operations are carried out along the selected dimension of ARRAY. If the MASK argument is provided, an element z of ARRAY contributes to r only if the element of MASK corresponding to z is true. It follows that array elements corresponding to positions where the MASK is false do not contribute anywhere to the result. However, the result is nevertheless defined at all positions, even positions where the MASK is false. If the SEGMENT argument is provided, an element z of ARRAY does not contribute if there is some intermediate element w of ARRAY, possibly z itself, with all of the following properties: (A) If the function is XXX_PREFIX, w does not precede z but does precede a in the array element ordering; if the function is XXX_SUFFIX, w does not follow z but does follow a in the array element ordering, (B) If the DIM argument is present, all the indices of w, excepting only the index for dimension DIM, are the same as the corresponding indices of (A) and, (C) The element of SEGMENT corresponding to w does not have the same value as the element of SEGMENT corresponding to a. In other words, z can contribute only if there is an unbroken string of SEGMENT values, all alike, extending from z through a. If the EXCLUSIVE argument is provided and is true, then a itself does not contribute to r. These general rules lead to the following important cases: Case (i) If ARRAY has rank one, element i of the result of XXX_PREFIX( ARRAY) is determined by the first i elements of ARRAY, element SIZE( ARRAY) - i + 1 of the result of XXX_SUFFIX( ARRAY) is determined by the last i elements of ARRAY Case (ii) If ARRAY has rank greater than one, then each element of the result of XXX_PREFIX( ARRAY) has a value determined by the corresponding element a of the ARRAY and all elements of ARRAY that precede a in array element order. For XXX_SUFFIX, a is determined by the elements of ARRAY that correspond to or follow a in array element order. Case (iii) Each element of the result of XXX_PREFIX( ARRAY, MASK=MASK) is determined by selected elements of ARRAY, namely the corresponding element a of the ARRAY and all elements of ARRAY that precede a in array element order, but an element of ARRAY may contribute to the result only if the corresponding element of MASK is true. If this restriction results in selecting no array elements to contribute to some element of the result, then that element of the result is set to the default value for the given function. Case (iv) Each element of the result of XXX_PREFIX( ARRAY, DIM=DIM) is determined by selected elements of ARRAY, namely the corresponding element a of the ARRAY and all elements of ARRAY that precede a along dimension DIM; for example, in SUM_PREFIX( A( 1: N, 1: N), DIM= 2), the result element ( i_1, i_2) could be computed as SUM( A( i_1, 1: i_2). More generally, in SUM_PREFIX( ARRAY, DIM), result element ( i_1, i_2, ... i_DIM, ... i_n) in could be computed as SUM( ARRAY( i_1, i_2, :i_DIM, i_n). (Note the colon before i_DIM in that last expression.) Case (v) If ARRAY has rank one, then element i of the result of XXX_PREFIX( ARRAY, EXCLUSIVE= .TRUE.) is determined by the first i - 1 elements of ARRAY. Case (vi) The options may be used in any combination." [298:12+} Add a new section "13.5.19 Array Scanning Functions ALL_PREFIX( MASK, DIM, SEGMENT, EXCLUSIVE) ALL_SUFFIX( MASK, DIM, SEGMENT, EXCLUSIVE) ANY_PREFIX( MASK, DIM, SEGMENT, EXCLUSIVE) ANY_SUFFIX( MASK, DIM, SEGMENT, EXCLUSIVE) COPY_PREFIX( ARRAY, DIM, SEGMENT) COPY_SUFFIX( ARRAY, DIM, SEGMENT) COUNT_PREFIX( MASK, DIM, SEGMENT, EXCLUSIVE) COUNT_SUFFIX( MASK, DIM, SEGMENT, EXCLUSIVE) IALL_PREFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) IALL_SUFFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) IANY_PREFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) IANY_SUFFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) IPARITY_PREFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) IPARITY_SUFFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) MAXVAL_PREFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) MAXVAL_SUFFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) MINVAL_PREFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) MINVAL_SUFFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) PARITY_PREFIX( MASK, DIM, SEGMENT, EXCLUSIVE) PARITY_SUFFIX( MASK, DIM, SEGMENT, EXCLUSIVE) PRODUCT_PREFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) PRODUCT_SUFFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) SUM_PREFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE) SUM_SUFFIX( ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE)" Note to Editor: these functions are paired, with XXX_PREFIX() and XXX_SUFFIX() versions. Editing placement instructions are between the pairs. Hopefully, the quotes so indicate. Please add section numbers as appropriate. [303:2+] Add "ALL_PREFIX( MASK, [ DIM, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented logical AND scan along dimension DIM of MASK. <> Transformational function. <> MASK is INTENT( IN) and shall be of type logical. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of MASK. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as MASK. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as MASK. <> Element r of the result has the value ALL( [ a_1, ... , a_m ]) where ( a_1, ... , a_m) is the (possibly empty) set of elements of MASK selected to contribute to r by the rules stated in Section 13.2.3. <> ALL_PREFIX( [ T, F, T, T, T ], SEGMENT= [ F, F, F, T, T ] ) is [ T, F, F, T, T ]. ALL_SUFFIX( MASK, [ DIM, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented logical AND scan along dimension DIM of MASK. <> Transformational function. <> MASK is INTENT( IN) and shall be of type logical. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of MASK. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as MASK. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar <> Same as MASK. <> Element r of the result has the value ALL( [ a_1, ..., a_m ] ) where (a_1, ... a_m) is the (possibly empty) set of elements of MASK selected to contribute to r by the rules stated in Section 13.2.3. <> ALL_SUFFIX( [ T, F, T, T, T ], SEGMENT= [ F, F, F, T,T ] ) is [ F, F, T, T, T ]." [304:10+] Add "ANY_PREFIX( MASK, [ DIM, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented logical OR scan along dimension DIM of MASK. <> Transformational function. <> MASK is INTENT( IN) and shall be of type logical. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of MASK. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as MASK. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as MASK. <> Element r of the result has the value ANY( [ a_1, ..., a_m ] ) where ( a_1, ... a_m) is the (possibly empty) set of elements of MASK selected to contribute to r by the rules stated in Section 13.2.3. <> ANY_PREFIX( [ F, T, F, F, F ], SEGMENT= [ F, F, F, T, T ] ) is [ F, T, T, F, F ]. ANY_SUFFIX( MASK, [ DIM, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented logical OR scan along dimension DIM of MASK. <> Transformational function. <> MASK is INTENT( IN) and shall be of type logical. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of MASK. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as MASK. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as MASK. <> Element r of the result has the value ANY( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of MASK selected to contribute to r by the rules stated in Section 13.2.3. <> ANY_SUFFIX( [ F, T, F, F, F ], SEGMENT= [ F, F, F, T, T ] ) is [ T, T, F, F, F ]." [308:27+] Add "COPY_PREFIX( ARRAY, [ DIM, SEGMENT ] ) <> Computes a segmented copy scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of any type. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. <> Same as ARRAY. <> Element r of the result has the value a_1 where ( a_1, ..., a_m ) is the set, in array element order, of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. Note that this set is never empty. <> COPY_PREFIX( [ 1, 2, 3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 1, 1, 1, 4, 4 ]. COPY_SUFFIX( ARRAY, [ DIM, SEGMENT ] ) <> Computes a reverse, segmented copy scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of any type. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. <> Same as ARRAY. <> Element r of the result has the value a_m where (a_1, ..., a_m ) is the set, in array element order, of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. Note that this set is never empty. <> COPY_SUFFIX( [ 1, 2, 3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 3, 3, 3, 5, 5]." [309:32+] Add "COUNT_PREFIX( MASK, [ DIM, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented COUNT scan along dimension DIM of MASK. <> Transformational function. <> MASK is INTENT( IN) and shall be of type logical. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of MASK. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as MASK. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> The result is of type default integer and of the same shape as MASK. <> Element r of the result has the value COUNT( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of MASK selected to contribute to r by the rules stated in Section 13.2.3. <> COUNT_PREFIX( [ F, T, T, T, T ], SEGMENT= [ F, F, F, T, T ] ) is [ 0, 1, 2, 1, 2 ]. COUNT_SUFFIX( MASK, [ DIM, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented COUNT scan along dimension DIM of MASK. <> Transformational function. <> MASK is INTENT( IN) and shall be of type logical. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of MASK. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as MASK. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> The result is of type default integer and of the same shape as MASK. <> Element r of the result has the value COUNT( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m,) is the (possibly empty) set of elements of MASK selected to contribute to r by the rules stated in Section 13.2.3. <> COUNT_SUFFIX( [ T, F, T, T, T ], SEGMENT= [ F, F, F, T, T ] ) is [ 2, 1, 1, 2, 1 ]." [320:14+] Add "IALL_PREFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented bitwise logical AND scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value IALL( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> IALL_PREFIX( [ 1, 2, 3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 1, 1, 0, 4, 4 ]. IALL_SUFFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented bitwise logical AND scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value IALL( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> IALL_SUFFIX( [ 1, 3, 2, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 0, 2, 2, 4, 5 ]." [320:25+] Add "IANY_PREFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented bitwise logical OR scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value IANY( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> IANY_PREFIX( [ 1, 2, 3, 2, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 1, 3, 3, 2, 7 ]. IANY_SUFFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented bitwise logical OR scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value IANY( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> IANY_SUFFIX( [ 4, 2, 3, 2, 5 ], SEGMENT= [ F, F, F,T, T ] ) is [ 7, 3, 3, 7, 5 ]." [324:7+] Add "IPARITY_PREFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented bitwise logical exclusive OR scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value IPARITY( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> IPARITY_PREFIX( [ 1, 2, 3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 1, 3, 0, 4, 1 ]. IPARITY_SUFFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented bitwise logical exclusive OR scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be be of type integer. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value IPARITY( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> IPARITY_SUFFIX( [ 1, 2, 3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 0, 1, 3, 1, 5 ]." [333:32+] Add "MAXVAL_PREFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented MAXVAL scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer or real. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value MAXVAL( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> MAXVAL_PREFIX( [ 3, 4, -5, 2, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 3, 4, 4, 2, 5 ]. MAXVAL_SUFFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented MAXVAL scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer or real. It shall not be scalar DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value MAXVAL( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> MAXVAL_SUFFIX( [ 3, 4, -5, 2, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 4, 4, -5, 5, 5 ]." [337:2+] Add "MINVAL_PREFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented MINVAL scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer or real. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value MINVAL( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> MINVAL_PREFIX( [ 1, 2, -3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 1, 1, -3, 4, 4 ]. MINVAL_SUFFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented MINVAL scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer or real. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value MINVAL( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> MINVAL_SUFFIX( [ 1, 2, -3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ -3, -3, -3, 4, 5 ]." [342:16+] Add "PARITY_PREFIX( MASK, [ DIM, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented logical exclusive OR scan along dimension DIM of MASK. <> Transformational function. <> MASK is INTENT( IN) and shall be of type logical. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of MASK. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as MASK. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as MASK. <> Element r of the result has the value PARITY( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the ( possibly empty) set of elements of MASK selected to contribute to r by the rules stated in Section 13.2.3. <> PARITY_PREFIX( [ T, F, T, T, T ], SEGMENT= [ F, F, F, T, T ] ) is [ T, T, F, T, F ]. PARITY_SUFFIX( MASK, [ DIM, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented logical exclusive OR scan along dimension DIM of MASK. <> Transformational function. <> MASK is INTENT( IN) and shall be of type logical. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of MASK. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as MASK. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as MASK. <> Element r of the result has the value PARITY( [ a_1, ..., a_m ] ) where ( a_1, ...., a_m) is the (possibly empty) set of elements of MASK selected to contribute to r by the rules stated in Section 13.2.3. <> PARITY_SUFFIX( [ T, F, T, T, T ], SEGMENT= [ F, F, F, T, T ] ) is [ F, T, T, F, T ]." [343:34+] Add "PRODUCT_PREFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented PRODUCT scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer, real, or complex. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value PRODUCT( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> PRODUCT_PREFIX( [ 1, 2, 3, 4, 5 ], SEGMENT= [ F, F, F, T, T ]) is [ 1, 2, 6, 4, 20 ]. PRODUCT_SUFFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented PRODUCT scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer, real, or complex. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value PRODUCT( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> PRODUCT_SUFFIX( [ 1, 2, 3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 6, 6, 3, 20, 5 ]." [354:38+] Add "SUM_PREFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a segmented SUM scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer, real, or complex. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value SUM( [ a_1, ..., a_m ]) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> SUM_PREFIX( [ 1, 2, 3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 1, 3, 6, 4, 9 ]. SUM_SUFFIX( ARRAY, [ DIM, MASK, SEGMENT, EXCLUSIVE ] ) <> Computes a reverse, segmented SUM scan along dimension DIM of ARRAY. <> Transformational function. <> ARRAY is INTENT( IN) and shall be of type integer, real, or complex. It shall not be scalar. DIM (optional) is INTENT( IN) and shall be scalar and of type integer with a value in the range 1 <= DIM <= n, where n is the rank of ARRAY. MASK (optional) is INTENT( IN) and shall be of type logical and shall be conformable with ARRAY. SEGMENT (optional) is INTENT( IN) and shall be of type logical and shall have the same shape as ARRAY. EXCLUSIVE (optional) is INTENT( IN) and shall be of type logical and shall be scalar. <> Same as ARRAY. <> Element r of the result has the value SUM( [ a_1, ..., a_m ] ) where ( a_1, ..., a_m ) is the (possibly empty) set of elements of ARRAY selected to contribute to r by the rules stated in Section 13.2.3. <> SUM_SUFFIX( [ 1, 2, 3, 4, 5 ], SEGMENT= [ F, F, F, T, T ] ) is [ 6, 5, 3, 9, 5 ]."