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ND-500/2 Double Precision Array Processing Functions¶

ND-05.018.01


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ND-500/2 Double Precision Array Processing Functions¶

ND-05.018.01

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Manual Information¶

This manual is in loose-leaf form for ease of updating. Old pages may be removed and new pages easily inserted if the manual is revised.

The loose-leaf form also allows you to place the manual in a ring binder (A) for greater protection and convenience of use. Ring binders with 4 rings corresponding to the holes in the manual may be ordered in two widths, 30 mm and 40 mm. Use the order form below.

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PRINTING RECORD¶

Printing	Notes
12/84	VERSION 01

ND-500/2 Double Precision Array Processing Functions
Publ.No. ND 05.018.01
December 1984

Norsk Data A.S
Graphic Center
P.O.Box 25, Bogerud
0621 Oslo 6, Norway

Page 8¶

Manual Updates¶

Manuals can be updated in two ways, new versions and revisions. New versions consist of a complete new manual which replaces the old manual. New versions incorporate all revisions since the previous version. Revisions consist of one or more single pages to be merged into the manual by the user, each revised page being listed on the new printing record sent out with the revision. The old printing record should be replaced by the new one.

New versions and revisions are announced in the ND Bulletin and can be ordered as described below.

The reader's comments form at the back of this manual can be used both to report errors in the manual and to give an evaluation of the manual. Both detailed and general comments are welcome.

Contact Information¶

These forms and comments should be sent to:

Documentation Department
Norsk Data A.S
P.O. Box 25, Bogerud
0621 Oslo 6, Norway

Requests for documentation should be sent to the local ND office or (in Norway) to:

Graphic Center
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P.O. Box 25, Bogerud
0621 Oslo 6, Norway

Page 9¶

Preface¶

THE PRODUCT¶

This manual describes the mathematical functions in the ND-500/2-APD library.

The APD library routines may be called from FORTRAN. The routines are designed to speed up the execution of operations on double precision real arrays.

The APD library utilizes a special microprogram for the ND-500/2 CPU. The special double precision functions within this microprogram are called ND-500/2 DAX functions. This microprogram is an extension of the CXA microprogram.

The ND-numbers for the product on the different ND-500/2 models are:

Computer	ND-number	Microprogram version
ND-550/2	ND-10786	152xx
ND-560/2	ND-10786	152xx
ND-570/2 (new CX)	ND-10786	152xx
ND-570/2 (old CXA)	ND-10786	152xx

NOTE The ND-530/2 can not use this product.

THE MANUAL¶

This manual provides a functional description of the APD library, and thereby the ND-500/2 DAX functions. A listing of each routine is used to describe the routines. Listing and parameter description is done in FORTRAN.

THE READER¶

This manual is written for people creating and running programs using array processing functions.

Page 10¶

PREREQUISITE KNOWLEDGE¶

The reader is assumed to be familiar with FORTRAN. It is also assumed that the reader is familiar with using ND-500/2 computers, and knows how to generate, load and run programs on such computers. Some knowledge of the mathematical theory of the implemented functions is of advantage, to be able to use them effectively.

Documentation further describing the use of ND-500 computers is found in these manuals:

Manual	Code
ND-500 Loader/Monitor	ND-60.136
ND FORTRAN Reference Manual	ND-60.145
ND-500 Reference Manual	ND-05.009
ND-500 Single Precision Array Processing Functions	ND-05.013

ND-05.018.01

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Table of Contents¶

Section	Page
1 BASIC CONCEPTS	1
1.1 Prerequisite Software for Using the APD Library	1
1.2 The Double Precision Floating Point Format	1
1.3 Hardware Concepts	1
1.4 Array Processing Definitions	2

| 2 USING THE ND-500/2 DAX FUNCTIONS | 5 |

| 3 ND-500/2 DAX FUNCTIONS PERFORMANCE | 11 |

| 4 ARRAY PROCESSING FUNCTIONS | 13 | | 4.1 Introduction | 13 | | 4.2 Vector Add (VADD) | 14 | | 4.3 Vector Subtract (VSUB) | 15 | | 4.4 Vector Multiply (VMUL) | 16 | | 4.5 Vector Divide (VDIV) | 17 | | 4.6 Vector Maximum (VMAX) | 18 | | 4.7 Vector Minimum (VMIN) | 19 | | 4.8 Vector Maximum Magnitude (VMAXMG) | 20 | | 4.9 Vector Minimum Magnitude (VMINMG) | 21 | | 4.10 Vector Square (VSQ) | 22 | | 4.11 Vector Signed Square (VSSQ) | 23 | | 4.12 Vector Absolute Value (VABS) | 24 | | 4.13 Vector Square Root (VSQRT) | 25 | | 4.14 Vector Move (VMOV) | 26 | | 4.15 Vector Swap (VSWAP) | 27 | | 4.16 Vector Negative (VNEG) | 28 | | 4.17 Sum of Vector Elements (SVE) | 29 | | 4.18 Sum of Vector Elements Magnitude (SVEMG) | 30 | | 4.19 Sum of Vector Elements Square (SVESQ) | 31 | | 4.20 Sum of Vector Elements Signed Square (SVS) | 32 | | 4.21 Mean Magnitude Value of Vector (MEAMGV) | 33 | | 4.22 Maximum Value in Vector (MAXV) | 34 | | 4.23 Minimum Value in Vector (MINV) | 35 | | 4.24 Maximum Magnitude Value in Vector (MAXMGV) | 36 | | 4.25 Minimum Magnitude Value in Vector (MINMGV) | 37 | | 4.26 Maximum and Minimum Value in Vector (MAXMIN) | 38 | | 4.27 Maximum and Minimum Magnitude Value in Vector (MXMNMG) | 39 | | 4.28 Vector Scalar Multiply and Add (VSMA) | 40 | | 4.29 Vector Scalar Add (VSADD) | 41 |

ND-05.018.01

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Table of Contents¶

Section	Page
4.30 Vector Scalar Multiply (VSMUL)	42
4.31 Vector Scalar Divide (VDIVS)	43
4.32 Dot Product (DOTPR)	44
4.33 Vector Clear (VCLR)	45
4.34 Complex Vector Multiply (CVMUL)	46
4.35 Vector Taper (VTAPER)	48
4.36 Vector Ramp Function (VRAMP)	50
4.37 Vector First and Last Non-Zero Value (VFLNZ)	51

Index¶

53

ND-05.018.01

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

1 BASIC CONCEPTS¶

1.1 PREREQUISITE SOFTWARE FOR USING THE APD LIBRARY¶

Together with the microprogram, the APD library must be installed. The actual file name is: ND-500-2-APD:NRF.

These are the only modifications to be performed on the system.

The APD library utilizes a special microprogram for the ND-500/2 CPU. This microprogram contains the double precision array processing functions. It is an extension of the ND-500/2 CXA microprogram.

The ND-500/2 DAX functions are floating point operations performed in 64 bits floating point format by the ND-500/2 floating point arithmetic.

1.2 THE DOUBLE PRECISION FLOATING POINT FORMAT¶

The number range for the double precision floating point format is:


8.6 * 10^-78	≤

The accuracy corresponds approximately to 16 decimal digits.

1.3 HARDWARE CONCEPTS¶

The ND-500 CPU gives possibility of parallel processing. This means that indexing, memory access, floating point arithmetic, integer arithmetic and loop control may be run in parallel. This is done as far as possible to obtain high speed operations. Temporary results to be used in later calculations, are kept in registers in the ND-500/2 CPU, accessed directly by both the floating point arithmetic and integer arithmetic. In this way unnecessary memory accesses are avoided.

Arrays involved in an operation are accessed through the ND-500/2 memory management system. This system will automatically cause allocation of memory and reservation of continuous memory space for array processing is not required. The result of an array processing function is present in output array when returning from the function.

The ND-500/2 DAX functions are fully interruptable to maintain the ND-500/2 CPU resources being shared by the different processes currently running on the system.

Page 14¶

1.4 Array Processing Definitions¶

An array contains a group of numbers that are related to each other in some way, and the array may be multi-dimensional. An array is termed a matrix in mathematical terminology.

An array is used to represent equations of different kinds, for example, linear equations. Each row in the array represents one particular equation, thus the array represents a system of equations of the same kind.

The entries in the array are the coefficients of the equations. They are called elements in this manual.

Each row of elements is named a vector in this manual, regardless of what kind of equation it mathematically represents. In those array processing functions which are closely related to mathematical vectors, the row of elements is referred to as a complex vector.

Most of the DAX functions are performed on one-dimensional vectors.

Example of Equations:¶

Mathematical equations:	Arrays:
(2x + 8y + 5z = 24)	[2 \ 8 \ 5 \ 24]
(3x + 2y + 1z = 0)	[3 \ 2 \ 1 \ 0]
(11x + 0y + 5z = 4)	[11 \ 0 \ 5 \ 4]

(2x^2 + y = 3)	[2 \ 1 \ 3]
(x^2 + y = 0)	[1 \ 1 \ 0]

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

BASIC CONCEPTS¶

Three parameters are necessary to specify a vector:

V - The logical name of the vector. A double precision real.
INC - The step value (increment) for the index in the array. An integer.
NN - Element count. Number of elements in the array. An integer.

NOTE It is assumed that the lower limit for the array index is 1!

Example of Use of a DAX Function¶

PROGRAM CLEAR

DOUBLE PRECISION VA(2000); % Remember to declare the vector as double precision real.
INTEGER INCA,NN;

<Other program statements>

INCA = 2
NN = 1000

CALL VCLR(VA,INCA,NN)

<Other program statements>

END

This DAX function causes each second element of the vector VA to be set to zero (increment is 2).

For vectors where the elements are stored in consecutive locations, the index increment is equal to 1. The flexibility to specify index increments is present to most of the functions.

For complex vectors, each complex equation is represented by two consecutive elements. This corresponds to the real and the imaginary part of the complex vector. The real element is immediately followed by the imaginary element, as the complex vector is represented in the rectangular coordinate system.

This means that for each index in the array there are one real and one imaginary element.

ND-05.018.01

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Example of Use of a Complex DAX Function¶

PROGRAM CVMULTIPLY

COMPLEX*16 VA(1:200)
COMPLEX*16 VB(1:200)
COMPLEX*16 VC(1:200)

{Other program statements}

CALL CVMUL(VA,1,VB,2,VC,1,100,1)

{Other program statements}

END

This DAX function causes each complex vector of the array VA to be multiplied with each second vector from VB. The results are stored in array VC. This function corresponds to mathematical multiplication of complex numbers.

Page 17¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS USING THE ND-500/2 DAX FUNCTIONS¶

2 USING THE ND-500/2 DAX FUNCTIONS¶

The ND-500/2 DAX functions can be called from FORTRAN. The array processing library is used to transfer the parameters from the call to the array processing instructions. Thus the array processing functions are connected to the main program at load time as a part of the program.

Writing a FORTRAN program for array processing with ND-500/2 DAX functions is much the same as using the FORTRAN equivalent for the array processing function. Before starting an array processing function, input and output arrays for the operations must be defined. Initialization of input arrays is also required. This means that data for processing must be placed in the input arrays for the actual array processing function. Then the array processing function may be called. The result of the operation is present in the output array when returning from an array processing function.

Example of Creating a FORTRAN Program Using DAX Functions¶

Source Program in FORTRAN:¶

PROGRAM DOKKT
C Set name and size of arrays to be used.
PARAMETER NN = 100; NC = 20
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(NN),VB(NN),VC(NN),VL(NC)
INTEGER*4 I I(NC)
C Initiate scalar values, index increment and element count
C for the VRAMP function.
DELTA = 1.0D+01
SC1 = 1.5
SC2 = 2.0D-01
INC1 = 1
INC2 = 2
INC4 = 4
C Initiate VA with a ramp.
CALL VRAMP(SC1,SC2,VA,INC1,NN)
C Clear result array to be used in next operation.
CALL VCLR(VC,INC1,NN)
NB = NN/2
DO 100 M=1,NB
  CALL SVE(VA(M),INC1,VC(M),NB)
100 CONTINUE
C Set scalar value.
B = 200.0
C 200.0 divided with each second element of VA.
C Result in VB.

The program continues on next page...¶

ND-05.018.01

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ND-500/2 Double Precision Array Processing Functions¶

Using the ND-500/2 DAX Functions¶

....Continued from previous page

Code Segment	Description
CALL DDIVS(VA,INC2,B,VB,INC1,NC)
C Set scalar value.
B = 150.0
CALL VSADD(VA,INC2,B,VB,INC1,NC)	Add 150.0 to each second of VA. Result in VB.
CALL VADD(VB,INC4,VC,INC1,VA,INC1,NC)	Add elements from VB and VC with result in VA.
B = 2.00D+03
CALL DDIVS(VA,INC4,B,VA,INC2,NC)	2000.0 divided with each fourth element in VA. Result in VA.
CALL VSMA(VB,INC4,B,VA,INC1,VB,INC1,NC)	Each fourth element in VB is multiplied with 2.5E-2, and added with each element of VA. Result in VB.
CALL VNEG(VB,INC2,VB,INC2,NC)	Negate each second element of VB. Result in VB.
CALL VMOV(VB,INC1,VL,INC1,NC)	Move each element of VB to VL (only NC elements).
CALL MAXV(VB,INC1,VMA,IMA,NC)	Find maximum value in VB. Value returned in VMA and index returned in IMA.
VMA = VMA+DELTA	Maximum value + delta.
DO 120 M=1,NC	Sort the elements in rising order.

CALL MINV(VL,INC1,VA(M),IL(M),NC)
IY = IL(M)
VL(IY) = VMA
120 CONTINUE
WRITE (1,1000)
WRITE (1,1001)
DO FOR I=1,NC
    WRITE (1,1002)I,VB(I),I,VA(I),IL(I)
ENDDO
WRITE (1,1001)
1000 FORMAT (' Finding minimum value and indices',/,
+  ' Input vector results in output vector found at VB index:')
1001 FORMAT (,
+  ' ..........................................................')
1002 FORMAT (1X,'VB(',I2,') ',F15.6,' VA(',I2,')',F15.6,
+  ' at index ',I3)
END

ND-05.018.01

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ND-500/2 Double Precision Array Processing Functions¶

Using the ND-500/2 DAX Functions¶

Compiling the Program¶

Command
@FORTRAN-500

ND-500 ANSI 77 FORTRAN Compiler - 203054F
FTN: COMPILE
Source-File DOKKT
List-File
Object-File "DOKKT"

Compilation Details
ND-500 ANSI 77 FORTRAN Compiler - 203054F 8:45 20 SEP 1984
Source File: DOKKT
- CPU Time Used: 0.8 seconds. 71 lines compiled.
- No Messages
- Program Size=567 Data Size=3188 Common Size=0

Command
FTN: EXIT

ND-05.018.01

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Loading the Program¶

@LINKAGE-LOADER

ND-Linkage-Loader - F	10. September 1983	Time: 00:07
N11 entered:	20. September 1984	Time: 8:45

N11: SET-DOMAIN DOKKT

N11: OPEN-SEGMENT DOKKT

N11: LOAD DOKKT.ND-500-2-APD-LIB

Program:	1073 P05	Data:	6170 D05
ND-500/2-APD-LIB-A
Program:	1616 P05	Data:	7100 D05
N11: CLOSE Y	Segment no.	30	is linked

September 1984 Time: 8:45

Unsatisfied references:

None!

Defined symbols:

DOKKT	4 P05	VADD	1073 P05
VMOV	1136 P05	SVE	1171 P05
MAXV	1224 P05	MINV	1273 P05
VSADD	1342 P05	VDIVS	1400 P05
VCLR	1436 P05	VSMA	1461 P05
VNEG	1530 P05	VRAMP	1564 P05

Program:	1616 P05	Data:	11100 D05

N11: EXIT

ND-05.018.01

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Executing the Program¶

@ND-500-MONITOR

ND-500 MONITOR VERSION E 83.12.20 / 83.12.21

N500: DOKKT

Finding minimum value and indices
Input vector results in output vector found at VB index:


VB( 1)	-8.029282	VA( 1)	-363.636364	at index 11
VB( 2)	486.927500	VA( 2)	-317.460317	at index 13
VB( 3)	-7.729249	VA( 3)	-281.690141	at index 15
VB( 4)	510.207500	VA( 4)	-253.164557	at index 17
VB( 5)	-8.947500	VA( 5)	-229.885057	at index 19
VB( 6)	370.000000	VA( 6)	-8.947500	at index 5
VB( 7)	-4.545455	VA( 7)	-8.029282	at index 1
VB( 8)	390.000000	VA( 8)	-7.729249	at index 3
VB( 9)	-4.166667	VA( 9)	-4.545455	at index 7
VB(10)	410.000000	VA(10)	-4.166667	at index 9
VB(11)	-363.636364	VA(11)	370.000000	at index 6
VB(12)	430.000000	VA(12)	390.000000	at index 8
VB(13)	-317.460317	VA(13)	410.000000	at index 10
VB(14)	450.000000	VA(14)	430.000000	at index 12
VB(15)	-281.690141	VA(15)	450.000000	at index 14
VB(16)	470.000000	VA(16)	470.000000	at index 16
VB(17)	-253.164557	VA(17)	486.927500	at index 2
VB(18)	490.000000	VA(18)	490.000000	at index 18
VB(19)	-229.885057	VA(19)	510.000000	at index 20
VB(20)	510.000000	VA(20)	510.207500	at index 4

N500: EXIT

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ND-05.018.01

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ND-500/2 DAX FUNCTIONS PERFORMANCE¶

3 ND-500/2 DAX FUNCTIONS PERFORMANCE¶

NAME	OPERATION	Number of elements	Typical execution time pr. loop (microsec.)	Improvement ratio to FFN function (1)
CVMUL	COMPLEX VECTOR MULTIPLY	750	4.88	5.30
DOTPR	DOT PRODUCT	750	4.13	1.61
MAXMGV	MAX. MAGNITUDE VALUE IN VECTOR	750	4.75	1.13
MAXMIN	MAX. AND MIN. VALUE IN VECTOR	750	4.00	1.73
MAXV	MAX. VALUE IN VECTOR	750	4.03	1.16
MEAMGV	MEAN MAGNITUDE OF VECTOR	750	5.70	0.83
MINMGV	MIN. MAGNITUDE VALUE IN VECTOR	750	4.80	1.13
MINV	MIN. VALUE IN VECTOR	750	4.03	1.15
MXMMG	MAX. AND MIN. MAG. VALUE IN VECTOR	750	4.15	1.75
SVE	SUM OF VECTOR ELEMENTS	750	5.10	0.83
SVEMG	SUM OF VECTOR ELEMENTS MAGNITUDE	750	5.90	0.80
SVESQ	SUM OF VECTOR ELEMENTS SQUARE	750	3.53	1.40
SVS	SUM OF VECTOR ELEMENTS SIGNED SQUARE	750	4.04	1.40
VABS	VECTOR ABSOLUTE VALUE	750	4.30	1.19
VADD	VECTOR ADD	750	4.11	1.75
VCLR	VECTOR CLEAR	750	3.71	0.85
VDIV	VECTOR DIVIDE	750	2.46	3.63
VDIVS	VECTOR SCALAR DIVIDE	750	2.34	3.36
VFLNZ	VECTOR FIRST AND LAST NON-ZERO VALUE	750	8.00	0.51
VMAX	VECTOR MAXIMUM	750	3.90	2.03
VMAXMG	VECTOR MAXIMUM MAGNITUDE	750	4.05	2.07
VMIN	VECTOR MINIMUM	750	3.90	2.03
VMINMG	VECTOR MINIMUM MAGNITUDE	750	4.05	2.07
VMOV	VECTOR MOVE	750	4.20	1.22
VMUL	VECTOR MULTIPLY	750	4.41	1.75
VNEG	VECTOR NEGATIVE	750	4.49	1.22
VRAMP	VECTOR RAMP FUNCTION	750	5.70	0.96
VSADD	VECTOR SCALAR ADD	750	4.30	1.40
VSMA	VECTOR SCALAR MULTIPLY AND ADD	750	4.05	1.93
VSMUL	VECTOR SCALAR MULTIPLY	750	4.30	1.40
VSQ	VECTOR SQUARE	750	3.48	1.55
VSQRT	VECTOR SQUARE ROOT	750	1.55	10.78
VSSQ	VECTOR SIGNED SQUARE	750	4.00	1.52
VSUB	VECTOR SUBTRACT	750	4.41	1.75
VSWAP	VECTOR SWAP	750	3.45	2.27
VTAPER	VECTOR TAPER	750	2.64	1.95

Timing measurement is done on a ND-570 system with 64K-byte cache.

1) (Time used by machine code) / (Time used by microcode).

ND-05.018.01

Page 24¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ND-500/2 DAX FUNCTIONS PERFORMANCE¶

The next table shows how the ND-500/2 DAX functions may be used to improve the performance even on small arrays. With high cache hit ratio, an improvement ratio of 4.4 can be obtained with the VADD function, while low cache hit ratio will reduce the improvement ratio over FORTRAN.

Element count	VADD	DOTPR	MAXV
5	1.6	1.7	1.4
10	2.2	2.2	2.1
50	3.5	3.5	2.8
100	3.8	3.9	3.6
500	4.1	4.3	4.0
1000	4.4	4.3	4.3
2000	2.5	3.7	4.1

ND-05.018.01

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

4 ARRAY PROCESSING FUNCTIONS¶

4.1 INTRODUCTION¶

This chapter contains a listing of each array processing function to describe the different functions. For each routine the required parameter list for calling the array processing function is included together with definitions.

The ND-500/2 double precision array processing functions are implemented as one instruction.

The different functions are using the same instruction code. The contents of the record register are the only difference between the functions and are used to distinguish between them.

For each routine, an identification number is given as a cross reference between the object code and the array processing function. This identification number is given as two octal numbers:
'Ident (R:I) : xxx:nnnnnB8'. 'xxx' are the contents of the record register. 'nnnnn' is the instruction code used for the DAX function.

The library for the ND-500 double precision array processing functions consists of one routine for each of the array processing functions. Each routine is building a data stack depending on the called array processing function. The data stack is used by the array processing functions to find addresses of input and output arrays, scalar values or addresses, index increments and element count.

Page 26¶

4.2 VECTOR ADD (VADD)¶

Format¶

VADD(VA,INCA,VB,INCB,VC,INCC,NN) Ident (R:I) : 001:177515B

Explanation¶

Add the corresponding elements of two vectors. VCn = VAn + VBn, 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VADD(VA,INCA,VB,INCB,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VB(1),VC(1)
IA = 1
IB = 1
IC = 1
DO FOR M = 1,NN
    VC(IC) = VB(IB) + VA(IA)
    IA = IA + INCA
    IB = IB + INCB
    IC = IC + INCC
ENDDO
RETURN
END

ND-05.018.01

Page 27¶

4.3 VECTOR SUBTRACT (VSUB)¶

Format¶

VSUB(VA,INCA,VB,INCB,VC,INCC,NN) Ident (R:I) : 002:177515B

Explanation¶

Subtract the corresponding elements of two vectors. VCn = VBn - VAn, 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of vector VA.
INCA	VA index increment.
VB	Name of vector VB.
INCB	VB index increment.
VC	Name of vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VSUB(VA,INCA,VB,INCB,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VB(1),VC(1)
IA = 1
IB = 1
IC = 1
DO FOR M = 1,NN
  VC(IC) = VB(IB) - VA(IA)
  IA = IA + INCA
  IB = IB + INCB
  IC = IC + INCC
ENDDO
RETURN
END

Page 28¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

4.4 VECTOR MULTIPLY (VMUL)¶

Format¶

VMUL(VA,INCA,VB,INCB,VC,INCC,NN) Ident (R:I) : 003:177515B

Explanation¶

Multiply the corresponding elements of two vectors. VCn = VBn * VAn, 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VMUL(VA,INCA,VB,INCB,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VB(1),VC(1)
IA = 1
IB = 1
IC = 1
DO FOR M = 1,NN
    VC(IC) = VB(IB) * VA(IA)
    IA = IA + INCA
    IB = IB + INCB
    IC = IC + INCC
ENDDO
RETURN 1
END

Page 29¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

4.5 VECTOR DIVIDE (VDIV)¶

Format¶

VDIV(VA,INCA,VB,INCB,VC,INCC,NN)
Ident (R:I) : 004:177515B

Explanation¶

Divide the corresponding elements of two vectors. Cn = VBn/VAn, 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VDIV(VA,INCA,VB,INCB,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VB(1),VC(1)
IA = 1
IB = 1
IC = 1
DO FOR M = 1,NN
VC(IC) = VB(IB) / VA(IA)
IA = IA + INCA
IB = IB + INCB
IC = IC + INCC
ENDDO
RETURN 1
END

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4.6 Vector Maximum (VMAX)¶

Format¶

VMAX(VA,INCA,VB,INCB,VC,INCC,NN) Ident (R:I) : 005:177515B

Explanation¶

Form a vector from the maximum value of each corresponding pair of elements of two vectors. VCn = VAn if VAn > VBn, else VCn = VBn. 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VMAX(VA,INCA,VB,INCB,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VB(1),VC(1)
IA = 1
IB = 1
IC = 1
DO FOR M = 1,NN
  VC(IC) = DMAX1(VA(IA),VB(IB))
  IA = IA + INCA
  IB = IB + INCB
  IC = IC + INCC
ENDDO
RETURN
END

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4.7 VECTOR MINIMUM (VMIN)¶

Format¶

VMIN(VA, INCA, VB, INCB, VC, INCC, NN)
Ident (R:I) : 006:177515B

Explanation¶

Form a vector from the minimum value of each corresponding pair of elements of two vectors. VCn = VAn if VAn < VBn, else VCn = VBn. 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VMIN(VA, INCA, VB, INCB, VC, INCC, NN)
IMPLICIT DOUBLE PRECISION (A-H, O-Z)
DIMENSION VA(1), VB(1), VC(1)
IA = 1
IB = 1
IC = 1
DO FOR M = 1, NN
  VC(IC) = DMIN1(VA(IA), VB(IB))
  IA = IA + INCA
  IB = IB + INCB
  IC = IC + INCC
ENDDO
RETURN
END

Page 32¶

4.8 VECTOR MAXIMUM MAGNITUDE (VMAXMG)¶

Format¶

VMAXMG(VA,INCA,VB,INCB,VC,INCC,NN) Ident (R:I) : 007:177515B

Explanation¶

Form a vector from the maximum absolute value of each corresponding pair of elements of two vectors. VCn = |VAn| if |VAn| > |VBn|, else VCn = |VBn|. 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VMAXMG(VA,INCA,VB,INCB,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VB(1),VC(1)
IA = 1
IB = 1
IC = 1
DO FOR M = 1,NN
  VC(IC) = DMAX1(ABS(VA(IA)),ABS(VB(IB)))
  IA = IA + INCA
  IB = IB + INCB
  IC = IC + INCC
ENDDO
RETURN
END

Page 33¶

4.9 VECTOR MINIMUM MAGNITUDE (VMINMG)¶

Format¶

VMINMG(VA,INCA,VB,INCB,VC,INCC,NN) Ident (R:I) : 010:177515B

Explanation¶

Form a vector from the minimum absolute value of each corresponding pair of elements of two vectors. VCn = |VAn| if |VAn| < |VBn|, else VCn = |VBn|. 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VMINMG(VA,INCA,VB,INCB,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VB(1),VC(1)
IA = 1
IB = 1
IC = 1
DO FOR M = 1,NN
    VC(IC) = DMIN1(ABS(VA(IA)),ABS(VB(IB)))
    IA = IA + INCA
    IB = IB + INCB
    IC = IC + INCC
ENDDO
RETURN
END

Page 34¶

4.10 VECTOR SQUARE (VSQ)¶

Format¶

VSQ(VA, INCA, VC, INCC, NN) Ident (R:I) : 042:177515B

Explanation¶

Square the elements of a vector. VCn = (VAn)². 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

      SUBROUTINE VSQ(VA,INCA,VC,INCC,NN)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION VA(1),VC(1)
      IA = 1
      IC = 1
      DO FOR M = 1,NN
          VC(IC) = VA(IA)**2
          IA = IA + INCA
          IC = IC + INCC
      ENDDO
      RETURN
      END

Page 35¶

4.11 VECTOR SIGNED SQUARE (VSSQ)¶

Format¶

VSSQ(VA,INCA,VC,INCC,NN) Ident (R:I) : 011:177515B

Explanation¶

Multiply each element of a vector with the absolute value of itself.
VCn = VAn * |VAn|. 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

      SUBROUTINE VSSQ(VA,INCA,VC,INCC,NN)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      DIMENSION VA(1),VC(1)
      IA = 1
      IC = 1
      DO FOR M = 1,NN
          VC(IC) = VA(IA)*ABS(VA(IA))
          IA = IA + INCA
          IC = IC + INCC
      ENDDO
      RETURN
      END

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4.12 VECTOR ABSOLUTE VALUE (VABS)¶

Format¶

VABS(VA,INCA,VC,INCC,NN) Ident (R:I) : 012:177515B

Explanation¶

Form a vector from the absolute value of the elements in a vector.
VCn = |VAn|. 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VABS(VA,INCA,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VC(1)
IA = 1
IC = 1
DO FOR M = 1,NN
    VC(IC) = ABS(VA(IA))
    IA = IA + INCA
    IC = IC + INCC
ENDDO
RETURN
END

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4.13 VECTOR SQUARE ROOT (VSQRT)¶

Format¶

VSQRT(VA,INCA,VC,INCC,NN)
Ident (R:I) : 013:177515B

Explanation¶

Take the square roots of the elements in a vector. VCn = √VAn. 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VSQRT(VA,INCA,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VC(1)
IA = 1
IC = 1
DO FOR M = 1,NN
  VC(IC) = SQRT(VA(IA))
  IA = IA + INCA
  IC = IC + INCC
ENDDO
RETURN
END

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

4.14 VECTOR MOVE (VMOV)¶

Format¶

VMOV(VA,INCA,VC,INCC,NN) Ident (R:I) : 016:177515B

Explanation¶

Move the elements from one vector into another. VCn = VAn, 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VMOV(VA,INCA,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VC(1)
IA = 1
IC = 1
DO FOR M = 1,NN
    VC(IC) = VA(IA)
    IA = IA + INCA
    IC = IC + INCC
ENDDO
RETURN
END

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ND-500/2 Double Precision Array Processing Functions¶

4.15 Vector Swap (VSWAP)¶

Format¶

VSWAP(VA, INCA, VC, INCC, NN) Ident (R:I) : 063:177515B

Explanation¶

Swap the elements between two vectors. VAn ↔ VBn and VBn ↔ VAn, 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input and output vector VA.
INCA	VA index increment.
VC	Name of input and output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VSWAP(VA, INCA, VC, INCC, NN)
IMPLICIT DOUBLE PRECISION (A-H, O-Z)
DIMENSION VA(1), VC(1)
IA = 1
IC = 1
DO FOR M = 1, NN
    HOLD = VC(IC)
    VC(IC) = VA(IA)
    VA(IA) = HOLD
    IA = IA + INCA
    IC = IC + INCC
ENDDO
RETURN
END

Page 40¶

4.16 VECTOR NEGATIVE (VNEG)¶

Format¶

VNEG(VA, INCA, VC, INCC, NN)
Ident (R:I) : 064:177515B

Explanation¶

Form a vector from the elements of another vector multiplied with -1.
VCn = -VAn, 'n' is the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VNEG(VA, INCA, VC, INCC, NN)
IMPLICIT DOUBLE PRECISION (A-H, O-Z)
DIMENSION VA(1), VC(1)
IA = 1
IC = 1
DO FOR M = 1, NN
  VC(IC) = -VA(IA)
  IA = IA + INCA
  IC = IC + INCC
ENDDO
RETURN
END

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ARRAY PROCESSING FUNCTIONS¶

4.17 SUM OF VECTOR ELEMENTS (SVE)¶

Format¶

SVE(VA,INCA,VC,NN) Ident (R:I) : 021:177515B

Explanation¶

Add the elements of a vector. VC = VA₁ + VA₂ + ....+ VAnn, 'nn' is the element count.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC.
NN	Element count.

Listing¶

SUBROUTINE SVE(VA,INCA,VC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1)
IA = 1
SUM = 0.0
DO FOR M = 1,NN
    SUM = SUM + VA(IA)
    IA = IA + INCA
ENDDO
VC = SUM
RETURN
END

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4.18 Sum of Vector Elements Magnitude (SVEMG)¶

Format¶

SVEMG(VA,INCA,VC,NN) Ident (R:I) : 065:177515B

Explanation¶

Form the sum of the absolute values of the elements of a vector.
VC = |VA₁| + |VA₂| + .... + |VAnn| , 'nn' is the element count.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC.
NN	Element count.

Listing¶

SUBROUTINE SVEMG(VA,INCA,VC,NN)  
IMPLICIT DOUBLE PRECISION (A-H,O-Z)  
DIMENSION VA(1)  
IA = 1  
SUM = 0.0  
DO FOR M = 1,NN  
   SUM = SUM + ABS(VA(IA))  
   IA = IA + INCA  
ENDDO  
VC = SUM  
RETURN  
END

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ARRAY PROCESSING FUNCTIONS¶

4.19 SUM OF VECTOR ELEMENTS SQUARE (SVESQ)¶

Format

SVESQ(VA,INCA,VC,NN) Ident (R:I) : 066:177515B

Explanation

Form the sum of the squared elements of a vector.
VC = (VA₁)² + (VA₂)² + ....+ (VAnn)², nn is the element count.

Parameters

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC.
NN	Element count.

Listing

SUBROUTINE SVESQ(VA,INCA,VC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1)
IA = 1
SUM = 0.0
DO FOR M = 1,NN
  SUM = SUM + VA(IA)**2
  IA = IA + INCA
ENDDO
VC = SUM
RETURN
END

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4.20 Sum of Vector Elements Signed Square (SVS)¶

Format¶

SVS(VA, INCA, VC, NN) Ident (R:I) : 022:177515B

Explanation¶

Form the sum of the elements of a vector, where each element at first is multiplied with the absolute value of itself.

[ VC = VA_1 \times |VA_1| + VA_2 \times |VA_2| + \ldots + VAnn \times |VAnn| ]

'nn' is the element count.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC.
NN	Element count.

Listing¶

SUBROUTINE SVS(VA, INCA, VC, NN)
IMPLICIT DOUBLE PRECISION (A-H, O-Z)
DIMENSION VA(1)
IA = 1
SUM = 0.0
DO FOR M = 1, NN
    SUM = SUM + VA(IA) * ABS(VA(IA))
    IA = IA + INCA
ENDDO
VC = SUM
RETURN
END

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ARRAY PROCESSING FUNCTIONS

4.21 MEAN MAGNITUDE VALUE OF VECTOR (MEAMGV)¶

Format¶

MEAMGV(VA,INCA,VC,NN) Ident (R:I) : 023:177515B

Explanation¶

Form the mean value of the absolute values of the elements of a vector. VC = ( |VA₁| + |VA₂| + ....+ |VAnn| ) / nn , 'nn' is the element count.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC.
NN	Element count.

Listing¶

SUBROUTINE MEAMGV(VA,INCA,VC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1)
IA = 1
SUM = 0.0
DO FOR M = 1,NN
    SUM = SUM + ABS(VA(IA))
    IA = IA + INCA
ENDDO
VC = SUM/NN
RETURN
END

Page 46¶

4.22 Maximum Value in Vector (MAXV)¶

Format¶

MAXV(VA,INCA,VC,IC,NN) Ident (R:I) : 024:177515B

Explanation¶

Scan a vector for its element with maximum value and return this together with the corresponding index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC, containing max. value.
IC	Index in VA for max. value.
NN	Element count.

Listing¶

SUBROUTINE MAXV(VA,INCA,VC,IC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1)
IA = 1
VC = VA(IA)
IC = IA
DO FOR M = 2,NN
  IA = IA + INCA
  IF (VA(IA) .GT. VC) THEN
    VC = VA(IA)
    IC = IA
  ENDIF
ENDDO
RETURN
END

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ND-500/2 Double Precision Array Processing Functions¶

4.23 Minimum Value in Vector (MINV)¶

Format¶

MINV(VA, INCA, VC, IC, NN) Ident (R:I) : 025:177515B

Explanation¶

Scan a vector for its element with minimum value and return this together with the corresponding index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC, containing min. value.
IC	Index in VA for min. value.
NN	Element count.

Listing¶

SUBROUTINE MINV(VA, INCA, VC, IC, NN)
IMPLICIT DOUBLE PRECISION (A-H, O-Z)
DIMENSION VA(1)
IA = 1
VC = VA(IA)
IC = IA
DO FOR M = 2, NN
  IA = IA + INCA
  IF (VA(IA) .LT. VC) THEN
    VC = VA(IA)
    IC = IA
  ENDIF
ENDDO
RETURN
END

Page 48¶

4.24 MAXIMUM MAGNITUDE VALUE IN VECTOR (MAXMGV)¶

Format¶

MAXMGV(VA,INCA,VC,IC,NN)
Ident (R:I) : 026:177515B

Explanation¶

Scan a vector for its element with maximum absolute value, and return this together with the corresponding index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC, containing max. absolute value.
IC	Index in VA for max. absolute value.
NN	Element count.

Listing¶

SUBROUTINE MAXMGV(VA,INCA,VC,IC,NN)  
IMPLICIT DOUBLE PRECISION (A-H,O-Z)  
DIMENSION VA(1)  
IA = 1  
VC = ABS(VA(IA))  
IC = IA  
DO FOR M = 2,NN  
    IA = IA + INCA  
    VAABS = ABS(VA(IA))  
    IF (VAABS .GT. VC) THEN  
        VC = VAABS  
        IC = IA  
    ENDIF  
ENDDO  
RETURN  
END

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

4.25 MINIMUM MAGNITUDE VALUE IN VECTOR (MINMGV)¶

Format¶

MINMGV(VA,INCA,VC,IC,NN)
Ident (R:I) : 027:177515B

Explanation¶

Scan a vector for its element with minimum absolute value, and return this together with the corresponding index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC, containing min. absolute value.
IC	Index in VA for min. absolute value.
NN	Element count.

Listing¶

SUBROUTINE MINMGV(VA,INCA,VC,IC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1)
IA = 1
VC = ABS(VA(IA))
IC = IA
DO FOR M = 2,NN
    IA = IA + INCA
    VAABS = ABS(VA(IA))
    IF (VAABS .LT. VC) THEN
        VC = VAABS
        IC = IA
    ENDIF
ENDDO
RETURN
END

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4.26 Maximum and Minimum Value in Vector (MAXMIN)¶

Format¶

MAXMIN(VA,INCA,VC,IC,VD,ID,NN) Ident (R:I) : 030:177515B

Explanation¶

Scan a vector for its element with minimum value and its element with maximum value, and return these together with the corresponding indices.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC, containing max. value.
IC	Index in VA for max. value.
VD	Name of output scalar VD, containing min. value.
ID	Index in VA for min. value.
NN	Element count.

Listing¶

SUBROUTINE MAXMIN(VA,INCA,VC,IC,VD,ID,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1)
IA = 1
VC = VA(IA)
VD = VA(IA)
IC = IA
ID = IA
DO FOR M = 2,NN
  IA = IA + INCA
  IF (VA(IA) .GT. VC) THEN
    VC = VA(IA)
    IC = IA
  ELSEIF (VA(IA) .LT. VD) THEN
    VD = VA(IA)
    ID = IA
  ENDIF
ENDDO
RETURN
END

Page 51¶

4.27 Maximum and Minimum Magnitude Value in Vector (MXMNMG)¶

Format¶

MXMNMG(VA,INCA,VC,IC,VD,ID,NN) Ident (R:I) : 031:177515B

Explanation¶

Scan a vector for its element with minimum absolute value and its element with maximum absolute value, and return these values together with the corresponding indices.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VC	Name of output scalar VC, containing max. absolute value.
IC	Index in VA for max. absolute value.
VD	Name of output scalar VD, containing min. absolute value.
ID	Index in VA for min. absolute value.
NN	Element count.

Listing¶

SUBROUTINE MXMNMG(VA,INCA,VC,IC,VD,ID,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1)
IA = 1
VC = ABS(VA(IA))
VD = ABS(VA(IA))
IC = IA
ID = IA
DO FOR M = 2,NN
  IA = IA + INCA
  VAABS = ABS(VA(IA))
  IF (VAABS .GT. VC) THEN
    VC = VAABS
    IC = IA
  ELSEIF (VAABS .LT. VD) THEN
    VD = VAABS
    ID = IA
  ENDIF
ENDDO
RETURN
END

Page 52¶

4.28 VECTOR SCALAR MULTIPLY AND ADD (VSMA)¶

Format¶

VSMA(VA,INCA,SC,VB,INCB,VC,INCC,NN) Ident (R:I) : 053:177515B

Explanation¶

Add the corresponding elements from two vectors, where the elements of one of the vectors are multiplied with a scalar value.
VCn = VAn * SC + VBn, where 'SC' denotes the scalar, and 'n' denotes the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
SC	Scalar value.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VSMA(VA,INCA,SC,VB,INCB,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1), VB(1), VC(1)
IA = 1
IB = 1
IC = 1
DO FOR I = 1,NN
    VC(IC) = VA(IA)*SC + VB(IB)
    IA = IA + INCA
    IB = IB + INCB
    IC = IC + INCC
ENDDO
RETURN
END

Page 53¶

4.29 VECTOR SCALAR ADD (VSADD)¶

Format¶

VSADD(VA,INCA,B,VC,INCC,NN) Ident (R:I) : 032:177515B

Explanation¶

Add the elements of a vector together with a scalar value.
VCn = VAn + b, where 'b' denotes the scalar, and 'n' denotes the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
B	Scalar B.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VSADD(VA,INCA,B,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1), VB(1), VC(1)
IA = 1
IC = 1
DO FOR M = 1,NN
  VC(IC) = B + VA(IA)
  IA = IA + INCA
  IC = IC + INCC
ENDDO
RETURN
END

Page 54¶

4.30 Vector Scalar Multiply (VSMUL)¶

Format¶

VSMUL(VA,INCA,B,VC,INCC,NN)
Ident (R:I) : 033:177515B

Explanation¶

Multiply the elements of a vector with a scalar value.
VCn = VAn * B, where 'b' denotes the scalar, and 'n' denotes the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
B	Scalar B.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VSMUL(VA,INCA,B,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1), VB(1), VC(1)
IA = 1
IC = 1
DO FOR M = 1,NN
    VC(IC) = B * VA(IA)
    IA = IA + INCA
    IC = IC + INCC
ENDDO
RETURN
END

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4.31 Vector Scalar Divide (VDIVS)¶

Format¶

VDIVS(VA,INCA,B,VC,INCC,NN) Ident (R:I) : 034:177515B

Explanation¶

Form a vector from a scalar value divided with the elements of another vector. VCn = b/VAn, 'b' denotes the scalar and 'n' denotes the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
B	Scalar B.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VDIVS(VA,INCA,B,VC,INCC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1), VB(1), VC(1)
IA = 1
IC = 1
DO FOR M = 1,NN
  VC(IC) = B / VA(IA)
  IA = IA + INCA
  IC = IC + INCC
ENDDO
RETURN
END

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4.32 DOT PRODUCT (DOTPR)¶

Format¶

DOTPR(VA,INCA,VB,INCB,VC,NN) \
Ident (R:I) : 035:177515B

Explanation¶

Add the product of the corresponding elements of two vectors. This function corresponds to the mathematical dot product, also called scalar product, of two vectors.
VC = VA * VB + VA * VB + .... + VAnn * VBnn , 'nn' is the element count.
1 1 2 2

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output scalar VC.
NN	Element count.

Listing¶

SUBROUTINE DOTPR(VA,INCA,VB,INCB,VC,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VB(1)
IA = 1
IB = 1
SUM = 0.0
DO FOR M = 1,NN
   SUM = SUM + VA(IA)*VB(IB)
   IA = IA + INCA
   IB = IB + INCB
ENDDO
VC = SUM
RETURN
END

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ARRAY PROCESSING FUNCTIONS¶

4.33 VECTOR CLEAR (VCLR)¶

Format¶

VCLR(VC, INCC, NN)  Ident (R:I) : 036:177515B

Explanation¶

Set the elements of a vector to all zeros.

Parameters¶

Parameter	Description
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VCLR(VC, INCC, NN)
IMPLICIT DOUBLE PRECISION (A-H, O-Z)
DIMENSION VC(1)
IC = 1
DO FOR M = 1, NN
    VC(IC) = 0.0
    IC = IC + INCC
ENDDO
RETURN
END

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4.34 Complex Vector Multiply (CVMUL)¶

Format¶

CVMUL(VA,INCA,VB,INCB,VC,INCC,NN,NE) Ident (R:I) : 040:177515B

Explanation¶

Multiply two complex vectors. This function corresponds to mathematical multiplication of complex numbers. An own flag selects whether the result should be conjugated or not. VA = VAr + VAi, VB = VBr + VBi.

If the conjugate flag ≥ 0 then:

VC = (VAr * VBr - VAiVBi)r + (VArVBi + VAi*VBr)i, else:

VC = (VAr * VBr - VAiVBi)r - (VArVBi + VAi*VBr)i.

'r' and 'i' denotes real and imaginary elements.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INCA	VA index increment.
VB	Name of input vector VB.
INCB	VB index increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.
NF	Conjugate flag.

NF = +1 : Normal complex multiply.
NF = -1 : Multiply with conjugate of VA.

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ARRAY PROCESSING FUNCTIONS¶

Listing¶

SUBROUTINE CVMUL(VA,INCA,VB,INCB,VC,INCC,NN,NF)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
COMPLEX*16 VA(1),VB(1),VC(1)
IA = 1
IB = 1
IC = 1
DO FOR M = 1,NN
    ARE = VA(IA)
    BRE = VB(IB)
    AIM = DIMAG(VA(IA))
    BIM = DIMAG(VB(IB))
    IF (NF .LT. 0) AIM = -AIM
    CRE = ARE*BRE - AIM*BIM
    CIM = ARE*BIM + AIM*BRE
    VC(IC) = CMPLX(CRE,CIM)
    IA = IA + INCA
    IB = IB + INCB
    IC = IC + INCC
ENDDO
RETURN
END

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4.35 VECTOR TAPER (VTAPER)¶

Format¶

VTAPER(VA,VC,NN,IFLAG) Ident (R:I) : 041:177515B

Explanation¶

Multiply each element of a vector with an increasing or decreasing factor. An own flag selects either the decreasing or the increasing factor. The factor is a function of the element count.

If flag > 0 then:

[ VC_1 = VA_1 * (1/nn) ]
[ VC_2 = VA_2 * (2/nn) ]
[ \ldots ]
[ VCnn = VAnn * (1) ]

So the general element equation is:
[ VCn = VAn * (n/nn) ]

If flag ≤ 0 then:

[ VC_1 = VA_1 * (1 - 1/nn) ]
[ VC_2 = VA_2 * (1 - 2/nn) ]
[ \ldots ]
[ VCnn = VAnn * (0) ]

So the general element equation is:
[ VCn = VAn * (1 - n/nn) ]

'nn' denotes the element count and 'n' the element index.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
VC	Name of output vector VC.
NN	Element count.
IFLAG	Flag.

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ND-500/2 Double Precision Array Processing Functions¶

Array Processing Functions¶

Listing¶

SUBROUTINE VTAPER(VA,VC,NN,IFLAG)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1),VC(1)
ONE = 1.0
IF (IFLAG .LE. 0) GO TO 10
DMULT = ONE/NN
DMINC = DMULT
GO TO 20
10 CONTINUE
DMULT = (NN-1)*ONE/NN
DMINC = -ONE/NN
20 CONTINUE
DO 30 I = 1,NN
  VC(I) = VA(I)*DMULT
  DMULT = DMULT + DMINC
30 CONTINUE
RETURN
END

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ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ARRAY PROCESSING FUNCTIONS

4.36 VECTOR RAMP FUNCTION (VRAMP)¶

Format¶

VRAMP(SCALAR, SCINC, VC, INCC, NN) Ident (R:I) : 043:177515B

Explanation¶

Form a vector as a ramp function with a start value and a slope as input parameters.

[ VC_1 = sc + scinc, \ VC_2 = sc + 2 \times scinc \ .. \ VC_{nn} = sc + nn \times scinc. ]

So the general element expression is: VCn = sc + n * scinc.

'nn' denotes the element count, 'n' the element index, 'sc' start value, and 'scinc' slope.

Parameters¶

Parameter	Description
SCALAR	Scalar for start value.
SCINC	Scalar for increment.
VC	Name of output vector VC.
INCC	VC index increment.
NN	Element count.

Listing¶

SUBROUTINE VRAMP(SCALAR, SCINC, VC, INCC, NN)
IMPLICIT DOUBLE PRECISION (A-H, O-Z)
DIMENSION VC(1)
IC = 1
SC = SCALAR
DO FOR I = 1, NN
  VC(IC) = SC
  IC = IC + INCC
  SC = SC + SCINC
ENDDO
RETURN
END

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4.37 VECTOR FIRST AND LAST NON-ZERO VALUE (VFLNZ)¶

Format¶

VFLNZ(VA,INDF,INDL,NN)
Ident (R:I) : 051:177515B

Explanation¶

Find the indices of the first and last non-zero elements in a vector.

Parameters¶

Parameter	Description
VA	Name of input vector VA.
INDF	Name for first non-zero index.
INDL	Name for last non-zero index.
NN	Element count.

Listing¶

SUBROUTINE VFLNZ(VA,INDF,INDL,NN)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION VA(1)
DO 100 I = 1,NN
    IF (VA(I) .NE. 0.0) THEN
        INDF = I
        GO TO 105
    ENDIF
100 CONTINUE
INDF = NN
INDL = 1
GO TO 205
105 CONTINUE
DO 200 I = NN,1,-1
    IF (VA(I) .NE. 0.0) THEN
        INDL = I
        GO TO 205
    ENDIF
200 CONTINUE
205 RETURN
END

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ND-500/2 Double Precision Array Processing Functions¶

Array Processing Functions¶

ND-05.018.01

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Index¶

APD library ....................................... 1
array processing, definition ...................... 1, 2
basic concepts .................................... 1
complex vector .................................... 3
complex vector, definition ........................ 2
complex vector multiply ........................... 46
CVMUL ............................................. 46
dot product ....................................... 44
DOTPR ............................................. 44
elements, definition .............................. 2
element count, definition ......................... 3
floating point
- accuracy ........................................ 1
- format .......................................... 1
hardware concepts ................................. 1
increment, definition ............................. 3
installation of software .......................... 1
maximum and minimum magnitude value in vector ..... 39
maximum and minimum value in vector ............... 38
maximum magnitude value in vector ................. 36
maximum value in vector ........................... 34
MAXMGV ............................................ 36
MAXMIN ............................................ 38
MAXMV ............................................. 34
MEAMGV ............................................ 33
mean magnitude value of vector .................... 33
memory management system .......................... 1
microprogram ...................................... 1
minimum magnitude value in vector ................. 37
minimum value in vector ........................... 35
MINMGV ............................................ 37
MINMV ............................................. 35
MXMNMG ............................................ 39
parallel processing ............................... 1
parameters, specification ......................... 3
performance ....................................... 11
sum of vector elements ............................ 29
sum of vector elements magnitude .................. 30
sum of vector elements signed square .............. 32
sum of vector elements square ..................... 31
SVE ............................................... 29
SVEMG ............................................. 30
SVESQ ............................................. 31
SVS ............................................... 32
use of processing functions ....................... 5
VABS .............................................. 24
VADD .............................................. 14
VCLR .............................................. 45
VDIV .............................................. 17
VDIVS ............................................. 43
vector
- absolute value .................................. 24

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ND-500/2 Double Precision Array Processing Functions¶

Index¶

Function	Page
add	14
clear	45
divide	17
first and last non-zero value	51
maximum	18
maximum magnitude	20
minimum	19
minimum magnitude	21
move	26
multiply	16
negative	28
ramp function	50
scalar add	41
scalar divide	43
scalar multiply	42
scalar multiply and add	40
signed square	23
square	22
square root	25
subtract	15
swap	27
taper	48

Vector¶

Definition	Page
definition	2
name	3
VFLNZ	51
VMAX	18
VMAXMG	20
VMIN	19
VMINMG	21
VMOV	26
VMUL	16
VNEG	28
VRAMP	50
VSADD	41
VSMA	40
VSMUL	42
VSQ	22
VSQRT	25
VSSQ	23
VSUB	15
VSWAP	27
VTAPER	48

ND-05.018.01

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Page 1¶

ND-500/2 Double Precision Array Processing Functions¶

Page 2¶

Page 3¶

ND-500/2 Double Precision Array Processing Functions¶

Page 4¶

Page 5¶

Manual Information¶

Bindings and Covers¶

Order Form¶

Page 6¶

Page 7¶

PRINTING RECORD¶

Page 8¶

Manual Updates¶

Contact Information¶

Page 9¶

Preface¶

THE PRODUCT¶

THE MANUAL¶

THE READER¶

Page 10¶

PREREQUISITE KNOWLEDGE¶

RELATED MANUALS¶

Page 11¶

Table of Contents¶

Page 12¶

Table of Contents¶

Index¶

Page 13¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

1 BASIC CONCEPTS¶

1.1 PREREQUISITE SOFTWARE FOR USING THE APD LIBRARY¶

1.2 THE DOUBLE PRECISION FLOATING POINT FORMAT¶

1.3 HARDWARE CONCEPTS¶

Page 14¶

1.4 Array Processing Definitions¶

Example of Equations:¶

Page 15¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

BASIC CONCEPTS¶

Example of Use of a DAX Function¶

Page 16¶

Example of Use of a Complex DAX Function¶

Page 17¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS USING THE ND-500/2 DAX FUNCTIONS¶

2 USING THE ND-500/2 DAX FUNCTIONS¶

Example of Creating a FORTRAN Program Using DAX Functions¶

Source Program in FORTRAN:¶

The program continues on next page...¶

Page 18¶

ND-500/2 Double Precision Array Processing Functions¶

Using the ND-500/2 DAX Functions¶

Page 19¶

ND-500/2 Double Precision Array Processing Functions¶

Using the ND-500/2 DAX Functions¶

Compiling the Program¶

Page 20¶

Loading the Program¶

Page 21¶

Executing the Program¶

Page 22¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

Page 23¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ND-500/2 DAX FUNCTIONS PERFORMANCE¶

3 ND-500/2 DAX FUNCTIONS PERFORMANCE¶

Page 24¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

ND-500/2 DAX FUNCTIONS PERFORMANCE¶

Page 25¶

ND-500/2 DOUBLE PRECISION ARRAY PROCESSING FUNCTIONS¶

4 ARRAY PROCESSING FUNCTIONS¶

4.1 INTRODUCTION¶

Page 26¶

4.2 VECTOR ADD (VADD)¶

Format¶

Explanation¶

Parameters¶

Listing¶