Open Document Format for Office Applications (OpenDocument) Version 1.2

Part 2: Recalculated Formula (OpenFormula) Format

Committee Draft 05

19 June 2010

Specification URIs:

This Version:

http://docs.oasis-open.org/office/v1.2/cd05/OpenDocument-v1.2-cd05-part2.odt (Authoritative)
http://docs.oasis-open.org/office/v1.2/cd05/OpenDocument-v1.2-cd05-part2.pdf
http://docs.oasis-open.org/office/v1.2/cd05/OpenDocument-v1.2-cd05-part2.html

Previous Version:

http://docs.oasis-open.org/office/v1.1/OS/OpenDocument-v1.1.odt
http://docs.oasis-open.org/office/v1.1/OS/OpenDocument-v1.1.pdf
http://docs.oasis-open.org/office/v1.1/OS/OpenDocument-v1.1-html/OpenDocument-v1.1.html

Latest Version:

http://docs.oasis-open.org/office/v1.2/OpenDocument-v1.2-part2.odt
http://docs.oasis-open.org/office/v1.2/OpenDocument-v1.2-part2.pdf
http://docs.oasis-open.org/office/v1.2/OpenDocument-v1.2-part2.html

Technical Committee:

OASIS Open Document Format for Office Applications (OpenDocument) TC

Chairs:

Robert Weir, IBM
Michael Brauer, Oracle Corporation

Editors:

David A. Wheeler <dwheeler@dwheeler.com>,

Patrick Durusau <patrick@durusau.net>
Eike Rathke, Oracle Corporation <erack@sun.com>
Robert Weir, IBM <robert_weir@us.ibm.com>

Related Work:

This document is part of the OASIS Open Document Format for Office Applications (OpenDocument) Version 1.2 specification.

The OpenDocument v1.2 specification has these parts:

OpenDocument v1.2 part 1; OpenDocument Schema
OpenDocument v1.2 part 2 (this part): Recalculated Formula (OpenFormula) Format
OpenDocument v1.2 part 3: Packages

Declared XML Namespaces:

None.

Abstract:

This document is part of the Open Document Format for Office Applications (OpenDocument) Version 1.2 specification.

It defines a formula language to be used in OpenDocument documents.

Status:

This document was last revised or approved by the OASIS Open Document Format for Office Applications (OpenDocument) Technical Committee on the above date. The level of approval is also listed above. Check the current location noted above for possible later revisions of this document. This document is updated periodically on no particular schedule.

Technical Committee members should send comments on this specification to the Technical Committee's email list. Others should send comments to the Technical Committee by using the "Send A Comment" button on the Technical Committee's web page at

www.oasis-open.org/committees/office.

For information on whether any patents have been disclosed that may be essential to implementing this specification, and any offers of patent licensing terms, please refer to the Intellectual Property Rights section of the Technical Committee web page

(www.oasis-open.org/committees/office/ipr.php.

The non-normative errata page for this specification is located at www.oasis-open.org/committees/office.

Notices

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Table of Contents

1 Introduction

1.1 Introduction

1.2 Terminology

1.3 Purpose

1.4 Normative References

1.5 Non-Normative References

2 Expressions and Evaluators

2.1 OpenDocument Formula Expression

2.2 Evaluators

2.2.1 OpenDocument Formula Evaluator

2.2.2 OpenDocument Formula Small Group Evaluator

2.2.3 OpenDocument Formula Medium Group Evaluator

2.2.4 OpenDocument Formula Large Group Evaluator

2.3 Variances (Implementation-defined, Unspecified, and Behavioral Changes)

3 Formula Processing Model

3.1 General

3.2 Expression Calculation

3.3 Non-Scalar Evaluation (aka 'Array expressions')

3.4 Host-Defined Behaviors

3.5 When recalculation occurs

3.6 Numerical Models

3.7 Basic Limits

4 Types

4.1 General

4.2 Text (String)

4.3 Number

4.3.1 General

4.3.2 Time

4.3.3 Date

4.3.4 DateTime

4.3.5 Percentage

4.3.6 Currency

4.3.7 Logical (Number)

4.4 Complex Number

4.5 Logical (Boolean)

4.6 Error

4.7 Empty Cell

4.8 Reference

4.9 ReferenceList

4.10 Array

4.11 Pseudotypes

4.11.1 General

4.11.2 Scalar

4.11.3 DateParam

4.11.4 TimeParam

4.11.5 Integer

4.11.6 Basis

4.11.7 Criterion

4.11.8 Database

4.11.9 Field

4.11.10 Criteria

4.11.11 Sequences (NumberSequence, NumberSequenceList, DateSequence, LogicalSequence, and ComplexSequence)

5 Expression Syntax

5.1 General

5.2 Basic Expressions

5.3 Constant Numbers

5.4 Constant Strings

5.5 Operators

5.6 Functions and Function Parameters

5.7 Nonstandard Function Names

5.8 References

5.9 Reference List

5.10 Quoted Label

5.10.1 General

5.10.2 Lookup of Defined Labels

5.10.3 Automatic Lookup of Labels

5.10.4 Implicit Intersection

5.10.5 Automatic Range

5.10.6 Automatic Intersection

5.11 Named Expressions

5.12 Constant Errors

5.13 Inline Arrays

5.14 Whitespace

6 Standard Operators and Functions

6.1 General

6.2 Common Template for Functions and Operators

6.3 Implicit Conversion Operators

6.3.1 General

6.3.2 Conversion to Scalar

6.3.3 Implied intersection

6.3.4 Force to array context (ForceArray)

6.3.5 Conversion to Number

6.3.6 Conversion to Integer

6.3.7 Conversion to NumberSequence

6.3.8 Conversion to NumberSequenceList

6.3.9 Conversion to DateSequence

6.3.10 Conversion to Complex Number

6.3.11 Conversion to ComplexSequence

6.3.12 Conversion to Logical

6.3.13 Conversion to LogicalSequence

6.3.14 Conversion to Text

6.3.15 Conversion to DateParam

6.3.16 Conversion to TimeParam

6.4 Standard Operators

6.4.1 General

6.4.2 Infix Operator "+"

6.4.3 Infix Operator "-"

6.4.4 Infix Operator "*"

6.4.5 Infix Operator "/"

6.4.6 Infix Operator "^"

6.4.7 Infix Operator "="

6.4.8 Infix Operator "<>"

6.4.9 Infix Operator Ordered Comparison ("<", "<=", ">", ">=")

6.4.10 Infix Operator "&"

6.4.11 Infix Operator Reference Range (":")

6.4.12 Infix Operator Reference Intersection ("!")

6.4.13 Infix Operator Reference Concatenation ("~") (aka Union)

6.4.14 Postfix Operator "%"

6.4.15 Prefix Operator "+"

6.4.16 Prefix Operator "-"

6.5 Matrix Functions

6.5.1 General

6.5.2 MDETERM

6.5.3 MINVERSE

6.5.4 MMULT

6.5.5 MUNIT

6.5.6 TRANSPOSE

6.6 Bit operation functions

6.6.1 General

6.6.2 BITAND

6.6.3 BITLSHIFT

6.6.4 BITOR

6.6.5 BITRSHIFT

6.6.6 BITXOR

6.7 Byte-position text functions

6.7.1 General

6.7.2 FINDB

6.7.3 LEFTB

6.7.4 LENB

6.7.5 MIDB

6.7.6 REPLACEB

6.7.7 RIGHTB

6.7.8 SEARCHB

6.8 Complex Number Functions

6.8.1 General

6.8.2 COMPLEX

6.8.3 IMABS

6.8.4 IMAGINARY

6.8.5 IMARGUMENT

6.8.6 IMCONJUGATE

6.8.7 IMCOS

6.8.8 IMCOT

6.8.9 IMCSC

6.8.10 IMCSCH

6.8.11 IMDIV

6.8.12 IMEXP

6.8.13 IMLN

6.8.14 IMLOG10

6.8.15 IMLOG2

6.8.16 IMPOWER

6.8.17 IMPRODUCT

6.8.18 IMREAL

6.8.19 IMSIN

6.8.20 IMSEC

6.8.21 IMSECH

6.8.22 IMSQRT

6.8.23 IMSUB

6.8.24 IMSUM

6.8.25 IMTAN

6.9 Database Functions

6.9.1 General

6.9.2 DAVERAGE

6.9.3 DCOUNT

6.9.4 DCOUNTA

6.9.5 DGET

6.9.6 DMAX

6.9.7 DMIN

6.9.8 DPRODUCT

6.9.9 DSTDEV

6.9.10 DSTDEVP

6.9.11 DSUM

6.9.12 DVAR

6.9.13 DVARP

6.10 Date and Time Functions

6.10.1 General

6.10.2 DATE

6.10.3 DATEDIF

6.10.4 DATEVALUE

6.10.5 DAY

6.10.6 DAYS

6.10.7 DAYS360

6.10.8 EDATE

6.10.9 EOMONTH

6.10.10 HOUR

6.10.11 ISOWEEKNUM

6.10.12 MINUTE

6.10.13 MONTH

6.10.14 NETWORKDAYS

6.10.15 NOW

6.10.16 SECOND

6.10.17 TIME

6.10.18 TIMEVALUE

6.10.19 TODAY

6.10.20 WEEKDAY

6.10.21 WEEKNUM

6.10.22 WORKDAY

6.10.23 YEAR

6.10.24 YEARFRAC

6.11 External Access Functions

6.11.1 General

6.11.2 DDE

6.11.3 HYPERLINK

6.12 Financial Functions

6.12.1 General

6.12.2 ACCRINT

6.12.3 ACCRINTM

6.12.4 AMORDEGRC

6.12.5 AMORLINC

6.12.6 COUPDAYBS

6.12.7 COUPDAYS

6.12.8 COUPDAYSNC

6.12.9 COUPNCD

6.12.10 COUPNUM

6.12.11 COUPPCD

6.12.12 CUMIPMT

6.12.13 CUMPRINC

6.12.14 DB

6.12.15 DDB

6.12.16 DISC

6.12.17 DOLLARDE

6.12.18 DOLLARFR

6.12.19 DURATION

6.12.20 EFFECT

6.12.21 FV

6.12.22 FVSCHEDULE

6.12.23 INTRATE

6.12.24 IPMT

6.12.25 IRR

6.12.26 ISPMT

6.12.27 MDURATION

6.12.28 MIRR

6.12.29 NOMINAL

6.12.30 NPER

6.12.31 NPV

6.12.32 ODDFPRICE

6.12.33 ODDFYIELD

6.12.34 ODDLPRICE

6.12.35 ODDLYIELD

6.12.36 PDURATION

6.12.37 PMT

6.12.38 PPMT

6.12.39 PRICE

6.12.40 PRICEDISC

6.12.41 PRICEMAT

6.12.42 PV

6.12.43 RATE

6.12.44 RECEIVED

6.12.45 RRI

6.12.46 SLN

6.12.47 SYD

6.12.48 TBILLEQ

6.12.49 TBILLPRICE

6.12.50 TBILLYIELD

6.12.51 VDB

6.12.52 XIRR

6.12.53 XNPV

6.12.54 YIELD

6.12.55 YIELDDISC

6.12.56 YIELDMAT

6.13 Information Functions

6.13.1 General

6.13.2 AREAS

6.13.3 CELL

6.13.4 COLUMN

6.13.5 COLUMNS

6.13.6 COUNT

6.13.7 COUNTA

6.13.8 COUNTBLANK

6.13.9 COUNTIF

6.13.10 COUNTIFS

6.13.11 ERROR.TYPE

6.13.12 FORMULA

6.13.13 INFO

6.13.14 ISBLANK

6.13.15 ISERR

6.13.16 ISERROR

6.13.17 ISEVEN

6.13.18 ISFORMULA

6.13.19 ISLOGICAL

6.13.20 ISNA

6.13.21 ISNONTEXT

6.13.22 ISNUMBER

6.13.23 ISODD

6.13.24 ISREF

6.13.25 ISTEXT

6.13.26 N

6.13.27 NA

6.13.28 NUMBERVALUE

6.13.29 ROW

6.13.30 ROWS

6.13.31 SHEET

6.13.32 SHEETS

6.13.33 TYPE

6.13.34 VALUE

6.14 Lookup Functions

6.14.1 General

6.14.2 ADDRESS

6.14.3 CHOOSE

6.14.4 GETPIVOTDATA

6.14.5 HLOOKUP

6.14.6 INDEX

6.14.7 INDIRECT

6.14.8 LOOKUP

6.14.9 MATCH

6.14.10 MULTIPLE.OPERATIONS

6.14.11 OFFSET

6.14.12 VLOOKUP

6.15 Logical Functions

6.15.1 General

6.15.2 AND

6.15.3 FALSE

6.15.4 IF

6.15.5 IFERROR

6.15.6 IFNA

6.15.7 NOT

6.15.8 OR

6.15.9 TRUE

6.15.10 XOR

6.16 Mathematical Functions

6.16.1 General

6.16.2 ABS

6.16.3 ACOS

6.16.4 ACOSH

6.16.5 ACOT

6.16.6 ACOTH

6.16.7 ASIN

6.16.8 ASINH

6.16.9 ATAN

6.16.10 ATAN2

6.16.11 ATANH

6.16.12 BESSELI

6.16.13 BESSELJ

6.16.14 BESSELK

6.16.15 BESSELY

6.16.16 COMBIN

6.16.17 COMBINA

6.16.18 CONVERT

6.16.19 COS

6.16.20 COSH

6.16.21 COT

6.16.22 COTH

6.16.23 CSC

6.16.24 CSCH

6.16.25 DEGREES

6.16.26 DELTA

6.16.27 ERF

6.16.28 ERFC

6.16.29 EUROCONVERT

6.16.30 EVEN

6.16.31 EXP

6.16.32 FACT

6.16.33 FACTDOUBLE

6.16.34 GAMMA

6.16.35 GAMMALN

6.16.36 GCD

6.16.37 GESTEP

6.16.38 LCM

6.16.39 LN

6.16.40 LOG

6.16.41 LOG10

6.16.42 MOD

6.16.43 MULTINOMIAL

6.16.44 ODD

6.16.45 PI

6.16.46 POWER

6.16.47 PRODUCT

6.16.48 QUOTIENT

6.16.49 RADIANS

6.16.50 RAND

6.16.51 RANDBETWEEN

6.16.52 SEC

6.16.53 SERIESSUM

6.16.54 SIGN

6.16.55 SIN

6.16.56 SINH

6.16.57 SECH

6.16.58 SQRT

6.16.59 SQRTPI

6.16.60 SUBTOTAL

6.16.61 SUM

6.16.62 SUMIF

6.16.63 SUMIFS

6.16.64 SUMPRODUCT

6.16.65 SUMSQ

6.16.66 SUMX2MY2

6.16.67 SUMX2PY2

6.16.68 SUMXMY2

6.16.69 TAN

6.16.70 TANH

6.17 Rounding Functions

6.17.1 General

6.17.2 CEILING

6.17.3 INT

6.17.4 FLOOR

6.17.5 MROUND

6.17.6 ROUND

6.17.7 ROUNDDOWN

6.17.8 ROUNDUP

6.17.9 TRUNC

6.18 Statistical Functions

6.18.1 General

6.18.2 AVEDEV

6.18.3 AVERAGE

6.18.4 AVERAGEA

6.18.5 AVERAGEIF

6.18.6 AVERAGEIFS

6.18.7 BETADIST

6.18.8 BETAINV

6.18.9 BINOM.DIST.RANGE

6.18.10 BINOMDIST

6.18.11 LEGACY.CHIDIST

6.18.12 CHISQDIST

6.18.13 LEGACY.CHIINV

6.18.14 CHISQINV

6.18.15 LEGACY.CHITEST

6.18.16 CONFIDENCE

6.18.17 CORREL

6.18.18 COVAR

6.18.19 CRITBINOM

6.18.20 DEVSQ

6.18.21 EXPONDIST

6.18.22 FDIST

6.18.23 LEGACY.FDIST

6.18.24 FINV

6.18.25 LEGACY.FINV

6.18.26 FISHER

6.18.27 FISHERINV

6.18.28 FORECAST

6.18.29 FREQUENCY

6.18.30 FTEST

6.18.31 GAMMADIST

6.18.32 GAMMAINV

6.18.33 GAUSS

6.18.34 GEOMEAN

6.18.35 GROWTH

6.18.36 HARMEAN

6.18.37 HYPGEOMDIST

6.18.38 INTERCEPT

6.18.39 KURT

6.18.40 LARGE

6.18.41 LINEST

6.18.42 LOGEST

6.18.43 LOGINV

6.18.44 LOGNORMDIST

6.18.45 MAX

6.18.46 MAXA

6.18.47 MEDIAN

6.18.48 MIN

6.18.49 MINA

6.18.50 MODE

6.18.51 NEGBINOMDIST

6.18.52 NORMDIST

6.18.53 NORMINV

6.18.54 LEGACY.NORMSDIST

6.18.55 LEGACY.NORMSINV

6.18.56 PEARSON

6.18.57 PERCENTILE

6.18.58 PERCENTRANK

6.18.59 PERMUT

6.18.60 PERMUTATIONA

6.18.61 PHI

6.18.62 POISSON

6.18.63 PROB

6.18.64 QUARTILE

6.18.65 RANK

6.18.66 RSQ

6.18.67 SKEW

6.18.68 SKEWP

6.18.69 SLOPE

6.18.70 SMALL

6.18.71 STANDARDIZE

6.18.72 STDEV

6.18.73 STDEVA

6.18.74 STDEVP

6.18.75 STDEVPA

6.18.76 STEYX

6.18.77 LEGACY.TDIST

6.18.78 TINV

6.18.79 TREND

6.18.80 TRIMMEAN

6.18.81 TTEST

6.18.82 VAR

6.18.83 VARA

6.18.84 VARP

6.18.85 VARPA

6.18.86 WEIBULL

6.18.87 ZTEST

6.19 Number Representation Conversion Functions

6.19.1 General

6.19.2 ARABIC

6.19.3 BASE

6.19.4 BIN2DEC

6.19.5 BIN2HEX

6.19.6 BIN2OCT

6.19.7 DEC2BIN

6.19.8 DEC2HEX

6.19.9 DEC2OCT

6.19.10 DECIMAL

6.19.11 HEX2BIN

6.19.12 HEX2DEC

6.19.13 HEX2OCT

6.19.14 OCT2BIN

6.19.15 OCT2DEC

6.19.16 OCT2HEX

6.19.17 ROMAN

6.20 Text Functions

6.20.1 General

6.20.2 ASC

6.20.3 CHAR

6.20.4 CLEAN

6.20.5 CODE

6.20.6 CONCATENATE

6.20.7 DOLLAR

6.20.8 EXACT

6.20.9 FIND

6.20.10 FIXED

6.20.11 JIS

6.20.12 LEFT

6.20.13 LEN

6.20.14 LOWER

6.20.15 MID

6.20.16 PROPER

6.20.17 REPLACE

6.20.18 REPT

6.20.19 RIGHT

6.20.20 SEARCH

6.20.21 SUBSTITUTE

6.20.22 T

6.20.23 TEXT

6.20.24 TRIM

6.20.25 UNICHAR

6.20.26 UNICODE

6.20.27 UPPER

7 Other Capabilities

7.1 General

7.2 Inline constant arrays

7.3 Inline non-constant arrays

7.4 Year 1583

8 Non-portable Features

8.1 General

8.2 Distinct Logical

8.3 Auto Text to Number

1Introduction

1.1Introduction

This document is part of the Open Document Format for Office Applications (OpenDocument) Version 1.2 specification. It defines a formula language for OpenDocument documents, which is also called OpenFormula.

OpenFormula is a specification of an open format for exchanging recalculated formulas between office applications, in particular, formulas in spreadsheet documents. OpenFormula defines data types, syntax, and semantics for recalculated formulas, including predefined functions and operations.

Using OpenFormula allows document creators to change the office application they use, exchange formulas with others (who may use a different application), and access formulas far in the future, with confidence that the recalculated formulas in their documents will produce equivalent results if given equivalent inputs.

OpenFormula is intended to be a supporting document to the Open Document Format for Office Applications (OpenDocument) format, particularly for defining its attributes table:formula and text:formula. It can also be used in other circumstances where a simple, easy-to-read infix text notation is desired for exchanging recalculated formulas.

 

 

1.2Terminology

All text is normative unless otherwise labeled.

Within the normative text of this specification, the terms "shall", "shall not", "should", "should not", "may" and “need not” are to be interpreted as described in Annex H of [ISO/IEC Directives].

1.3Purpose

OpenFormula defines:

  1. 1.data types 

  2. 2.syntax 

  3. 3.semantics 

for recalculated formulas.

OpenFormula also defines functions.

OpenFormula does not define:

  1. 1.a user interface 

  2. 2.a general notation for mathematical expressions 

 

1.4Normative References

[ISO/IEC Directives]        ISO/IEC Directives, Part 2 (Fifth Edition) Rules for the structure and drafting of International Standards, International Organization for Standardization and International Electrotechnical Commission, 2004.

[ODF11]        OASIS Standard, Open Document Format for Office Applications (OpenDocument) v1.1, February 2007, http://docs.oasis-open.org/office/v1.1/OS/OpenDocument-v1.1.pdf.

[RFC3986]        T. Berners-Lee, R. Fielding, L. Masinter, Uniform Resource Identifier (URI): Generic Syntax, http://www.ietf.org/rfc/rfc3986.txt, IETF, 2005.

[RFC3987]        M. Duerst, M. Suignard, Internationalized Resource Identifiers (IRIs), http://www.ietf.org/rfc/rfc3987.txt, IETF, 2005.

[UNICODE]        The Unicode Consortium. The Unicode Standard, Version 5.2.0, defined by: The Unicode Standard, Version 5.2 (Mountain View, CA, The Unicode Consortium, 2009. ISBN 978-1-936213-00-9). (http://www.unicode.org/versions/Unicode5.2.0/).

[XML1.0]        Tim Bray, Jean Paoli, C. M. Sperberg-McQueen, Eve Maler, François Yergeau , Extensible Markup Language (XML) 1.0 (Fourth Edition), http://www.w3.org/TR/2006/REC-xml-20060816/, W3C, 2006.

1.5Non-Normative References

[JISX0201]        JIS X 0201 (1976) to Unicode 1.1 Table, 1994, http://www.unicode.org/Public/MAPPINGS/OBSOLETE/EASTASIA/JIS/JIS0201.TXT.

[JISX0208]        JIS X 0208 (1990) to Unicode, 1994,  http://www.unicode.org/Public/MAPPINGS/OBSOLETE/EASTASIA/JIS/JIS0208.TXT.

[UAX11]        Asmus Freytag, East Asian Width, Unicode Standard Annex #11, http://www.unicode.org/reports/tr11/tr11-19.html, 2009.

2Expressions and Evaluators

2.1OpenDocument Formula Expression

An OpenDocument formula expression shall adhere to the expression syntax defined in chapter 4. It may use subsets or supersets of OpenFormula.

2.2Evaluators

2.2.1OpenDocument Formula Evaluator

An OpenDocument Formula Evaluator is a program that can parse and recalculate OpenDocument formula expressions, and that meets the following additional requirements:

  1. A)It may implement subsets or supersets of this specification. 

  2. B)It shall conform to one of: (C16) OpenDocument Formula Small Group Evaluator, (C17) OpenDocument Formula Medium Group Evaluator or (C18) OpenDocument Formula Large Group Evaluator 

  3. C)It may implement additional functions beyond those defined in this specification. It may further implement additional formula syntax, additional operations, additional optional parameters for functions, or may consider function parameters to be optional when they are required by this specification. 

  4. D)Applications should clearly document their extensions in their user documentation, both online and paper, in a manner so users would be likely to be aware when they are using a non-standard extension. 

Note: An expression may reference a nonstandard function by name, or depend on implementation-defined behavior, or on semantics not guaranteed by this specification.  Reference to or dependence upon functions or behavior not defined by this standard may impair the interoperability of the resulting expression(s).

Note: This specification defines formulas in terms of a canonical text representation used for exchange. If formulas are contained in XML attributes some characters shall be escaped as required by the XML specification (e.g., the character & shall be escaped in XML attributes using notations such as &amp;). All string and character literals references by this specification are in the value space defined by [UNICODE] thus, “A” is U+0041, “Z” is U+005A, and the range of characters “A-Z” is the range U+0041 through U+005A inclusive.

2.2.2OpenDocument Formula Small Group Evaluator

An OpenDocument Formula Small Group Evaluator is an OpenDocument Formula Evaluator that meets the following additional requirements:

  1. A)It shall implement at least the limits defined in the “Basic Limits” section. 

  2. B)It shall implement the syntax defined in these sections on syntax: Criteria; Basic Expressions; Constant Numbers; Constant Strings; Operators; Functions and Function Parameters; Nonstandard Function Names; References; Simple Named Expressions; Errors; Whitespace. 

  3. C)It shall implement all implicit conversions for the types it implements, at least Text, Conversion to Number, Reference, Conversion to Logical, and Error. 

  4. D)It shall implement the following operators (which are all the operators except reference union (~)): Infix Operator Ordered Comparison ("<", "<=", ">", ">="); Infix Operator "&”; Infix Operator "+”; Infix Operator "-”; Infix Operator "*”; Infix Operator "/”; Infix Operator "^”; Infix Operator "=”; Infix Operator "<>”; Postfix Operator “%”; Prefix Operator “+”; Prefix Operator “-”; Infix Operator Reference Intersection ("!"); Infix Operator Range (":"). 

  5. E)It shall implement at least the following functions as defined in this specification: ABS 6.16.2 ; ACOS 6.16.3 ; AND 6.15.2 ; ASIN 6.16.7 ; ATAN 6.16.9 ; ATAN2 6.16.10 ; AVERAGE 6.18.3 ; AVERAGEIF 6.18.5 ; CHOOSE 6.14.3 ; COLUMNS 6.13.5 ; COS 6.16.19 ; COUNT 6.13.6 ; COUNTA 6.13.7 ; COUNTBLANK 6.13.8 ; COUNTIF 6.13.9 ; DATE 6.10.2 ; DAVERAGE 6.9.2 ; DAY 6.10.5 ; DCOUNT 6.9.3 ; DCOUNTA 6.9.4 ; DDB 6.12.15 ; DEGREES 6.16.25 ; DGET 6.9.5 ; DMAX 6.9.6 ; DMIN 6.9.7 ; DPRODUCT 6.9.8 ; DSTDEV 6.9.9 ; DSTDEVP 6.9.10 ; DSUM 6.9.11 ; DVAR 6.9.12 ; DVARP 6.9.13 ; EVEN 6.16.30 ; EXACT 6.20.8 ; EXP 6.16.31 ; FACT 6.16.32 ; FALSE 6.15.3 ; FIND 6.20.9 ; FV 6.12.21 ; HLOOKUP 6.14.5 ; HOUR 6.10.10 ; IF 6.15.4 ; INDEX 6.14.6 ; INT 6.17.3 ; IRR 6.12.25 ; ISBLANK 6.13.14 ; ISERR 6.13.15 ; ISERROR 6.13.16 ; ISLOGICAL 6.13.19 ; ISNA 6.13.20 ; ISNONTEXT 6.13.21 ; ISNUMBER 6.13.22 ; ISTEXT 6.13.25 ; LEFT 6.20.12 ; LEN 6.20.13 ; LN 6.16.39 ; LOG 6.16.40 ; LOG10 6.16.41 ; LOWER 6.20.14 ; MATCH 6.14.9 ; MAX 6.18.45 ; MID 6.20.15 ; MIN 6.18.48 ; MINUTE 6.10.12 ; MOD 6.16.42 ; MONTH 6.10.13 ; N 6.13.26 ; NA 6.13.27 ; NOT 6.15.7 ; NOW 6.10.15 ; NPER 6.12.30 ; NPV 6.12.31 ; ODD 6.16.44 ; OR 6.15.8 ; PI 6.16.45 ; PMT 6.12.37 ; POWER 6.16.46 ; PRODUCT 6.16.47 ; PROPER 6.20.16 ; PV 6.12.42 ; RADIANS 6.16.49 ; RATE 6.12.43 ; REPLACE 6.20.17 ; REPT 6.20.18 ; RIGHT 6.20.19 ; ROUND 6.17.6 ; ROWS 6.13.30 ; SECOND 6.10.16 ; SIN 6.16.55 ; SLN 6.12.46 ; SQRT 6.16.58 ; STDEV 6.18.72 ; STDEVP 6.18.74 ; SUBSTITUTE 6.20.21 ; SUM 6.16.61 ; SUMIF 6.16.62 ; SYD 6.12.47 ; T 6.20.22 ; TAN 6.16.69 ; TIME 6.10.17 ; TODAY 6.10.19 ; TRIM 6.20.24 ; TRUE 6.15.9 ; TRUNC 6.17.9 ; UPPER 6.20.27 ; VALUE 6.13.34 ; VAR 6.18.82 ; VARP 6.18.84 ; VLOOKUP 6.14.12 ; WEEKDAY 6.10.20 ; YEAR 6.10.23 

  6. F)It need not evaluate references that contain more than one area. 

  7. G)It need not implement inline arrays, complex numbers, and the reference union operator. 

  8. H)For expressions embedded in an OpenDocument document, it shall consider the values of the following host-defined properties: HOST-CASE-SENSITIVE, HOST-PRECISION-AS-SHOWN, HOST-SEARCH-CRITERIA-MUST-APPLY-TO-WHOLE-CELL, HOST-AUTOMATIC-FIND-LABELS, HOST-USE-REGULAR-EXPRESSIONS, HOST-USE-WILDCARDS, HOST-NULL-YEAR, HOST-NULL-DATE. 

  9. I)It shall support international characters for named expression identifiers. 

Note: This specification does not mandate a user interface for international characters, so a resource-constrained application may choose to not show the traditional glyph (e.g., it may show the [UNICODE] numeric code instead).

2.2.3OpenDocument Formula Medium Group Evaluator

An OpenDocument Formula Medium Group Evaluator is an OpenDocument Small Group Formula Evaluator that meets the following additional requirements:

  1. A)It shall implement the following functions as defined in this specification: ACCRINT 6.12.2 ; ACCRINTM 6.12.3 ; ACOSH 6.16.4 ; ACOT 6.16.5 ; ACOTH 6.16.6 ; ADDRESS 6.14.2 ; ASINH 6.16.8 ; ATANH 6.16.11 ; AVEDEV 6.18.2 ; BESSELI 6.16.12 ; BESSELJ 6.16.13 ; BESSELK 6.16.14 ; BESSELY 6.16.15 ; BETADIST 6.18.7 ; BETAINV 6.18.8 ; BINOMDIST 6.18.10 ; CEILING 6.17.2 ; CHAR 6.20.3 ; CLEAN 6.20.4 ; CODE 6.20.5 ; COLUMN 6.13.4 ; COMBIN 6.16.16 ; CONCATENATE 6.20.6 ; CONFIDENCE 6.18.16 ; CONVERT 6.16.18 ; CORREL 6.18.17 ; COSH 6.16.20 ; COT 6.16.21 ; COTH 6.16.22 ; COUPDAYBS 6.12.6 ; COUPDAYS 6.12.7 ; COUPDAYSNC 6.12.8 ; COUPNCD 6.12.8 ; COUPNUM 6.12.10 ; COUPPCD 6.12.11 ; COVAR 6.18.18 ; CRITBINOM 6.18.19 ; CUMIPMT 6.12.12 ; CUMPRINC 6.12.13 ; DATEVALUE 6.10.4 ; DAYS360 6.10.7 ; DB 6.12.14 ; DEVSQ 6.18.20 ; DISC 6.12.16 ; DOLLARDE 6.12.17 ; DOLLARFR 6.12.18 ; DURATION 6.12.19 ; EFFECT 6.12.20 ; EOMONTH 6.10.9 ; ERF 6.16.27 ; ERFC 6.16.28 ; EXPONDIST 6.18.21 ; FISHER 6.18.26 ; FISHERINV 6.18.27 ; FIXED 6.20.10 ; FLOOR 6.17.4 ; FORECAST 6.18.28 ; FTEST 6.18.30 ; GAMMADIST 6.18.31 ; GAMMAINV 6.18.32 ; GAMMALN 6.16.35 ; GCD 6.16.36 ; GEOMEAN 6.18.34 ; HARMEAN 6.18.36 ; HYPGEOMDIST 6.18.37 ; INTERCEPT 6.18.38 ; INTRATE 6.12.23 ; ISEVEN 6.13.17 ; ISODD 6.13.23 ; ISOWEEKNUM 6.10.11 ; KURT 6.18.39 ; LARGE 6.18.40 ; LCM 6.16.38 ; LEGACY.CHIDIST 6.18.11 ; LEGACY.CHIINV 6.18.13 ; LEGACY.CHITEST 6.18.15 ; LEGACY.FDIST 6.18.23 ; LEGACY.FINV 6.18.25 ; LEGACY.NORMSDIST 6.18.54 ; LEGACY.NORMSINV 6.18.55 ; LEGACY.TDIST 6.18.77 ; LINEST 6.18.41 ; LOGEST 6.18.42 ; LOGINV 6.18.43 ; LOGNORMDIST 6.18.44 ; LOOKUP 6.14.8 ; MDURATION 6.12.27 ; MEDIAN 6.18.47 ; MINVERSE 6.5.3 ; MIRR 6.12.28 ; MMULT 6.5.4 ; MODE 6.18.50 ; MROUND 6.17.5 ; MULTINOMIAL 6.16.43 ; NEGBINOMDIST 6.18.51 ; NETWORKDAYS 6.10.14 ; NOMINAL 6.12.29 ; ODDFPRICE 6.12.32 ; ODDFYIELD 6.12.33 ; ODDLPRICE 6.12.34 ; ODDLYIELD 6.12.35 ; OFFSET 6.14.11 ; PEARSON 6.18.56 ; PERCENTILE 6.18.57 ; PERCENTRANK 6.18.58 ; PERMUT 6.18.59 ; POISSON 6.18.62 ; PRICE 6.12.39 ; PRICEMAT 6.12.41 ; PROB 6.18.63 ; QUARTILE 6.18.64 ; QUOTIENT 6.16.48 ; RAND 6.16.50 ; RANDBETWEEN 6.16.51 ; RANK 6.18.65 ; RECEIVED 6.12.44 ; ROMAN 6.19.17 ; ROUNDDOWN 6.17.7 ; ROUNDUP 6.17.8 ; ROW 6.13.29 ; RSQ 6.18.66 ; SERIESSUM 6.16.53 ; SIGN 6.16.54 ; SINH 6.16.56 ; SKEW 6.18.67 ; SKEWP 6.18.68 ; SLOPE 6.18.69 ; SMALL 6.18.70 ; SQRTPI 6.16.59 ; STANDARDIZE 6.18.71 ; STDEVA 6.18.73 ; STDEVPA 6.18.75 ; STEYX 6.18.76 ; SUBTOTAL 6.16.60 ; SUMPRODUCT 6.16.64 ; SUMSQ 6.16.65 ; SUMX2MY2 6.16.66 ; SUMX2PY2 6.16.67 ; SUMXMY2 6.16.68 ; TANH 6.16.70 ; TBILLEQ 6.12.48 ; TBILLPRICE 6.12.49 ; TBILLYIELD 6.12.50 ; TIMEVALUE 6.10.18 ; TINV 6.18.78 ; TRANSPOSE 6.5.6 ; TREND 6.18.79 ; TRIMMEAN 6.18.80 ; TTEST 6.18.81 ; TYPE 6.13.33 ; VARA 6.18.83 ; VDB 6.12.51 ; WEEKNUM 6.10.21 ; WEIBULL 6.18.86 ; WORKDAY 6.10.22 ; XIRR 6.12.52 ; XNPV 6.12.53 ; YEARFRAC 6.10.24 ; YIELD 6.12.54 ; YIELDDISC 6.12.55 ; YIELDMAT 6.12.56 ; ZTEST 6.18.87 

  2. B)It shall implement the Infix Operator Reference Union ("~") 6.4.13 

  3. C)It shall evaluate references with more than one area. 

2.2.4OpenDocument Formula Large Group Evaluator

An OpenDocument Formula Large Group Evaluator is an OpenDocument Medium Group Formula Evaluator that meets the following additional requirements:

  1. A)It shall implement the syntax defined in these sections on syntax: Inline Arrays; Automatic Intersection; External Named Expressions. 

  2. B)It shall implement the complex number type as discussed in the section on Complex Number, array formulas, and Sheet-local Named Expressions. 

It shall implement the following functions as defined in this specification: AMORDEGRC 6.12.4 ; AMORLINC 6.12.5 ; ARABIC 6.19.2 ; AREAS 6.13.2 ; ASC 6.20.2 ; AVERAGEA 6.18.4 ; AVERAGEIFS 6.18.6 ; BASE 6.19.3 ; BIN2DEC 6.19.4 ; BIN2HEX 6.19.5 ; BIN2OCT 6.19.6 ; BINOM.DIST.RANGE 6.18.9 ; BITAND 6.6.2 ; BITLSHIFT 6.6.3 ; BITOR 6.6.4 ; BITRSHIFT 6.6.5 ; BITXOR 6.6.6 ; CHISQDIST 6.18.12 ; CHISQINV 6.18.14 ; COMBINA 6.16.17 ; COMPLEX 6.8.2 ; COUNTIFS 6.13.10 ; CSC 6.16.23 ; 6.16.23CSCH 6.16.24 ; DATEDIF 6.10.3 ; DAYS 6.10.6 ; DDE 6.11.2 ; DEC2BIN 6.19.7 ; DEC2HEX 6.19.8 ; DEC2OCT 6.19.9 ; DECIMAL 6.19.10 ; DELTA 6.16.26 ; EDATE 6.10.8 ; ERROR.TYPE 6.13.11; EUROCONVERT 6.16.29 ; FACTDOUBLE 6.16.33 ; FDIST 6.18.22 ; FINDB 6.7.2 ; FINV 6.18.24 ; FORMULA 6.13.12 ; FREQUENCY 6.18.29 ; FVSCHEDULE 6.12.22 ; GAMMA 6.16.34 ; GAUSS 6.18.33 ; GESTEP 6.16.37 ; GETPIVOTDATA 6.14.4 ; GROWTH 6.18.35 ; HEX2BIN 6.19.11 ; HEX2DEC 6.19.12 ; HEX2OCT 6.19.13 ; HYPERLINK 6.11.3 ; IFERROR 6.15.5 ; IFNA 6.15.6 ; IMABS 6.8.3 ; IMAGINARY 6.8.4 ; IMARGUMENT 6.8.5 ; IMCONJUGATE 6.8.6 ; IMCOS 6.8.7 ; IMCOT 6.8.8 ; IMCSC 6.8.9 ; IMCSCH 6.8.10 ; IMDIV 6.8.11 ; IMEXP 6.8.12 ; IMLN 6.8.13 ; IMLOG10 6.8.14 ; IMLOG2 6.8.15 ; IMPOWER 6.8.16 ; IMPRODUCT 6.8.17 ; IMREAL 6.8.18 ; IMSEC 6.8.20 ; IMSECH 6.8.20 ; IMSIN 6.8.19 ; IMSQRT 6.8.22 ; IMSUB 6.8.23 ; IMSUM 6.8.24 ; IMTAN 6.8.25 ; INDIRECT 6.14.7 ; INFO 6.13.13 ; IPMT 6.12.24 ; ISFORMULA 6.13.18 ; ISPMT 6.12.26 ; ISREF 6.13.24 ; JIS 6.20.11 ; LEFTB 6.7.3 ; LENB 6.7.4 ; MAXA 6.18.46 ; MDETERM 6.5.2 ; MULTIPLE.OPERATIONS 6.14.10 ; MUNIT 6.5.5 ; MIDB 6.7.5 ; MINA 6.18.49 ; NORMDIST 6.18.52 ; NORMINV 6.18.53 ; NUMBERVALUE 6.13.28 ; OCT2BIN 6.19.14 ; OCT2DEC 6.19.15 ; OCT2HEX 6.19.16 ; PDURATION 6.12.36 ; PERMUTATIONA 6.18.60 ; PHI 6.18.61 ; PPMT 6.12.38 ; PRICEDISC 6.12.40 ; REPLACEB 6.7.6 ; RIGHTB 6.7.7 ; RRI 6.12.45 ; SEARCH 6.20.20 ; SEARCHB 6.7.8 ; SEC 6.16.52 ; SECH 6.16.57 ; SHEET 6.13.31 ; SHEETS 6.13.32 ; SUMIFS 6.16.63 ; TEXT 6.20.23 ; UNICHAR 6.20.25 ; UNICODE 6.20.26 ; VARPA 6.18.85 ; XOR 6.15.10

Note: The following functions are documented by this specification, but not included even in the Large group:CELL 6.13.3 ; DOLLAR 6.20.7

2.3Variances (Implementation-defined, Unspecified, and Behavioral Changes)

Applications should document all implementation-defined and variances from this standard in a manner that the application users can obtain the information (e.g., in the application help for the relevant function).

In a few cases a specific approach is required (e.g., string indexes begin at one), which may be different than the user interface of some implementations.

In practice, for nearly all documents the differences are irrelevant. The primary variances and differences from OpenFormula and some existing applications are:

Note: Interoperability is improved by the use of the DATE and TIME functions or the textual ISO 8601 date representation because dates in that format do not rely upon epoch or locale-specific settings.

In an OpenDocument file, calculation settings impact formula recalculation, which can be the same or different from a particular application's defaults. These include whether or not text comparisons are case-sensitive, or if search criteria shall apply to the whole cell.

3Formula Processing Model

3.1General

This section describes the basic formula processing model: how expressions are calculated, when recalculation occurs, and limits on formulas.

3.2Expression Calculation

Conceptually, formulas are recalculated from the “outside in”. Any formula is an expression that produces a result. An expression is calculated as follows:

  1. 1.If an expression is a constant number or string, that constant is returned 

  2. 2.If it is a reference, the reference is returned. If a reference is to be displayed, the value of the reference is displayed, not the reference itself. 

  3. 3.Otherwise, it is one or more operations or functions; in the case of operations, the highest-precedence operation not processed is processed first. 

    1. a)The values of all argument expressions are computed, that is, formulas are normally “eagerly” evaluated. Exceptions to eager evaluation are noted in the function or operation's specification; in particular, the IF() function does not calculate the “else” parameter if the the condition is true, and does not calculate the “then” parameter if the condition is false. The CHOOSE() function does not calculate parameters other than the chosen. Function parameters shall act as if they had been computed in left-to-right order. Operators should act as if they had been computed in the order of precedence and associativity (so they are computed left-to-right for +, *, and so on, but right-to-left for the exponentiation operator ^). 

    2. b)If any of the arguments of the function/operation are not of the correct type, the appropriate implicit conversion function is called to convert it to the correct type for the operator or function. 

    3. c)The operation or function is then called with the resulting values of its arguments. 

The above model only describes how recalculation appears to the end-user. Applications may, and typically do, optimize this process as long as the final results produce the same answer. For example, applications may parse a formula and translate it into some intermediate form (such as a byte code), which immediately descends to the “innermost” computation that needs to be calculated and then works out to the final result.

When a formula is computed, it is notionally provided a "context" as input. The context may include formula variables (including named ranges, document variables, fields, and so on), and/or additional function definitions that the formula can call. A formula may also be provided as input an ordered list of zero or more parameters (though the syntax for parameters is not given in this version of the specification). In an OpenDocument formula, this context also includes calculation settings (such as whether or not text comparisons are case-sensitive).

A formula may include calls to functions, which are normally provided the same context but with their own set of ordered parameters.

Any formula computes a single result, though that single result may actually be a set of values.

3.3Non-Scalar Evaluation (aka 'Array expressions')

Non-scalar values passed as arguments to functions are evaluated by intersection or iteration.

  1. 1)Evaluation as an implicit intersection of the argument with the expression's evaluation position. 

    1. 1.1)Inline Arrays
      Element (0;0) of the array is used in place of the array. 

      Note:
      =ABS({-3;-4})         => ABS(-3)        // row vector
      =ABS({-3|-4})        => ABS(-3)        // column vector
      =ABS({-3;-4|-6;-8})        => ABS(-3)        // matrix
      ={1;2;3|4;5;6}        => 1                // simple display 

    2. 1.2)References 

      1. 1.2.1)If the target reference is a row-vector (Nx1) use the value at the intersection of the evaluation position's column and the reference's row. 

        Note:
        in cell B2 : =ABS(A1:C1) => ABS(B1)
        If there is no intersection the result is #VALUE! 

        Note: in cell D4 : =ABS(A1:C1) => #VALUE! 

      2. 1.2.2)If the target reference is a column-vector (1xM) the value at the intersection of the evaluation position's row and the reference's column. 

        Note:
        in cell B2 : =ABS(A1:A3) => ABS(A2)
        in cell D4 : =ABS(A1:A3) => #VALUE! 

  2. 2)Matrix evaluation. 


    If an expression is being evaluated in a cell flagged as a being part of a 'Matrix' (OpenDocument 8.1.3 table:number-matrix-columns-spanned): 

    1. 2.1)The portion of a non-scalar result to be displayed may not be co-extensive with a specified display area. The portion of the non-scalar result to be displayed is determined by: 

      1. 2.1.1)If the position to be displayed exists in the result, display that position. 

      2. 2.1.2)If the non-scalar result is 1 column wide, subsequent columns in the display area display the value in the first column. This applies to
        - scalars '3'
        - singletons '{3}'
        - column vectors '{1|2|3}' 

      3. 2.1.3)If the non-scalar result is 1 row high, subsequent rows in the display area use the value of the first row.This applies to
        - scalars '3'
        - singletons '{3}'
        - row vectors '{1;2;3}' 

      4. 2.1.4)If none of the other rules apply #N/A 

        Note:
        in matrix A1:B3 with ={1;2|3;4|5;6}        : cell B2 contains 4.        [Rule 2.1.1]
        in matrix A1:B3 with ={1|3|5}                : cell B2 contains 3.        [Rule 2.1.1 for row, and Rule 2.1.2 column]
        in matrix A1:B3 with ={2;4}                : cell B2 contains 4.        [Rule 2.1.3 for row, and Rule 2.1.1 column]
        in matrix A1:C4 with ={1;2|3;4|5;6}        : cell C1,A4 contain #N/A. [Rule 2.1.4]

        NOTE : if a value is not requested it is not displayed
        in matrix A1:B2 with ={1;2|3;4|5;6}        : the value '6' is not displayed because B3 is not part of the display matrix. 

    2. 2.2)Calculations with non-scalar inputs are a generalization of (2.1). 


      When evaluating a formula in 'matrix' mode, and a non-scalar value is passed to a function argument that expects a scalar, the function is evaluated multiple times, iterating over the non-scalar input(s) and putting the function result into a matrix at the position corresponding to the input. Unary/Binary operators, other than range and union, follow the rules for scalar functions when passed non-scalar values. 

      Inline arrays and references are interchangeable. 

      1. 2.2.1)Functions returning arrays are not eligible for implicit iteration. When evaluated in 'matrix' mode the {0;0}th element is used. 

        Note:
        e.g. =SUM(INDIRECT({"A1";"A2")) would produce the value in A1 when evaluated in array mode. 

      2. 2.2.2)The result matrix is rectangular, sized with the maximum number of rows and columns from all non-scalar arguments. 

        Note:
        ={1;2}+{3;4;5}        => {4;6;#N/A}
        ={1}+{1;2}        => {2;3} 

      3. 2.2.3)The result matrix is populated by extracting the corresponding value from each of the non-scalar arguments based on the following rules, and evaluating the function with that set of arguments. 

        1. 2.2.3.1)If the argument data is a singleton array or a scalar the value is repeated for each evaluation. 

          Note:
          = 1 + {1;2;3|4;5;6}        => {2;3;4|5;6;7}
          = {1} + {1;2;3|4;5;6}        => {2;3;4|5;6;7} 

        2. 2.2.3.2)If the argument data is 1 column wide the value in the corresponding row is used to evaluate all columns in the result matrix. 

          Note:
          = {1|2} + {10;20|30;40}        => {11;21|32;42} 

        3. 2.2.3.3)If the argument data is 1 row height the value in the corresponding column is used to evaluate all rows in the result matrix. 

          Note:
          = {1;2} + {10;20|30;40}        => {11;22|31;42} 

        4. 2.2.3.4)If one argument data is 1 column wide and another argument data is 1 row height the value of the corresponding row respectively column is used to evaluate all elements in the result matrix. 

          Note:
          ={1;2} + {10|20}                => {11;12|21;22} 

        5. 2.2.3.5)If an argument is a 2d matrix the argument value in the position corresponding to the current output position is used if it is within range of the supplied argument, otherwise #N/A is used in the calculation. 

          Note:
          =MID("abcd";{1;2};{1;2;3})        => {"a";"bc";#VALUE!} 

3.4Host-Defined Behaviors

A Formula Evaluator operates in an execution environment (a "host"). The behavior of the Formula Evaluator is parametrized by host-defined properties and functions.

The following properties are host-defined:

  1. 1)HOST-CASE-SENSITIVE: if true, text comparisons are case-sensitive. This influences the operators =, <>, <, <=, >, and >=, as well as database query functions that use them. Note that the EXACT function is always case-sensitive, regardless of this calculation setting. 

  2. 2)HOST-PRECISION-AS-SHOWN: If true, calculations are performed using rounded values of those displayed; otherwise, calculations are performed using the precision of the underlying numeric representation. Note: This does not impose a particular numeric model. Since implementations may use binary representations, this rounding may be inexact for decimal value. 

  3. 3)HOST-SEARCH-CRITERIA-MUST-APPLY-TO-WHOLE-CELL If true, the specified search criteria shall apply to the entire cell contents if it is a text match using = or <>; if not, only the initial text needs to match. 

  4. 4)HOST-AUTOMATIC-FIND-LABELS: if true, row and column labels are automatically found. 

  5. 5)HOST-USE-REGULAR-EXPRESSIONS: If true, regular expressions are used for character string comparisons and when searching. 

  6. 6)HOST-USE-WILDCARDS: If true, wildcards question mark '?' and asterisk '*' are used for character string comparisons and when searching. Wildcards may be escaped with a tilde '~' character. 

  7. 7)HOST-NULL-YEAR: This defines how to convert a two-digit year into a four-digit year. All two-digit year values are interpreted as a year that equals or follows this year. 

  8. 8)HOST-NULL-DATE: Defines the beginning of the epoch; a numeric date of 0 equals this date. 

  9. 9)HOST-LOCALE: The locale to be used for locale-dependent operations, such as conversion of text to dates, or text to numbers. 

The function HOST-REFERENCE-RESOLVER(Reference) is implementation defined. This function takes as input a Unicode string containing a Reference according to section 4.8 and returns a resolved value.

3.5When recalculation occurs

Implementations of OpenFormula typically recalculate formulas when its information is needed. Typical implementations will note what values a formula depends on, and when those dependent values are changed and the formula's results are displayed, it will re-execute the formulas that depend on them to produce the new results (choosing the formulas in the right order based on their dependencies). Implementations may recalculate when a value changes (this is termed automatic recalculation) or on user command (this is termed manual recalculation).

Some functions' dependencies are difficult to determine and/or should be recalculated more frequently. These include functions that return today's date or time, random number generator functions (such as RAND 6.16.50), or ones that indirectly determine the cells to act on. Many implementations always recalculate formulas including such functions whenever a recalculation occurs. Functions that are always recalculated whenever a recalculation occurs are termed volatile functions. Functions that are often volatile functions include CELL 6.13.3, HYPERLINK 6.11.3, INDIRECT 6.14.7, INFO 6.13.13, NOW 6.10.15, OFFSET 6.14.11, RAND 6.16.50 and TODAY 6.10.19. Functions that depend on the cell position of the formula they are contained in or the position of a cell they reference need to be recalculated whenever that cell is moved, such functions are COLUMN 6.13.4, ROW 6.13.29 and SHEET 6.13.31. In addition, formulas may indicate that they should always be recalculated during a recalculation process by including a forced recalculation marker, as described in the syntax below.

3.6Numerical Models

This specification does not, by itself, specify a numerical implementation model, though it does imply some minimal levels of accuracy for most functions. For example, an application cannot say that it implements the infix operator “/” as specified in this document if it implements integer-only arithmetic.

In practice, applications tend to use at least one IEEE 754-1985 binary floating-point representation, using at least the 64-bit representation and possibly larger widths for intermediate results. When IEEE 754 representations are used, results such as Inf (infinity) and Nan (not a number) are considered an Error value. Applications may use IEEE 854-1987 (which covers decimal arithmetic). In general, applications are encouraged to use appropriate standards for their numerical models. This means that applications will often not produce “exact” results, but only approximate results for a large number of places.

3.7Basic Limits

Evaluators which claim to support “basic limits” shall support at least the following limits:

  1. 1.formulas up to at least 1024 characters long, as measured when in OpenDocument interchange format not counting the square brackets around cell addresses, or the “.” in a cell address when the sheet name is omitted. 

  2. 2.at least 30 parameters per function when the function prototype permits a list of parameters. 

  3. 3.permit strings of ASCII characters of up to 32,767 (2^15-1) characters. 

  4. 4.support at least 7 nesting levels of functions. 

4Types

4.1General

All values defined by OpenFormula have a type. OpenFormula defines Text, Number, Complex Number, Logical, Error, Reference, ReferenceList and Array types.

4.2Text (String)

A Text value (also called a string value) is a sequence of zero or more characters.

Evaluators should accept [UNICODE] strings, but shall accept strings of ASCII (Unicode U+0020 through U+007F, inclusive) characters.

A text value of length zero is termed the empty string.

Index positions in a text value begin at 1.

4.3Number

4.3.1General

A number is a numeric value.

Numbers shall be able to represent fractional values (they shall not be limited to only integers). Evaluators may implement Number with an arbitrary fixed or with a variable bit length. A cell with a constant numeric value has the Number type.

Note: Many evaluators implement numbers as 64-bit IEEE floating point values and use the CPU's floating-point instructions where available (so intermediate values may be represented using more than 64 bits).

Implementations typically support many subtypes of Number, including Date, Time, DateTime, Percentage, fixed-point arithmetic, and arithmetic supporting arbitrarily long integers, and determine the display format from this. All such Number subtypes shall yield True for the ISNUMBER 6.13.22 function. This specification does not require that specific subtypes be distinguishable from each other, or that the subtype be tracked, but in practice most implementations do such tracking because requiring users to manually format every cell appropriately becomes tedious very quickly. Automatically determining the most likely subtype is especially important for a good user interface when generating OpenDocument format, since some subtypes (such as date, time, and currency) are stored in a different manner depending on their subtype. Thus, this specification identifies some common subtypes and identifies those subtypes where relevant in some function definitions, as an aid to implementing good user interfaces. Many applications vary in the subtype produced when combining subtypes (e.g., what is the result when percentages are multiplied together), so unless otherwise noted these are unspecified. Typical implementations try to heuristically determine the "right" format for a cell when a formula is first created, based on the operations in the formula. Users can then override this format, so as a result the heuristics are not important for data exchange (and thus outside the scope of this specification).

All Number subtypes shall yield True for the ISNUMBER function.

Note: This specification does not require that specific subtypes be distinguishable from each other, or that the subtype be tracked, but in practice most evaluators do such tracking. Automatically determining the most likely subtype is important for a good user interface and when generating OpenDocument format, since some subtypes (such as date, time, and currency) are stored in a different manner depending on their subtype. Typical implementations try to heuristically determine the "right" format for a cell when a formula is first created, based on the operations in the formula. Expression authors can then override this display format, so as a result the heuristics are not important for data exchange (and thus outside the scope of this specification).

4.3.2Time

Time is a subtype of Number.

Time is represented as a fraction of a day.

4.3.3Date

Date is a subtype of Number.

Date is represented by an integer value.

A serial date is the expression of a date as the number of days elapsed from a start date called the epoch.

Evaluators shall support all dates from 1904-01-01 through 9999-12-31 (inclusive) in calculations, should support dates from 1899-12-30 through 9999-12-31 (inclusive) and may support a wider date range.

Note: Using expressions that assume serial numbers are based on a particular epoch may cause interoperability issues.

Evaluators shall support positive serial numbers. Evaluators may support negative serial numbers to represent dates before an epoch.

Note: It is implementation-defined if the year 1900 is treated as a leap year.

Note: Evaluators that treat 1900 as a non-leap year can use the epoch date 1899-12-30 to compensate for serial numbers that originate from evaluators that treat 1900 as a leap year and use 1899-12-31 as an epoch date.

4.3.4DateTime

DateTime is a subtype of Number.  It is a Date plus Time.

4.3.5Percentage

A percentage is a subtype of Number that may be displayed by multiplying the number by 100 and adding the sign “%” or with other formatting depending upon the number format assigned to the cell where it appears.

4.3.6Currency

A currency is a subtype of Number that may appear with or without a currency symbol or with other formatting depending upon the number format assigned to the cell where it appears.

4.3.7Logical (Number)

A Logical value is a subtype of Number where TRUE() returns 1 and FALSE() returns 0.

The implicit conversion operator “Convert to Logical” 6.3.12, when a Number is passed as a condition, 0 is considered False and all other numeric values are considered True.

Note: Logical values can be a distinct type from Number. 4.5

4.4Complex Number

A complex number (sometimes also called an imaginary number) is a pair of real numbers including a real part and an imaginary part. In mathematics, complex numbers are often written as x + iy, where x (the real part) and y (the imaginary part) are real numbers and i is
. A complex number can also be written as reiθ = rcos(θ) + irsin(θ), where r is the modulus of the complex number (a real number) and θ is the argument or phase (a real number representing an angle in radians).
 

A complex number may, but need not be, represented as a Number or Text. The results of the functions ISNUMBER() and ISTEXT() are implementation-defined when applied to a complex number.

Functions and operators that accept complex numbers shall accept Text values as complex numbers (6.3.10 Conversion to Complex Number, as well as Numbers that are not complex numbers.

Note: IMSUM("3i";4) will produce the same result as COMPLEX(4;3).

Note: Expression authors should be aware that use of functions that are not defined by OpenFormula as accepting complex numbers as input may impair interoperability.

Equality can be tested using IMSUB to compute the difference, use IMABS to find the absolute difference, and then ensure the absolute difference is smaller than or equal to some nonnegative value (for exact equality, compare for equality with 0).

4.5Logical (Boolean)

A Logical value (also called a Boolean value) is a value with one of two values: TRUE() and FALSE().

Note: Logical values can be represented as a subtype of Number. 4.3.7

 

 

4.6Error

An Error is one of a set of possible error values. Implementations may have many different error values, but one error value in particular is distinct: #N/A, the result of the NA() function. Users may choose to enter some data values as #N/A, so that this error value propagates to any other formula that uses it, and may test for this using the function ISNA().

Functions and operators that receive one or more error values as an input shall produce one of those input error values as their result, except when the formula or operator is specifically defined to do otherwise.

In an OpenDocument document, if an error value is the result of a cell computation it shall be stored as if it was a string. That is, the office:value-type of an error value is string; if the computed value is stored, it is stored in the attribute office:string-value.

Note: This does not change an Error into a string type (since the Error will be restored on recalculation); this enables applications which cannot recalculate values to display the error information.

4.7Empty Cell

An empty cell is neither zero nor the empty string, and an empty cell can be distinguished from cells containing values (including zero and the empty string).  An empty cell is not the same as an Error, in particular, it is distinguishable from the Error #N/A (not available).

4.8Reference

A cell strip consists of cell positions in the same row and in one or more contiguous columns.

A cell rectangle consists of cell positions in the same cell strips of one or more contiguous rows.

A cell cuboid consists of cell positions in the same cell rectangles of one or more contiguous sheets.

A reference is the smallest cuboid that (1) contains specifically-identified cell positions and/or specifically-identified complete columns/rows such that (2) removal of any cell positions either violates condition (1) or does not leave a cuboid.

Cell positions in a cell cuboid/rectangle/strip can resolve to empty cells (section 3.7).

The definitions of specific operations and functions that allow references as operands and parameters stipulate any particular limitations there are on forms of references and how empty cells, when permitted, are interpreted.

4.9ReferenceList

A reference list contains 1 or more references, in order. A reference list can be passed as an argument to functions where passing one reference results in an identical computation as an arbitrary sequence of single references occupying the identical cell range.

Note: For example, SUM([.A1:.B2]) is identical to SUM([.A1]~[.B2]~[.A2]~[.B1]), but COLUMNS([.A1:.B2]), resulting in 2 columns, is not identical to COLUMNS([.A1]~[.B2]~[.A2]~[.B1]), where iterating over the reference list would result in 4 columns.

A reference list cannot be converted to an array.

Note: For example, in array context {ABS([.A1]~[.B2]~[.A2]~[.B1])} is an invalid expression, whereas {ABS([.A1:.B2])} is not.

Passing a reference list where a function does not expect one shall generate an Error. Passing a reference list in array iteration context to a function expecting a scalar value shall generate an Error.

4.10Array

An array is a set of rows each with the same number of columns that contain one or more values. There is a maximum of one value per intersection of row and column. The intersection of a row and column may contain no value.

4.11Pseudotypes

4.11.1General

Many functions require a type or a set of types with special properties, and/or process them specially. For example, a "Database" requires headers that are the field names. These specialized types are called pseudotypes.

4.11.2Scalar

A Scalar value is a value that has a single value. A reference to more than one cell is not a scalar (by itself), and shall be converted to one as described below. An array with more than one element is not a scalar. The types Number (including a complex number), Logical, and Text are scalars.

4.11.3DateParam

A DateParam is a value that is either a Number (interpreted as a serial number; 4.3.3) or Text; text is automatically converted to a date value. 6.3.15

4.11.4TimeParam

A TimeParam is a value that is either a Number (interpreted as a serial number; 4.3.2) or Text; text is automatically converted to a time value (fraction of a day). 6.3.16

4.11.5Integer

An integer is a subtype of Number that has no fractional value. An integer X is equal to INT(X). Division of one integer by another integer may produce a non-integer.

4.11.6Basis

A basis is a subtype of Integer (and thus of Number) that indicates the calendar system conventions to be used.   If basis is omitted from a financial function, the default is basis 0.

Basis values are defined as follows (where x/y indicates x days per month and y days per year):

4.11.7Criterion

A criterion is a single cell Reference, Number or Text. It is used in comparisons with cell contents.

A reference to an empty cell is interpreted as the numeric value 0.

A matching expression can be:

4.11.8Database

A database is a rectangular organized set of data.  Any database has a set of one or more fields that determine the structure of the database. A database has a set of zero or more records with data, and each record contains data for every field (though that field may be empty).

Evaluators shall support the use of ranges as databases if they support any database functions. The first row of a range is interpreted as a set of field names.

Note: Field names of type Text and unique without regard to case enhance the interoperability of data. It is also a common expectation that rows following the first row of data are data records that correspond to field names in the first row.

A single cell containing text can be used as a database; if it is, it is a database with a single field and no data records.

Evaluators supporting databases and named ranges shall support the use of named ranges as a range, and the use of a Text value as a database (which, if it matches the name of a named range, will be considered the named range).

Note: It is considered good practice to define a named range for a database because it eases maintenance (the range can be changed for all functions by changing just one definition).  However, the use of named ranges for a database is not required by this specification.

4.11.9Field

A field is a value that selects a field in a database; it is also called a field selector. If the field selector is Text, it selects the field in the database with the same name.

Evaluators should match the database field name case insensitive.

If a field selector is a Number, it is a positive integer and used to select the fields. Fields are numbered from left to right beginning with the number 1.

All functions that accept a field parameter shall, when evaluated, return an Error if the selected field does not exist.

4.11.10Criteria

A criteria is a rectangular set of values, with at least one column and two rows, that selects matching records from a database. The first row lists fields against which expressions will be matched. 4.11.9 Rows after the first row contain fields with expressions for matching against database records.

For a record to be selected from a database, all of the expressions in a row of criteria shall match.

A reference to an empty cell is interpreted as the numeric value 0.

4.11.11Sequences (NumberSequence, NumberSequenceList, DateSequence, LogicalSequence, and ComplexSequence)

Some functions accept a sequence, i.e., a value that is to be treated as a sequential series of values. The following are sequences: NumberSequence, NumberSequenceList, DateSequence, LogicalSequence, and ComplexSequence.

When evaluating a function that accepts a sequence, the evaluator shall follow the rules for that sequence as defined in section 5.3. When processing a ReferenceList, the references are processed in order (first, second if any, and so on). In a cuboid, the first sheet is first processed, followed by later sheets (if any) in order. Inside a sheet, it is implementation-defined as to whether the values are processed row-at-a-time or column-at-a-time, but it must be one of these two processing orders. If processing row-at-a-time, the sequence must be produced by processing each row in turn, from smallest to largest column value (e.g., A1, B1, C1). If processing column-at-a-time, the sequence must be produced by processing each column at a time, from the smallest to the largest row value (e.g., A1, A2, A3).

5Expression Syntax

5.1General

The OpenFormula syntax is defined using the BNF notation of the XML specification, chapter 6 [XML1.0]. Each syntax rule is defined using "::=".

Note: Formulas are typically embedded inside an XML document. When this occurs, characters (such as "<", ">", '"', and "&") shall be escaped, as described in section 2.4 of the XML specification [XML1.0]. In particular, the less-than symbol "<" is typically represented as “&lt;”, the double-quote symbol as “&quot;”, and the ampersand symbol as “&amp;” (alternatively, a numeric character reference can be used).

5.2Basic Expressions

Formulas may start with a '=' (EQUALS SIGN, U+003D), which if present may be followed by a “forced recalculate” marker '=' (EQUALS SIGN, U+003D), followed by an expression. If the second '=' (EQUALS SIGN, U+003D) is present, this formula is a "forced recalculation" formula.  If a formula is marked as a "forced recalculation" formula, then it should be recalculated whenever one of its predecessors it depends on changes.

Expressed in BNF grammar, a formula is specified:

Formula ::= Intro? Expression

Intro ::= '=' ForceRecalc?

ForceRecalc ::= '='

The primary component of a formula is an Expression . Formulas are composed of Expression s, which may in turn be composed from other Expression s.

Expression ::=

Whitespace* (

Number |

String |

Array |

PrefixOp Expression |

Expression PostfixOp |

Expression InfixOp Expression |

'(' Expression ')' |

FunctionName Whitespace* '(' ParameterList ')' |

Reference |

QuotedLabel |

AutomaticIntersection |

NamedExpression |

Error

) Whitespace*

SingleQuoted ::= "'" ([^'] | "''")+ "'"

5.3Constant Numbers

Constant numbers are written using '.' (FULL STOP, U+002E) dot as the decimal separator. Optional "E" or "e" denotes scientific notation. Syntactically, negative numbers are positive numbers with a prefix "-" (HYPHEN-MINUS, U+002D) operator.  A constant number is of type Number.

Number ::= StandardNumber |

   '.' [0-9]+ ([eE] [-+]? [0-9]+)?

StandardNumber ::= [0-9]+ ('.' [0-9]+)? ([eE] [-+]? [0-9]+)?

Evaluators should be able to read the Number format, which accepts a decimal fraction that starts with decimal point '.' (FULL STOP, U+002E), without a leading zero. Evaluators shall write numbers only using the StandardNumber format, which requires a leading digit, and shall not write numbers with a leading '.' (FULL STOP, U+002E).

5.4Constant Strings

Constant strings are surrounded by double-quote characters (QUOTATION MARK, U+0022); a literal double-quote character '"' (QUOTATION MARK, U+0022) as string content is escaped by duplicating it. When a formula is stored in an XML attribute, XML escaping rules apply: thus inside an XML attribute double-quote characters shall be escaped (e.g., as &quot;) and carriage return characters in a String (e.g., as &#x0D;) . A constant string is of type Text.

String ::= '"' ([^"#x00] | '""')* '"'

5.5Operators

Operators are functions with one or more parameters.

PrefixOp ::= '+' | '-'

PostfixOp ::= '%'

InfixOp ::= ArithmeticOp | ComparisonOp | StringOp | ReferenceOp

ArithmeticOp ::= '+' | '-' | '*' | '/' | '^'

ComparisonOp ::= '=' | '<>' | '<' | '>' | '<=' | '>='

StringOp ::= '&'

There are three predefined reference operators: reference intersection , reference concatenation , and range. The result of these operators may be a 3 dimensional range, with front-upper-left and back-lower-right corners, or even a list of such ranges in the case of cell concatenation.

ReferenceOp ::= IntersectionOp | ReferenceConcatenationOp | RangeOp

IntersectionOp ::= '!'

ReferenceConcatenationOp ::= '~'

RangeOp ::= ':'

Table 1 - Operators defines the associativity and precedence of operators, from hightest to lowest precedence.

Table 1 - Operators

Associativity

Operator(s)

Comments

left

:

Range.

left

!

Reference intersection ([.A1:.C4]![.B1:.B5] is [.B1:.B4]). Displayed as the space character in some implementations.

left

~

Reference union. Displayed as the function parameter separator in some implementations.

right

+,-

Prefix unary operators, e.g., -5 or -[.A1]. Note that these have a different precedence than add and subtract.

left

%

Postfix unary operator % (divide by 100). Note that this is legal with expressions (e.g., [.B1]%), it can be duplicated (1%%), and it does not change the meaning of other operations such as "+".

left

^

Power (2 ^ 3 is 8).

left

*,/

Multiply, divide.

left

+,-

Binary operations add, subtract. Note that unary (prefix) + and - have a different precedence.

left

&

Binary operation string concatenation. Note that unary (prefix) + and - has a different precedence. Note that "&" shall be escaped when included in an XML document

left

=, <>, <, <=,
>, >=

Comparison operators equal to, not equal to, less than, less than or equal to, greater than, greater than or equal to

Note: Prefix “-” has a higher precedence than “^”, that “^” is left-associative, and that reference intersection has a higher precedence than reference union.

Note: Prefix “+” and “–“ are defined to be right-associative. However, note that typical applications which implement at most the operators defined in this specification (as specified) may implement them as left-associative, because the calculated results will be identical.

Note: Precedence can be overridden by using parentheses, so "=2+3*4" computes to 14 but "=(2+3)*4" computes 20. Implementations should retain "unnecessary" parentheses and white space, since these are added by people to improve readability.

5.6Functions and Function Parameters

Functions are called by name, followed by parentheses surrounding a list of parameters. Parameters are separated using the semicolon ';' (SEMICOLON, U+003B) character:

FunctionName ::= Identifier

Identifier ::= LetterXML (LetterXML | DigitXML |

'_' | '.' | CombiningCharXML)*

Where LetterXML, DigitXML, and CombiningCharXML are Letter, Digit, and CombiningChar as they are defined in [XML1.0].

Function names are case-insensitive.

Function calls shall be given a parameter list, though it may be empty. An empty list of parameters is considered a call with 0 parameters, not a call with one parameter that happens to be empty. TRUE() is syntactically a function call with 0 parameters. It is syntactically legitimate to provide empty parameters, though functions may not accept empty parameters unless otherwise noted:

ParameterList ::= /* empty */ |

Parameter (Separator EmptyOrParameter )* |

Separator EmptyOrParameter /* First param empty */

(Separator EmptyOrParameter )*

EmptyOrParameter ::= /* empty */ Whitespace* | Parameter

Parameter ::= Expression

Separator ::= ';'

5.7Nonstandard Function Names

When writing a document using function(s) not defined in this specification, an evaluator should include a prefix in such function names to identify the original definer of the function's semantics.

The prefix should begin with a domain name owned by the definer, in reverse order, and should be in uppercase letters (where lower/uppercase letters apply). This prefix should be the shortest prefix sufficient to identify the application company/project, followed by a period, optionally followed by version information or more specific product identification and a period, followed by the original function name itself. The version information should be included if an application substantially changes the semantics of a function (as viewed by users of that function) and one of those later versions of the function is intended. Evaluators may implement functions originally defined by another evaluator, and thus may read and/or write function names that use another evaluator's prefix.

Note: Examples of such names include COM.MICROSOFT.CUBEMEMBER, ORG.OPENOFFICE.STYLE, ORG.GNUMERIC.RANDRAYLEIGH, and COM.LOTUS.V98.FOO.

Evaluators should avoid defining evaluator-unique functions beginning with a top-level domain name followed by a period. Evaluators should avoid defining application functions beginning with “NET.”, “COM.”, “ORG.”, or a country code followed by a period.

Evaluators that do not support a function should compute its result as some Error value other than NA().

5.8References

References refer to a specific cell or set of cells. The syntax for a constant reference:

Reference ::= '[' Source? RangeAddress ']'

RangeAddress ::=
 SheetLocatorOrEmpty '.' Column Row (':' '.' Column Row )? |
 SheetLocatorOrEmpty '.' Column ':' '.' Column |
 SheetLocatorOrEmpty '.' Row ':' '.' Row |
 SheetLocator '.' Column Row ':' SheetLocator '.' Column Row |
 SheetLocator '.' Column ':' SheetLocator '.' Column |
 SheetLocator '.' Row ':' SheetLocator '.' Row

SheetLocatorOrEmpty ::= SheetLocator | /* empty */

SheetLocator ::= SheetName ('.' SubtableCell)*

SheetName ::= QuotedSheetName | '$'? [^\]\. #$']+

QuotedSheetName ::= '$'? SingleQuoted | Error

SubtableCell ::= ( Column Row ) | QuotedSheetName

Column ::= '$'? [A-Z]+

Row ::= '$'? [1-9] [0-9]*

Source ::= "'" IRI "'" "#"

CellAddress ::= SheetLocatorOrEmpty '.' Column Row /* Not used directly */

References always begin with '[' (LEFT SQUARE BRACKET, U+005B); this disambiguates cell addresses from function names and named expressions. SheetNames include single-quote“'” (APOSTROPHE, U+0027) characters by doubling them and having the entire name surrounded by single-quotes. Column labels shall be in uppercase. The syntax supports whole-row and whole-column references. A reference is of type Reference.

Columns are named by a sequence of one or more uppercase letters A-Z (U+0041 through U+005A).  Columns are named A, B, C, ... X, Y, Z, AA, AB, AC, ... AY, AZ, BA, BB, BC, ... ZX, ZY, ZZ, AAA, AAB, AAC, AAZ, ABA, ABB, and so on.

If a RangeAddress does not contain a Column element or does not contain a Row element, it specifies a cell rectangle (4.8 Reference). If it contains Row elements, the cell rectangle starts on the first column and ends on the last column the evaluator supports. If it contains Column elements, the cell rectangle starts on the first row and ends on the last row the evaluator supports.

If in a RangeAddress the first part (left of ':' colon) contains a SheetLocator and the second part (right of ':' colon) does not contain a SheetLocator, the second part inherits the SheetLocator from the first part.

If a RangeAddress contains two different SheetLocators, it specifies a cell cuboid (4.8 Reference).

A reference with an explicit row or column value beyond the capabilities of an evaluator shall be computed as an Error, and not as a reference.

Note that references can include a single embedded “:” separator.  Evaluators should use references with embedded “:” separators inside the [..] markers, instead of the general-purpose “:” operator, when saving files, and where there is a choice of cells to join, and evaluators should choose the leftmost pair.

Source location's IRI is described in [RFC3987], Internationalized Resource Identifiers (IRIs), based on [RFC3986], Uniform Resource Identifier (URI): General Syntax. Evaluators should support absolute IRIs (URLs are IRIs too). Evaluators should support relative IRIs, which can be distinguished because they do not begin with [A-Za-z]+ ":". Relative IRIs are formed according to section 6.5 of RFC3987, respectively section 4.2 of RFC3986. Evaluators should always use a “./” prefix when writing a relative IRI, since this is unambiguous. Evaluators should support the file scheme (file:// prefix).

Evaluators may support a variety of IRI/URI/URL schemes (such as “http:”).

 

5.9Reference List

A reference list is the result of the Infix Operator Reference Concatenation 6.4.13 '~', the syntax is:

ReferenceList ::= Reference (Whitespace* ReferenceConcatenationOp Whitespace* Reference)*

A reference list can be passed as an argument to functions expecting a reference parameter where passing one reference results in an identical computation as an arbitrary sequence of single references occupying the identical cell range.  A reference list cannot be converted to an array.

5.10Quoted Label

5.10.1General

A quoted label is Text contained in a table as cell content, either literally or as a formula result.

QuotedLabel ::= SingleQuoted

A quoted label identifies a column or a row, depending on the label range in which its text appears.

5.10.2Lookup of Defined Labels

For a QuotedLabel, first the cells defined in column label ranges (cell ranges of the table:label-cell-range-address attribute in the elements <table:label-range> with attribute table:orientation set to column) are searched for the string content of QuotedLabel (without the quotes). If found, the corresponding column's range of the data cell range of the table:data-cell-range-address attribute is taken as a reference. If not found, the cells defined in row label ranges (attribute table:orientation set to row) are searched and if found the corresponding row's range of the data cell range is taken. Label ranges of the current formula's sheet take precedence over label ranges of other sheets if a name occurs in both.

5.10.3Automatic Lookup of Labels

For a QuotedLabel where no defined label is found, an automatic lookup is performed on the sheet where the formula cell resides, if that document setting is enabled (HOST-AUTOMATIC-FIND-LABELS value true ).

Matches to the upper left of the formula cell are preferred over other matches, followed by matches with a smaller distance. The following algorithm is used:

Cells on the same sheet as the formula cell are examined column-wise from left to right whether they contain the text of QuotedLabel (without the quotes). If more than one cell match, the distance and direction from the formula cell's position is taken into account. The distance is calculated by Distance= ColumnDifference*ColumnDifference+ RowDifference*Row Difference using an idealized layout of quadratic cells. For the direction, during the run two independent match positions are remembered each time Distance is smaller than a previous Distance: Match2 for positions right of and/or below the formula position (FormulaColumn < MatchColumn || FormulaRow < MatchRow), Match1 for all others (not right of and not below). Match1 also holds the very first match, in case there is only one match or all matches are somewhere below or right of the formula cell. After having found the smallest distances the conditions are:

  1. 1.If Match1 has the smallest distance, that match is taken. 

  2. 2.Else, Match2 (right and/or below) has the smallest or an equal distance: 

    1. 2.1 A match to the upper left (FormulaColumn >= Match1Column && FormulaRow >= Match1Row) takes precedence over matches to other directions. 

    2. 2.2 Else, if there is no match to the upper left: 

      1. 2.2.1 If Match1 is somewhere right of the formula cell (FormulaColumn < Match1Column) it was the first match found in column-wise lookup. 

        1. 2.2.1.1 If Match2 is above the formula cell (FormulaRow >= Match2Row) it is to the upper right of the formula cell and either nearer than Match1 or Match1 is below. Match2 is taken. 

        2. 2.2.1.2 Else Match2 is below the formula cell and Match1 is taken. 

      2. 2.2.2 Else (Match1 not right of the formula cell => two matches below or below and right) the match with the smallest distance is taken. 

If the resulting cell is below or above another cell containing Text a row lable is assumed, else a column label is assumed.

5.10.4Implicit Intersection

For the reference resulting from a single QuotedLabel an implicit intersection is generated if the operator or function where it is used with expects a scalar value. The intersection is generated with the current formula's cell position, thus for a column label an intersection is generated with the formula cell's row, for a row label with the formula cell's column.

5.10.5Automatic Range

When passed as a non-scalar argument (e.g. Array or NumberSequence) to a function, a column or row label is converted to an automatic range reference that is adjusted each time the formula is interpreted. The range is generated from the corresponding column respectively row intersecting an area directly below respectively right of the label cell that is constructed by encompassing contiguous cells. A blank cell interrupts contiguousness, one blank cell directly below respectively right of the label cell is ignored.

Example:

Table 2 - Automatic Range

Row

Data

Expression

Result

Comment

1

Label

2

 

3

1

4

2

5

 

6

8

7

 

8

32

=SUM('Label')

3

Blank cell in row 2 is skipped (two blank cells in row 2 and 3 would not and stop), blank cell in row 5 stops the automatic range.

If any cell content is entered in row 5 the range is regenerated as follows:

Table 3 - Automatic Range

Row

Data

Expression

Result

Comment

1

Label

2

 

3

1

4

2

5

4

6

8

7

 

8

32

=SUM('Label')

15

Blank cell in row 2 is skipped, blank cell in row 7 stops the automatic range.

5.10.6Automatic Intersection

An automatic intersection may be used to identify the intersection of two quoted labels. Note that this is different from the IntersectionOp, which takes two references instead of two labels:

AutomaticIntersection ::= QuotedLabel Whitespace* '!!' Whitespace* QuotedLabel

In an automatic intersection, one of the labels identifies a row, the other a column; they may be in either order. Each QuotedLabel is looked up as defined above under "Lookup of Defined Lables" and "Automatic Lookup of Labels". If two data cell ranges are found, the intersection of the column's data cell range and the row's data cell range is generated. If the intersection result is not exactly one cell, an Error is generated.

5.11Named Expressions

A NamedExpression references another expression, possibly in a completely different spreadsheet or any other document type that can be imported into a spreadsheet.

NamedExpression ::= SimpleNamedExpression |
SheetLocalNamedExpression | ExternalNamedExpression

SimpleNamedExpression ::= Identifier |
'$$' (Identifier | SingleQuoted)

SheetLocalNamedExpression ::=
QuotedSheetName '.' SimpleNamedExpression

ExternalNamedExpression ::=
Source '#' (SimpleNamedExpression | SheetLocalNamedExpression)

Evaluators supporting named expressions shall support Simple Named Expressions that are global to all the sheets in a (spreadsheet) document in the current document. This is a named expression without a Source, QuotedSheetName, or SubtableCell. The type of a named expression is the type of the value that the named expression returns.

Named expressions are case-consistent, meaning that matching is done case-insensitive and identifiers can not differ ONLY in their case. Evaluators should write identifiers with identical case in all locations.

Evaluators may support Sheet-local Named Expressions that are local (attached) to individual sheets. In that case, a non-empty QuotedSheetName can be used to reference a sheet-specific named expression. The most specific named expression for a given expression is used. If the QuotedSheetName is empty, the search for the named expression begins with the current sheet, then up through the container(s) of the sheet (the same is true if the QuotedSheetName rule fragment is not included at all). If there is a non-empty QuotedSheetName, search begins with that named sheet, then up through its container(s) for the given name.

Note: There is no syntax for referencing a named expression without first looking at the current sheet's named expressions; where this is a problem, a user can define a blank sheet and reference that sheet as the starting location for finding the named expression.

If a sheetname is not empty, it shall be quoted using “'” (APOSTROPHE, U+0027). While both Source and QuotedSheetName can begin with the single-quote character “'” (APOSTROPHE, U+0027), they are distinguished: after the closing single-quote character, a non-empty source shall have the '#' (NUMBER SIGN, U+0023) character as the next non-whitespace; a non-empty sheetname shall be followed by the '.' (FULL STOP, U+002E) character as the next non-whitespace.

Expressions should limit the names of their identifiers to only ([UNICODE]) letters, underscores, and digits, not including patterns that look like cell references or the words True or False.

Note: Some evaluators do not support the use of Unicode for identifiers.

Identifier ::= ( LetterXML

5.12Constant Errors

Evaluators shall support the Error value #N/A. Evaluators may support other Error values. Evaluators may allow entry of errors directly, parse them and recognize them as Errors. Functions shall propagate Errors unless stated otherwise.

Inline Error constants shall have the following syntax:

Error ::= '#' [A-Z0-9]+ ([!?] | ('/' ([A-Z] | ([0-9] [!?]))))

Specific Error values are indicated by an identifier.

Table 4 is a list of constant error names that are used by several existing implementations. Evaluators may implement other constant Error values.

Table 4 - Possible Other Constant Error Values

Name

Comments

#DIV/0!

Attempt to divide by zero, including division by an empty cell. ERROR.TYPE of 2

#NAME?

Unrecognized/deleted name. ERROR.TYPE of 5.

#N/A

Not available. ISNA() applied to this value will return True. Lookup functions which failed, and NA(), return this value. ERROR.TYPE of 7.

#NULL!

Intersection of ranges produced zero cells. ERROR.TYPE of 1.

#NUM!

Failed to meet domain constraints (e.g., input was too large or too small). ERROR.TYPE of 6.

#REF!

Reference to invalid cell (e.g., beyond the application’s abilities). ERROR.TYPE of 4.

#VALUE!

Parameter is wrong type. ERROR.TYPE of 3.

An unknown constant Error value shall be mapped into an Error value supported by the evaluator when read (e.g., the application's equivalent of #NAME?), though an evaluator may warn the user if this has or will take place. It is desirable to preserve the original specific Error name when writing an Error constant back out, where possible, but evaluators may write a different Error value for a formula than they did when reading it for Errors other than #N/A. Whitespace shall not be included in an Error name.

Evaluators should use a human-comprehensible name, not a numeric id, for constant Error values they write.

5.13Inline Arrays

Inline arrays are enclosed with curly braces. Inside, they contain one or more rows, with each row separated by a row separator:

Array ::= '{' MatrixRow ( RowSeparator MatrixRow )* '}'

MatrixRow ::= Expression ( ';' Expression )*

RowSeparator ::= '|'

Evaluators that support inline arrays shall accept a matrix with one or more rows, each with one or more columns, with the same number of columns in each row, with constant values for each expression. Evaluators that do not support inline arrays, or cannot support a particular use permitted by this syntax, should compute an Error value for such arrays. An inline array is of type Array.

Note: Expression authors should be aware that use of Expression other than constant Number or constant String may impair interoperability.

5.14Whitespace

Whitespace ::= #x20 | #x09 | #x0a | #x0d

For calculation purposes, whitespace is ignored unless it is inside the contents of string constants or text surrounded by single quotes. Evaluators shall ignore any whitespace characters before and/or after any operators, constant numbers, constant strings, constant errors, inline arrays, parentheses used for controlling precedence, and the closing parenthesis of a function call. Whitespace shall be ignored following the initial equal sign(s). Whitespace shall be ignored just before a function name, but whitespace shall not separate a function name from its initial opening parentheses. Whitespace shall not be used in the interior of a terminating grammar rule (a rule that references no other rule other than character sets, internally or externally-defined), unless specifically permitted by the terminating grammar rule, since these rules define the lexical properties of a component. Evaluators shall not write formulas with whitespace embedded in any unquoted identifier, constant Number, or constant Error.  Evaluators shall treat SPACE (U+0020), CHARACTER TABULATION (U+0009), LINE FEED (U+000A), and CARRIAGE RETURN (U+000D) as whitespace characters.

An embedded line break shall be represented by a single LINE FEED character (U+000A), not by a carriage return-linefeed pair. When embedded in an XML attribute the linefeed character is represented as “&#x0A;”.

Evaluators should retain whitespace entered by the original formula creator and use it when saving or presenting the formula, and should not add additional whitespace unless directed to do so during the process of editing a formula.

6Standard Operators and Functions

6.1General

OpenFormula defines commonly used operators and functions.

Function names ignore case. Evaluators should write function names in all uppercase letters when writing OpenFormula formulas.

Unless otherwise noted, if any value being provided is an Error, the result is an Error; if more than one Error is provided, one of them is returned (evaluators should return the leftmost Error result).

6.2Common Template for Functions and Operators

For every function or operator, the following are defined in this specification:

Evaluators may extend functions by permitting fewer or additional parameters, which documents may use. Extended functions may result in a lack of interoperability.

The implicit conversion operators omit many of these items, e.g., the syntax (since there is none).

6.3Implicit Conversion Operators

6.3.1General

Any given function or operand takes 0 or more parameters, and each of those parameters has an expected type. The expected type can be one of the base types, identified above. It can also be of some conversion type that controls conversion, e.g., Any means that no conversion is done (it can be of any type); NumberSequence causes a conversion to an ordered sequence of zero or more numbers. If the passed-in type does not match the expected type, an attempt is made to automatically convert the value to the expected type. An Error is returned if the type cannot be converted (this can never happen if the expected type is Any). Unless otherwise noted, any conversion operation applied to a value of type Error returns the same value.

6.3.2Conversion to Scalar

To convert to a scalar, if the value is of type:

6.3.3Implied intersection

In some cases a reference to a single cell is needed, but a reference to multiple cells is provided. In this case an "implied intersection" is performed. To perform an implied intersection:

6.3.4Force to array context (ForceArray)

A ForceArray attribute forces calculation of the argument's expression into non-scalar array mode. This means that no implied intersection is performed, instead where a reference to a single cell is expected and multiple cells are provided, iteration over the multiple cells is performed and results are stored in an array that is passed on.

See also Non-Scalar Evaluation 3.3

6.3.5Conversion to Number

If the expected type is Number, then if value is of type:

6.3.6Conversion to Integer

If the expected type is Integer for a function or operator, apply the “Conversion to Number” operation. 6.3.5 Then, if the result is a Number but not an integer, apply the specific conversion from Number to integer specified by that particular function/operator. If the function or operator does not specify any particular conversion operation, then the conversion from a non-integer Number into an integer is implementation-defined.

Many different conversions from a non-integer number into an integer are possible. The conversion direction may be towards negative infinity, towards positive infinity, towards zero, away from zero, towards the nearest even number, or towards the nearest odd number. A conversion can select the nearest integer, the nearest even or odd integer, or the “next” integer in the given direction if it is not already an integer. If a conversion selects the nearest integer, a direction is still needed (for when a value is halfway between two integers). In this specification, this conversion is referred to as “rounding” or “truncation”; these terms by themselves do not specify any specific operation.

If a function specifies its rounding operation using a series of capital letters, the function defined in this specification for that function is used to do the conversion to integer. Common such functions are:

6.3.7Conversion to NumberSequence

If the expected type is NumberSequence, then if value is of type:

6.3.8Conversion to NumberSequenceList

Identical to Conversion to NumberSequence 6.3.7 , with the addition that instead of a Reference also a ReferenceList is accepted as argument. Each Reference in the list is converted to a NumberSequence in the order of occurrence.

6.3.9Conversion to DateSequence

Identical to Conversion to NumberSequence 6.3.7 except that each element in the list represents a serial date value of subtype Date.

6.3.10Conversion to Complex Number

An evaluator may accept complex numbers as Text, Number, or a different distinguishable type.

If the value is:

([+-]?Number [+-])?Number[ij]

[+-]?Number[ij]

6.3.11Conversion to ComplexSequence

If the expected type is ComplexSequence, then if value is of type:

6.3.12Conversion to Logical

If the expected type is Logical, then if value is of type:

6.3.13Conversion to LogicalSequence

If the expected type is LogicalSequence, then if value is of type:

6.3.14Conversion to Text

If the expected type is Text, then if value is of type:

6.3.15Conversion to DateParam

If the expected type is the pseudotype DateParam, then if value is of type:

6.3.16Conversion to TimeParam

If the expected type is the pseudotype TimeParam, then if value is of type:

6.4Standard Operators

6.4.1General

The functions defined under standard operators differ from other functions only on the basis of their frequency of use. That frequency of use has lead to the colloquial terminology, standard operators.

6.4.2Infix Operator "+"

Summary: Add two numbers.

Syntax: Number Left + Number Right

Returns: Number

Constraints: None

Semantics: Adds numbers together.

See also Infix Operator "-" 6.4.3, Prefix Operator "+" 6.4.15

6.4.3Infix Operator "-"

Summary: Subtract the second number from the first.

Syntax: Number Left - Number Right

Returns: Number

Constraints: None

Semantics: Subtracts one number from another number.

See also Infix Operator "+" 6.4.2, Prefix Operator "-" 6.4.16

6.4.4Infix Operator "*"

Summary: Multiply two numbers.

Syntax: Number Left * Number Right

Returns: Number

Constraints: None

Semantics: Multiplies numbers together.

See also Infix Operator "+" 6.4.2, Infix Operator "/" 6.4.5

6.4.5Infix Operator "/"

Summary: Divide the second number into the first.

Syntax: Number Left / Number Right

Returns: Number

Constraints: None

Semantics: Divides numbers.  Dividing by zero returns an Error.

See also Infix Operator "-" 6.4.3, Infix Operator "*" 6.4.4

6.4.6Infix Operator "^"

Summary: Exponentiation (Power).

Syntax: Number Left ^ Number Right

Returns: Number

Constraints: NOT(AND(Left=0; Right=0)); Evaluators may evaluate expressions where OR(Left != 0; Right != 0) evaluates to a non-Error value.

Semantics: Returns POWER(Left, Right).

See also Infix Operator "*" 6.4.4, POWER 6.16.46

6.4.7Infix Operator "="

Summary: Report if two values are equal

Syntax: Scalar Left = Scalar Right

Returns: Logical

Constraints: None

Semantics: Returns TRUE if two values are equal. If the values differ in type, return FALSE. If the values are both Number, return TRUE if they are considered equal, else return FALSE. If they are both Text, return TRUE if the two values match, else return FALSE. For Text values, if the calculation setting HOST-CASE-SENSITIVE is false, text is compared but characters differencing only in case are considered equal. If they are both Logicals, return TRUE if they are identical, else return FALSE. Error values cannot be compared to a constant Error value to determine if that is the same Error value.

Evaluators may approximate and test equality of two numeric values with an accuracy of the magnitude of the given values scaled by the number of available bits in the mantissa, ignoring some least significant bits and thus providing compensation for not exactly representable values.

The result of “1=TRUE()” is FALSE for evaluators that implement a distinct Logical type and TRUE if they don't.

See also Infix Operator "<>" 6.4.8

6.4.8Infix Operator "<>"

Summary: Report if two values are not equal

Syntax: Any Left <> Any Right

Returns: Logical

Constraints: None

Semantics: Returns NOT(Left = Right) if Left and Right are not Error. For Text values, if the calculation setting HOST-CASE-SENSITIVE is false, text is compared but characters differencing only in case are considered equal.

If either Left and Right are an Error, the result is an Error; this operator cannot be used to determine if two Errors are the same kind of Error.

Note: In some user interfaces the infix operator “<>” is displayed (or accepted) as “!=” or “≠”.

See also Infix Operator "=" 6.4.7

6.4.9Infix Operator Ordered Comparison ("<", "<=", ">", ">=")

Summary: Report if two values have the given order

Syntax: Scalar Left op Scalar Right

where op is one of: "<", "<=", ">", or ">="

Returns: Logical

Constraints: None

Semantics: Returns TRUE if the two values are less than, less than or equal, greater than, or greater than or equal (respectively). If both Left and Right are Numbers, compare them as numbers. If both Left and Right are Text, compare them as text; if the calculation setting HOST-CASE-SENSITIVE is false, text is compared but characters are compared ignoring case. If the values are both Logical, convert both to Number and then compare as Number.

These functions return one of True, False, or an Error if Left and Right have different types, but it is implementation-defined which of these results will be returned when the types differ.

See also Infix Operator "<>" 6.4.8, Infix Operator "=" 6.4.7

6.4.10Infix Operator "&"

Summary: Concatenate two strings.

Syntax: Text Left & Text Right

Returns: Text

Constraints: None

Semantics: Concatenates two text (string) values.

Note: The infix operator “&” is equivalent to CONCATENATE(Left,Right).

See also Infix Operator "+" 6.4.2, CONCATENATE 6.20.6

6.4.11Infix Operator Reference Range (":")

Summary: Computes an inclusive range given two references

Syntax: Reference Left : Reference Right

Returns: Reference

Constraints: None

Semantics: Takes two references and computes the range, that is, a reference to the smallest 3-dimensional cube of cells that include both Left and Right including the cells on sheets positioned between Left and Right. Left and Right need not be a single cell. For an expression such as [.B4:.B5]:[.C5] the resulting range is B4:C5. In case Left and/or Right involve a reference list (result of operator reference union), the range is computed and extended for each element of the list(s).

Note: For example, (a,b,c,d denoting one reference each)
(a~b):(c~d) computes a:b:c:d
determining the outermost front-top-left and rear-bottom-right corners.

Left and Right may also be defined names or the result of a function returning a reference, such as INDIRECT.

See also Infix Operator Reference Union 6.4.13, Infix Operator Reference Intersection 6.4.12, INDIRECT 6.14.7

6.4.12Infix Operator Reference Intersection ("!")

Summary: Compute the intersection of two references

Syntax: Reference Left ! Reference Right

Returns: Reference

Constraints: None

Semantics: Takes two references and computes the intersection - a reference to the intersection of cells in both Left and Right. If there are no cells in common, returns an Error.

If Left or Right are not of type Reference or ReferenceList, an Error shall be returned.

If Left and/or Right are reference lists (result of infix operator reference concatenation), the intersection is computed for each combination of Left and Right, producing a reference list of intersections.

Note: For example (a,b,c,d denoting one reference each):
(a~b)!(c~d) will compute (a!c)~(a!d)~(b!c)~(b!d)

If for a resulting intersection there are no cells in common, the element is ignored and omitted from the result list. If for all intersections there are no cells in common and the result list is empty, Error #NULL! is returned.

Note: Intersection is notated as "!" in OpenFormula format, but as a space character in some user interfaces.

See also Infix Operator Reference Union 6.4.13

6.4.13Infix Operator Reference Concatenation ("~") (aka Union)

Summary: Concatenate two references

Syntax: Reference Left ~ Reference Right

Returns: ReferenceList

Constraints: None

Semantics: Takes two references and computes the "cell union", which is a concatenation of the reference Left followed by the reference Right. This is not the same as a union in set theory; duplicate references to cells are not removed. The resulting reference will have the number of areas, as reported by AREAS, as AREAS(Left)+AREAS(Right).

Note: Concatenation is notated as "~" in OpenFormula format, but as a comma or “+” in some user interfaces.

If Left or Right are not of type Reference or ReferenceList, an Error shall be returned.

Test Cases:

See also Infix Operator Reference Range 6.4.11, Infix Operator Reference Intersection 6.4.12

6.4.14Postfix Operator "%"

Summary: Divide the operand by 100

Syntax: Number Left %

Returns: Number

Constraints: None

Semantics: Computes Left / 100.

See also Prefix Operator "-" 6.4.16, Prefix Operator "+" 6.4.15

6.4.15Prefix Operator "+"

Summary: No operation; returns its one argument.

Syntax: + Any Right

Returns: Any

Constraints: None

Semantics: Returns the value given to it. Note that this does not convert a value to the Number type. In fact, it does no conversion at all of a Number, Logical, or Text value - it returns the same Number, Logical, or Text value (respectively). The "+" applied to a reference may return the reference, or an Error.

See also Infix Operator "+" 6.4.2

6.4.16Prefix Operator "-"

Summary: Negate its one argument.

Syntax: - Number Right

Returns: Number

Constraints: None

Semantics: Computes 0 - Right.

See also Infix Operator "-" 6.4.3

6.5Matrix Functions

6.5.1General

Matrix functions operate on matrices.

A matrix with M columns and N rows is defined by

 
The dimension subscript may be omitted, if the context allows it, i.e.
. Matrices are represented by upper case letters. The elements of a matrix are denoted by the corresponding lower case letter and a subscript, which defines the column and the row.
Square matrices have the same amount of columns and rows, i.e.
.
 

6.5.2MDETERM

Summary: Calculates the determinant of a matrix.

Syntax: MDETERM( ForceArray Array matrix )

Returns: Number

Constraints: Only square matrices are allowed.

Semantics: Returns the determinant of the matrix. The determinant is defined by

 
where P denotes a permutation of the numbers 1, 2, ..., n and
is the sign of the permutation, which is +1 for an even amount of permutations and -1 for an odd amount.
Matrices with a non-zero determinant are invertible.
 

See also MINVERSE 6.5.3

6.5.3MINVERSE

Summary: Returns the inverse of a matrix.

Syntax: MINVERSE( ForceArray Array matrix )

Returns: Array

Constraints: Only square matrices are allowed.

Semantics: Calculates the inverse
 
of matrix A. The matrix A multiplied with its inverse
results in the unity matrix of the same dimension as A:
 
 

Invertible matrices have a non-zero determinant. If the matrix is not invertible, this function should return an Error value.

See also MDETERM 6.5.2

6.5.4MMULT

Summary: Multiplies the matrices A and B.

Syntax: MMULT( ForceArray Array A ; ForceArray Array B )

Returns: Array

Constraints: COLUMNS(A)=ROWS(B)

Semantics: Returns the matrix product of the two matrices. The elements
of the resulting matrix
, are defined by:
 
 

6.5.5MUNIT

Summary: Creates a unit matrix of a specified dimension N.

Syntax: MUNIT( Integer N )

Returns: Array

Constraints: The dimension has to be greater than zero.

Semantics: Creates the unit matrix (identity matrix) of dimension N.

 

6.5.6TRANSPOSE

Summary: Returns the transpose of a matrix.

Syntax: TRANSPOSE( Array A )

Returns: Array

Constraints: None

Semantics: Returns the transpose AT of a matrix A, i.e. rows and columns of the matrix are exchanged.

 

6.6Bit operation functions

6.6.1General

Evaluators shall support unsigned integer values and results of at least 48 bits (values from 0 to 2^48-1 inclusive).

6.6.2BITAND

Summary: Returns bitwise “and” of its parameters

Syntax: BITAND( Integer X ; Integer Y )

Returns: Number

Constraints:  X 0, Y 0

Semantics: Returns bitwise “and” of its parameters. In the result, each bit position is 1 if and only if all parameters' bits at that position are also 1; else it is 0.

6.6.3BITLSHIFT

Summary: Returns left shift of value x by n bits (“<<”)

Syntax: BITLSHIFT( Integer x ; Integer n )

Returns: Number

Constraints: x 0

Semantics: Returns left shift of value x by n bit positions:

6.6.4BITOR

Summary: Returns bitwise “or” of its parameters

Syntax: BITOR( Integer X ; Integer Y )

Returns: Number

Constraints: X 0, Y 0

Semantics: Returns bitwise “or” of its parameters. In the result, each bit position is 1 if any of its parameters' bits at that position are also 1; else it is 0.

6.6.5BITRSHIFT

Summary: Returns right shift of value x by n bits (“>>”)

Syntax: BITRSHIFT( Integer x ; Integer n )

Returns: Number

Constraints: x 0

Semantics: Returns right shift of value x by n bit positions:

See also BITAND 6.6.2, BITXOR 6.6.6, BITLSHIFT 6.6.3

6.6.6BITXOR

Summary: Returns bitwise “exclusive or” of its parameters

Syntax: BITXOR( Integer X ; Integer Y )

Returns: Number

Constraints: X 0, Y 0

Semantics: Returns bitwise “exclusive or” (xor) of its parameters. In the result, each bit position is 1 if one or the other parameters' bits at that position are 1; else it is 0.

See also BITAND 6.6.2, BITOR 6.6.4, OR 6.15.8

6.7Byte-position text functions

6.7.1General

Byte-position text functions are like their equivalent ordinary text functions, but manipulate byte positions rather than a count of the number of characters.  Byte positions are integers that may depend on the specific text representation used by the implementation. Byte positions are by definition implementation-dependent and reliance upon them reduces interoperability.

The pseudotypes ByteLength and BytePosition are Integers, but their exact meanings and values are not further defined by this specification.

6.7.2FINDB

Summary: Returns the starting position of a given text, using byte positions.

Syntax: FINDB( Text Search ; Text T [ ; BytePosition Start ] )

Returns: BytePosition

Semantics: The same as FIND, but using byte positions.

See also FIND 6.20.9 , LEFTB 6.7.3 , RIGHTB 6.7.7

6.7.3LEFTB

Summary: Returns a selected number of text characters from the left, using a byte position.

Syntax: LEFTB( Text T [ ; ByteLength Length ] )

Returns: Text

Semantics: As LEFT, but using a byte position.

See also LEFT 6.20.12, RIGHT 6.20.19, RIGHTB 6.7.7

6.7.4LENB

Summary: Returns the length of given text in units compatible with byte positions

Syntax: LENB( Text T )

Returns: ByteLength

Constraints: None.

Semantics: As LEN, but compatible with byte position values.

See also LEN 6.20.13, LEFTB 6.7.3, RIGHTB 6.7.7

6.7.5MIDB

Summary: Returns extracted text, given an original text, starting position using a byte position, and length.

Syntax: MIDB( Text T ; BytePosition Start ; ByteLength Length )

Returns: Text

Constraints: Length >= 0.

Semantics: As MID, but using byte positions.

See also MID 6.20.15, LEFTB 6.7.3, RIGHTB 6.7.7, REPLACEB 6.7.6

6.7.6REPLACEB

Summary: Returns text where an old text is replaced with a new text, using byte positions.

Syntax: REPLACEB( Text T ; BytePosition Start ; ByteLength Len ; Text New )

Returns: Text

Semantics: As REPLACE, but using byte positions.

See also REPLACE 6.20.17, LEFTB 6.7.3, RIGHTB 6.7.7, MIDB 6.7.5, SUBSTITUTE 6.20.21

6.7.7RIGHTB

Summary: Returns a selected number of text characters from the right, using byte position.

Syntax: RIGHTB( Text T [ ; ByteLength Length ] )

Returns: Text

Semantics: As RIGHT, but using byte positions.

See also RIGHT 6.20.19, LEFTB 6.7.3

6.7.8SEARCHB

Summary: Returns the starting position of a given text, using byte positions.

Syntax: SEARCHB( Text Search ; Text T [ ; BytePosition Start ] )

Returns: BytePosition

Semantics: As SEARCH, but using byte positions.

See also SEARCH 6.20.20, EXACT 6.20.8, FIND 6.20.9, FINDB 6.7.2

6.8Complex Number Functions

6.8.1General

Functions for complex numbers.

6.8.2COMPLEX

Summary: Creates a complex number from a given real coefficient and imaginary coefficient.

Syntax: COMPLEX( Number Real ; Number Imaginary [ ; Text Suffix ] )

Returns: Complex

Constraints: None

Semantics: Constructs a complex number by the given coefficients. The third parameter Suffix is optional, and should be either “i” or “j”. Upper case “I” or “J” are not accepted for the suffix parameter.

6.8.3IMABS

Summary: Returns the absolute value of a complex number

Syntax: IMABS( Complex X )

Returns: Number

Constraints: None

Semantics: If X=a+bi or X=a+bj, the absolute value =
 
; if N=r(cosφ + isinφ), the absolute value = r.

6.8.4IMAGINARY

Summary: Returns the imaginary coefficient of a complex number

Syntax: IMAGINARY( Complex X )

Returns: Number

Constraints: None

Semantics: If X=a+bi or X=a+bj, then the imaginary coefficient is b.

See also IMREAL 6.8.18

6.8.5IMARGUMENT

Summary: Returns the complex argument of a complex number

Syntax: IMARGUMENT( Complex X )

Returns: Number

Constraints: None

Semantics: If X=a+bi=r(cosφ + isinφ), a or b is not 0 and -π < φ ≤ π, then the complex argument is φ. φ is expressed by radians. If X=0, then IMARGUMENT(X) is implementation-defined and either 0 or an error.

See also IMABS 6.8.3

6.8.6IMCONJUGATE

Summary: Returns the complex conjugate of a complex number

Syntax: IMCONJUGATE( Complex X )

Returns: Complex

Constraints: None

Semantics: If X=a+bi, then the complex conjugate is a-bi.

6.8.7IMCOS

Summary: Returns the cosine of a complex number

Syntax: IMCOS( Complex X )

Returns: Complex

Constraints: None

Semantics: If X=a+bi, then cos(X)=cos(a)cosh(b)-sin(a)sinh(b)i.

See also IMSIN 6.8.19

6.8.8IMCOT

Summary: Returns the cotangent of a complex number

Syntax: IMCOT(Complex N)

Returns: Complex

Constraints: None

Semantics: Equivalent to the following (except N is computed only once):

IMDIV(IMCOS(N);IMSIN(N))

See also IMTAN 6.8.19

6.8.9IMCSC

Summary: Returns the cosecant of a complex number

Syntax: IMCSC(Complex N)

Returns: Complex

Constraints: None

Semantics: Equivalent to the following:

IMDIV(1;IMSIN(N))

See also IMSIN 6.8.19

6.8.10IMCSCH

Summary: Returns the hyperbolic cosecant of a complex number

Syntax: IMCSCH( Complex N )

Returns: Number

Constraints: None

Semantics: Computes the hyperbolic cosecant. This is equivalent to:

IMDIV(1;IMSINH(N))

See also IMSINH, CSCH

6.8.11IMDIV

Summary: Divides the second number into the first.

Syntax: IMDIV( Complex X ; Complex Y )

Returns: Complex

Constraints: None

Semantics: Given X=a+bi and Y=c+di, return the quotient

 

Division by zero returns an Error.

See also IMDIV 6.8.11

6.8.12IMEXP

Summary: Returns the exponent of e and a complex number.

Syntax: IMEXP( Complex X )

Returns: Complex

Constraints: None

Semantics: If X=a+bi, the result is
 
.

See also IMLN 6.8.13

6.8.13IMLN

Summary: Returns the natural logarithm of a complex number.

Syntax: IMLN( Complex X )

Returns: Complex

Constraints: None

Semantics: If X=r(cos φ + isin φ) , φ is expressed by radians, then the natural logarithm is returned.

See also IMEXP 6.8.12 , IMLOG10 6.8.14

6.8.14IMLOG10

Summary: Returns the common logarithm of a complex number.

Syntax: IMLOG10( Complex X )

Returns: Complex

Constraints: None

Semantics: If X=r(cos φ + isin φ) , φ is expressed by radians, then the common logarithm is returned.

See also IMLN 6.8.13 , IMPOWER 6.8.16

6.8.15IMLOG2

Summary: Returns the binary logarithm of a complex number.

Syntax: IMLOG2( Complex X )

Returns: Complex

Constraints: None

Semantics: If X=r(cos φ + isin φ) , φ is expressed by radians, then the binary logarithm is returned.

See also IMLN 6.8.13 , IMPOWER 6.8.16

6.8.16IMPOWER

Summary: Returns the power of N and a complex number.

Syntax: IMPOWER( Complex X ; Number n )

Returns: Complex

Constraints: None

Semantics: If X=a+bi=r(cos φ + isin φ) , the result is
 
.

See also IMEXP 6.8.12

6.8.17IMPRODUCT

Summary: Returns the product of complex numbers.

Syntax: IMPRODUCT( { ComplexSequence N }+ )

Returns: Complex

Constraints: None

Semantics: Multiply the complex numbers together. Given two complex numbers X=a+bi and Y=c+di, the product X*Y = (ac-bd) + (ad+bc)i

See also IMDIV 6.8.11

6.8.18IMREAL

Summary: Returns the real coefficient of a complex number

Syntax: IMREAL( Complex N )

Returns: Number

Constraints: None

Semantics: If N=a+bi or N=a+bj, then the real coefficient is a.

See also IMAGINARY 6.8.4

6.8.19IMSIN

Summary: Returns the sine of a complex number

Syntax: IMSIN( Complex N )

Returns: Complex

Constraints: None

Semantics: If N=a+bi, then sin(N)=sin(a)cosh(b)-cos(a)sinh(b)i.

See also IMCOS 6.8.7

6.8.20IMSEC

Summary: Returns the secant of a complex number

Syntax: IMSEC(Complex N)

Returns: Complex

Constraints: None

Semantics: Equivalent to the following:

IMDIV(1;IMCOS(N))

See also IMCOS 6.8.7

6.8.21IMSECH

Summary: Returns the hyperbolic secant of a complex number

Syntax: IMSECH( Complex N )

Returns: Number

Constraints: None

Semantics: Computes the hyperbolic secant. This is equivalent to:

IMDIV(1;IMCOSH(N))

See also IMCOSH, SECH

6.8.22IMSQRT

Summary: Returns the square root of a complex number

Syntax: IMSQRT( Complex N )

Returns: Complex

Constraints: None

Semantics: If N=r(cosφ + isinφ), φ is expressed by radians, then the square root of N is returned.

See also IMPOWER 6.8.16

6.8.23IMSUB

Summary: Subtracts the second complex number from the first.

Syntax: IMSUB( Complex X ; Complex Y )

Returns: Complex

Constraints: None

Semantics: Subtract complex number Y from X.

See also IMSUM 6.8.24

6.8.24IMSUM

Summary: Sums (add) a set of complex numbers, including all numbers in ranges

Syntax: IMSUM( { ComplexSequence N }+ )

Returns: Complex Number

Constraints: None

Semantics: Adds complex numbers together. Text that cannot be converted to a complex number is ignored.

It is implementation-defined what happens if this function is given zero parameters; an evaluator may either produce an Error or the Number 0 if it is given zero parameters.

See also IMSUB 6.8.23

6.8.25IMTAN

Summary: Returns the tangent of a complex number

Syntax: IMTAN(Complex N)

Returns: Complex

Constraints: None

Semantics: Equivalent to the following (except N is computed only once):

IMDIV(IMSIN(N);IMCOS(N))

See also IMSIN, IMCOS, IMCOT 6.8.23

6.9Database Functions

6.9.1General

Database functions use the variables, Database 4.11.8, Field 4.11.9, and Criteria 4.11.10.

The results of database functions may change when the values of the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties change. 3.4

6.9.2DAVERAGE

Summary: Finds the average of values in a given field from the records (rows) in a database that match a search criteria.

Syntax: DAVERAGE( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: Nonef

Semantics: Perform AVERAGE on data records in database D field F that match criteria C.

See also AVERAGE 6.18.3, COUNT 6.13.6, DSUM 6.9.11, DCOUNT 6.9.3, SUM 6.16.61

6.9.3DCOUNT

Summary: Counts the number of records (rows) in a database that match a search criteria and contain numerical values.

Syntax: DCOUNT( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Perform COUNT on data records in database D field F that match criteria C.

See also COUNT 6.13.6, COUNTA 6.13.7, DCOUNTA 6.9.4, DSUM 6.9.11

6.9.4DCOUNTA

Summary: Counts the number of records (rows) in a database that match a search criteria and contain values (as COUNTA).

Syntax: DCOUNTA( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Perform COUNTA on data records in database D field F that match criteria C.

See also COUNT 6.13.6, COUNTA 6.13.7, DCOUNT 6.9.3, DSUM 6.9.11

6.9.5DGET

Summary: Gets the single value in the field from the single record (row) in a database that matches a search criteria.

Syntax: DGET( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Extracts the value in field F of the one data record in database D that matches criteria C. If no records match, or more than one matches, it returns an Error.

See also DMAX 6.9.6, DMIN 6.9.7, DSUM 6.9.11

6.9.6DMAX

Summary: Finds the maximum value in a given field from the records (rows) in a database that match a search criteria.

Syntax: DMAX( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Perform MAX on only the data records in database D field F that match criteria C.

See also MAX 6.18.45, DMIN 6.9.7, MIN 6.18.48

6.9.7DMIN

Summary: Finds the minimum value in a given field from the records (rows) in a database that match a search criteria.

Syntax: DMIN( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Perform MIN on only the data records in database D field F that match criteria C.

See also MIN 6.18.48, DMAX 6.9.6, MAX 6.18.45

6.9.8DPRODUCT

Summary: Finds the product of values in a given field from the records (rows) in a database that match a search criteria.

Syntax: DPRODUCT( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Multiply together only the data records in database D field F that match criteria C.

See also SUM 6.16.61, DSUM 6.9.11

6.9.9DSTDEV

Summary: Finds the sample standard deviation in a given field from the records (rows) in a database that match a search criteria.

Syntax: DSTDEV( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Perform STDEV on only the data records in database D field F that match criteria C.

See also STDEV 6.18.72, DSTDEVP 6.9.10

6.9.10DSTDEVP

Summary: Finds the population standard deviation in a given field from the records (rows) in a database that match a search criteria.

Syntax: DSTDEVP( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Perform STDEVP on only the data records in database D field F that match criteria C.

See also STDEVP 6.18.74, DSTDEV 6.9.9

6.9.11DSUM

Summary: Finds the sum of values in a given field from the records (rows) in a database that match a search criteria.

Syntax: DSUM( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Perform SUM on only the data records in database D field F that match criteria C.

See also SUM 6.16.61, DMIN 6.9.7, DMAX 6.9.6

6.9.12DVAR

Summary: Finds the sample variance in a given field from the records (rows) in a database that match a search criteria.

Syntax: DVAR( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Perform VAR on only the data records in database D field F that match criteria C.

See also VAR 6.18.82, DVARP 6.9.13

6.9.13DVARP

Summary: Finds the population variance in a given field from the records (rows) in a database that match a search criteria.

Syntax: DVARP( Database D ; Field F ; Criteria C )

Returns: Number

Constraints: None

Semantics: Perform VARP on only the data records in database D field F that match criteria C.

See also VARP 6.18.84, DVAR 6.9.12

6.10Date and Time Functions

6.10.1General

6.10.2DATE

Summary: Constructs a date from year, month, and day of month.

Syntax: DATE( Integer Year ; Integer Month ; Integer Day )

Returns: Date

Constraints: 1904 <= Year <= 9956; 1 <= Month <= 12; 1 <= Day <= 31; Evaluators may evaluate expressions that do no meet this constraint.

Semantics: This computes the date's serial number given Year, Month, and Day of the Gregorian calendar. Fractional values are truncated. Month > 12 and Day > days of Month will roll over the date, computing the result by adding months and days as necessary. The value of the serial number depends on the current epoch.

See also TIME 6.10.17, DATEVALUE 6.10.4

6.10.3DATEDIF

Summary: Returns the difference in years, months, or days of two date numbers.

Syntax: DATEDIF( DateParam StartDate ; DateParam EndDate ; Text Format )

Returns: Number

Constraints: None

Semantics: Compute difference of StartDate and EndDate, in the units given by Format.

The Format is a code from the following table, entered as text, that specifies the format you want the result of DATEDIF to have.

Table 5 - DATEDIF

format

Returns the number of

y

Years

m

Months. If there is not a complete month between the dates, 0 will be returned.

d

Days

md

Days, ignoring months and years

ym

Months, ignoring years

yd

Days, ignoring years

See also DAYS360 6.10.7, DAYS 6.10.6, Infix Operator “-” 6.4.3

6.10.4DATEVALUE

Summary: Returns the date serial number from given text.

Syntax: DATEVALUE( Text D )

Returns: Date

Constraints: None

Semantics: This computes the serial number of the text string D, using the current locale. This function shall accept ISO date format (YYYY-MM-DD), which is locale-independent. It is semantically equal VALUE(Date) if Date has a date format, since text matching a date format is automatically converted to a serial number when used as a Number. If the text of D has a combined date and time format, e.g. YYYY-MM-DD HH:MM:SS, the integer part of the date serial number is returned. If the text of Date does not have a date or time format, an evaluator may return an Error. See VALUE for more information on date formats. The value of the serial number depends on the current epoch.

See also TIME 6.10.17, DATE 6.10.2, TIMEVALUE 6.10.18, VALUE 6.13.34

6.10.5DAY

Summary: Returns the day from a date.

Syntax: DAY( DateParam Date )

Returns: Number

Constraints: None

Semantics: Returns the day portion of a date.

See also MONTH 6.10.13, YEAR 6.10.23

6.10.6DAYS

Summary: Returns the number of days between two dates

Syntax: DAYS( DateParam EndDate ; DateParam StartDate )

Returns: Number

Constraints: None

Semantics: Returns the number of days between two dates. If StartDate and EndDate are Numbers, this is EndDate – StartDate. If they are both Text, this is DATEVALUE(StartDate) – DATEVALUE(EndDate).

See also DATEDIF 6.10.3, DAYS360 6.10.7, MONTH 6.10.13, YEAR 6.10.23, Infix Operator “-” 6.4.3

6.10.7DAYS360

Summary: Returns the number of days between two dates using the 360-day year

Syntax: DAYS360( DateParam StartDate ; DateParam EndDate [ ; Integer Method = 0 ] )

Returns: Number

Constraints: 0 <= Method <= 1

Semantics: Returns the number of days between two dates, using the 360-day year system (12 30-month days). In this system, February always has 30 days and there are no leap years.

If method is 0, it uses the National Association of Securities Dealers (NASD) method, also known as the U.S. method. If the method is 1, the European method is used.

The US/NASD Method (30US/360):

  1. 1.Truncate date values, set sign=1. 

  2. 2.If StartDate's day-of-month is 31, it is changed to 30. 

  3. 3.Otherwise, if StartDate's day-of-month is the last day of February, it is changed to 30. 

  4. 4.If EndDate's day-of-month is 31 and StartDate's day-of-month is 30 (after having applied a change for #2 or #3, if necessary), EndDate's day-of-month is changed to 30. 

    Note: This calculation is slightly different from Basis 0 (4.11.6 Basis). Dates are never swapped. 

The European Method (30E/360):

  1. 1.Truncate date values, set sign=1. 

  2. 2.If StartDate is after EndDate then swap dates and set sign=-1. 

  3. 3.If StartDate's day-of-month is 31, it is changed to 30. 

  4. 4.If EndDate's day-of-month is 31, it is changed to 30. 

    Note: Days in February are never changed. 

    Note: This calculation is identical to Basis 4 (4.11.6 Basis) 

For both methods the value then returned is
sign * ((EndDate.year*360 + EndDate.month*30 + EndDate.day) - (StartDate.year*360 + StartDate.month*30 + StartDate.day))

See also DAYS 6.10.6, DATEDIF 6.10.3

6.10.8EDATE

Summary: Returns the serial number of a given date when MonthAdd months is added

Syntax: EDATE( DateParam StartDate ; Number MonthAdd )

Returns: Number

Constraints: None

Semantics: First truncate StartDate and MonthAdd, then add MonthAdd number of months. MonthAdd can be positive, negative, or 0; if zero, the number representing StartDate (in the current epoch) is returned.

If after adding the given number of months, the day of month in the new month is larger than the number of days in the given month, the day of month is adjusted to the last day of the new month. Then the serial number of that date is returned.

See also DAYS 6.10.6, DATEDIF 6.10.3, EOMONTH 6.10.9

6.10.9EOMONTH

Summary: Returns the serial number of the end of a month, given date plus MonthAdd months

Syntax: EOMONTH( DateParam StartDate ; Integer MonthAdd )

Returns: Number

Constraints: None

Semantics: First truncate StartDate and MonthAdd, then add MonthAdd number of months. MonthAdd can be positive, negative, or 0. Then return the serial number representing the end of that month. Due to the semantics of this function, the value of DAY(StartDate) is irrelevant.

See also EDATE 6.10.8

6.10.10HOUR

Summary: Extracts the hour (0 through 23) from a time.

Syntax: HOUR( TimeParam T )

Returns: Number

Constraints: None

Semantics: Extract from T the hour value, 0 through 23, as per a 24-hour clock. This is equal to:

DayFraction=(T-INT(T))

Hour=INT(DayFraction*24)

See also MONTH 6.10.13, DAY 6.10.5, MINUTE 6.10.12, SECOND 6.10.16

6.10.11ISOWEEKNUM

Summary: Determines the ISO week number of the year for a given date.

Syntax: ISOWEEKNUM( DateParam Date [ ; Integer Mode = 2 ] )

Returns: Number

Constraints: None

Semantics: Returns the number of the ISO 8601 week in the year for the given date. Note that this is not the “conventional” week number used by some applications (for that, see WEEKNUM). In this system, week number 1 of any year is the week that contains January 4, because (1) Monday is considered the first day of the week, and (2) a week that lies partly in one year and partly in another is assigned a number in the year in which most of its days lie.

Mode determines the starting day of the week:

Table 6 - ISOWEEKNUM

Mode

Week starts on

1

Sunday

2

Monday

See also DAY 6.10.5, MONTH 6.10.13, YEAR 6.10.23, WEEKDAY 6.10.20, WEEKNUM 6.10.21

6.10.12MINUTE

Summary: Extracts the minute (0 through 59) from a time.

Syntax: MINUTE( TimeParam T )

Returns: Number

Constraints: None

Semantics: Extract from T the minute value, 0 through 59, as per a clock. This is equal to:

DayFraction=(T-INT(T))

HourFraction=(DayFraction*24-INT(DayFraction*24))

Minute=INT(HourFraction*60)

See also MONTH 6.10.13, DAY 6.10.5, HOUR 6.10.10, SECOND 6.10.16

6.10.13MONTH

Summary: Extracts the month from a date.

Syntax: MONTH( DateParam Date )

Returns: Number

Constraints: None

Semantics: Takes a date and returns the month portion.

See also YEAR 6.10.23, DAY 6.10.5

6.10.14NETWORKDAYS

Summary: Returns the whole number of work days between two dates.

Syntax: NETWORKDAYS( DateParam Date1 ; DateParam Date2 [ ; [ DateSequence holidays ] [ ; LogicalSequence workdays ] ] )

Returns: Number

Constraints: None

Semantics: Returns the whole number of days between two dates, ignoring weekends.

Work days are defined as non-weekend, non-holiday days. By default, weekends are Saturdays and Sundays and there are no holidays.

The optional 3rd parameter Holidays can be used to specify a list of dates to be treated as holidays. Note that this parameter can be omitted as an empty parameter (two consecutive ;; semicolons) to be able to pass the set of Workdays without Holidays.

The optional 4th parameter Workdays can be used to specify a different definition for the standard work week by passing in a list of Logical values which define which days of the week are workdays. So, the default definition of the work week excludes Saturday and Sunday and is: {1;0;0;0;0;0;1}. To define the workweek as excluding Friday and Saturday, the third parameter would be: {0;0;0;0;0;1;1}.

6.10.15NOW

Summary: Returns the serial number of the current date and time.

Syntax: NOW()

Returns: DateTime

Constraints: None

Semantics: This returns the current day and time serial number, using the current locale. If you want only the serial number of the current day, use TODAY 6.10.19.

See also DATE 6.10.2, TIME 6.10.17, TODAY 6.10.19

6.10.16SECOND

Summary: Extracts the second (the integer 0 through 59) from a time. This function presumes that leap seconds never exist.

Syntax: SECOND( TimeParam T )

Returns: Number

Constraints: None

Semantics: Extract from T the second value, 0 through 59, as per a clock. Note that this returns an integer, without a fractional part. Note also that this rounds to the nearest second, instead of returning the integer part of the seconds. This is equal to:

DayFraction=(T-INT(T))

HourFraction=(DayFraction*24-INT(DayFraction*24))

MinuteFraction=(HourFraction*60-INT(HourFraction*60))

Second=ROUND(MinuteFraction*60)

See also MONTH 6.10.13, DAY 6.10.5, HOUR 6.10.10, MINUTE 6.10.12

6.10.17TIME

Summary: Constructs a time value from hours, minutes, and seconds.

Syntax: TIME( Number hours ; Number minutes ; Number seconds )

Returns: Time

Constraints: None. Evaluators may first perform INT() on the hour, minute, and second before doing the calculation.

Semantics: Returns the fraction of the day consumed by the given time, i.e.:

((hours*60*60)+(minutes*60)+seconds)/(24*60*60)

Time is a subtype of number, where a time value of 1 = 1 day = 24 hours.

Hours, minutes, and seconds may be arbitrary numbers (they shall not be limited to the ranges 0..24, 0..59, or 0..60 respectively).

See also DATE 6.10.2

6.10.18TIMEVALUE

Summary: Returns a time serial number from given text.

Syntax: TIMEVALUE( Text T )

Returns: Time

Constraints: None

Semantics: This computes the serial number of the text string T, which is a time, using the current locale. This function shall accept ISO time format (HH:MM:SS), which is locale-independent. If the text of T has a combined date and time format, e.g. YYYY-MM-DD HH:MM:SS, the fractional part of the date serial number is returned. If the text of T does not have a time format, an evaluatormay attempt to convert the number another way (e.g., using VALUE), or it may return an Error (this is implementation-dependent).

See also TIME 6.10.17, DATE 6.10.2, DATEVALUE 6.10.4, VALUE 6.13.34

6.10.19TODAY

Summary: Returns the serial number of today.

Syntax: TODAY()

Returns: Date

Constraints: None

Semantics: This returns the current day's serial number, using current locale. This only returns the date, not the datetime value.  For the specific time of day as well, use NOW 6.10.15.

See also TIME 6.10.17, NOW 6.10.15

6.10.20WEEKDAY

Summary: Extracts the day of the week from a date; if text, uses current locale to convert to a date.

Syntax: WEEKDAY( DateParam Date [ ; Integer Type = 1 ] )

Returns: Number

Constraints: None

Semantics: Returns the day of the week from a date, as a number from 0 through 7. The exact meaning depends on the value of Type:

  1. 1.When Type is 1, Sunday is the first day of the week, with value 1; Saturday has value 7. 

  2. 2.When Type is 2, Monday is the first day of the week, with value 1; Sunday has value 7. 

  3. 3.When Type is 3, Monday is the first day of the week, with value 0; Sunday has value 6. 

Table 7 - WEEKDAY

Day of Week

Type=1 Result

Type=2 Result

Type=3 Result

Sunday

1

7

6

Monday

2

1

0

Tuesday

3

2

1

Wednesday

4

3

2

Thursday

5

4

3

Friday

6

5

4

Saturday

7

6

5

See also DAY 6.10.5, MONTH 6.10.13, YEAR 6.10.23

6.10.21WEEKNUM

Summary: Determines the week number of the year for a given date.

Syntax: WEEKNUM( DateParam Date [ ; Number Mode = 1 ] )

Returns: Number

Constraints: 1 ≤ Mode ≤ 2, or 11 ≤ Mode ≤ 17, or Mode = 21, or Mode = 150

Semantics: Returns the number of the week in the year for the given date.

For Mode={1, 2, 11, 12, ..., 17} the week containing January 1 is the first week of the year, and is numbered week 1. The week starts on {Sunday, Monday, Monday, Tuesday, ..., Sunday}.

Mode 21 or 150 are both ISO 8601, the week starts on Monday and the week containing the first Thursday of the year is the first week of the year, and is numbered week 1.

See also DAY 6.10.5, MONTH 6.10.13, YEAR 6.10.23, WEEKDAY 6.10.20, ISOWEEKNUM 6.10.11

6.10.22WORKDAY

Summary: Returns the date serial number which is a specified number of days before or after an input date.

Syntax: WORKDAY( DateParam Date ; Number Offset [ ; [ DateSequence Holidays ] [ ; LogicalSequence Workdays ] ] )

Returns: DateTime

Constraints: None

Semantics: Returns the date serial number for the day that is offset from the input Date parameter by the number of work days specifed in the Offset parmameter. If Offset is negative, the offset will return a date prior to Date. If Offset is positive, a date later Date is returned. If Offset is zero, then Date is returned.

Work days are defined as non-weekend, non-holiday days. By default, weekends are Saturdays and Sundays and there are no holidays.

The optional 3rd parameter Holidays can be used to specify a list of dates to be treated as holidays. Note that this parameter can be omitted as an empty parameter (two consecutive ;; semicolons) to be able to pass the set of Workdays without Holidays.

The optional 4th parameter Workdays can be used to specify a different definition for the standard work week by passing in a list of Logical values which define which days of the week are workdays.

Note: The default definition of the work week that excludes Saturday and Sunday and is: {1;0;0;0;0;0;1}. To define the workweek as excluding Friday and Saturday, the third parameter would be: {0;0;0;0;0;1;1}.

6.10.23YEAR

Summary: Extracts the year from a date given in the current locale of the evaluator.

Syntax: YEAR( DateParam D )

Returns: Number

Constraints: None

Semantics: Parses a date-formatted string in the current locale's format and returns the year portion.

If a year is given as a two-digit number, as in "05-21-15", then the year returned is either 1915 or 2015, depending upon the break point in the calculation context.  In an OpenDocument document, this break point is determined by HOST-NULL-YEAR.

Evaluators shall support extracting the year from a date beginning in 1900. Three-digit year numbers precede adoption of the Gregorian calendar, and may return either an Error or the year number. Four-digit year numbers preceding 1582 (inception of the Gregorian Calendar) may return either an Error or the year number. Four-digit year numbers following 1582 should return the year number.

See also MONTH 6.10.13, DAY 6.10.5, VALUE 6.13.34

6.10.24YEARFRAC

Summary: Extracts the number of years (including fractional part) between two dates

Syntax: YEARFRAC( DateParam StartDate ; DateParam EndDate [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: None

Semantics: Computes the fraction of the number of years between a StartDate and EndDate.  Basis is the system for determining how many days are in a month or year.

Note: The Basis default is not the actual number of days in a month or year.   4.11.6

See also DATEDIF 6.10.3

6.11External Access Functions

6.11.1General

OpenFormula defines two functions, DDE and HYPERLINK, for accessing external data.

6.11.2DDE

Summary: Returns data from a DDE request

Syntax: DDE( Text server ; Text topic ; Text item [ ; Integer Mode = 0 ] )

Returns: Number|Text

Constraints: None

Semantics: Performs a DDE request and returns its result. The request invokes the service server on the topic named as topic, requesting that it reply with the information on item.

Evaluators may choose to not perform this function on every recalculation, but instead cache an answer and require a separate action to re-perform these requests. Evaluators shall perform this request on initial load when their security policies permit it.

Mode is an optional parameter that determines how the results are returned:

Table 8 - DDE

Mode

Effect

0 or missing

Data converted to number using VALUE in the number style's locale of the default table cell style

1

Data converted to number using VALUE in the English-US (en_US) locale

2

Data retrieved as text (not converted to number)

In an OpenDocument spreadsheet document the default table cell style is specified with table:default-cell-style-name. Its number:number-style specified by style:data-style-name specifies the locale to use in the conversion.

The DDE function is non-portable because it depends on availability of external programs (server parameter) and their interpretation of the topic and item parameters.

6.11.3HYPERLINK

Summary: Returns a Text or Number result and adds a string to the IRI part of a hyperlink cell.

Syntax: HYPERLINK( Text IRI [ ; Text|Number FunctionResult ] )

Returns: Text or Number

Constraints: None

Semantics: The IRI parameter specifies the link target added to the hyperlink cell, while the FunctionResult parameter is shown as part of the formula result in the cell. If FunctionResult is omitted, the IRI will be used for both the IRI and the cell result. If FunctionResult is Text, a Text result is returned. If FunctionResult is Number, a Number result is returned.

If a formula contains a HYPERLINK function, the cell becomes a "hyperlink cell". Clicking on this cell will execute the contained hyperlink. Therefore it is irrelevant if the HYPERLINK function is really evaluated (it may i.e. be located in a non-executed part of an IF function) – the cell will always be a hyperlink cell, even if the formula evaluates to a number or a Boolean value. The only exception to this rule is if an Error code would be part of the IRI. In this case no hyperlink cell will be created.

In a hyperlink cell, all other functions affect both the current IRI and the cell text. Therefore the formula has to be evaluated twice. In the first run using the IRI part of all hyperlink functions, and in the second run using the FunctionResult part.

6.12Financial Functions

6.12.1General

The financial functions are defined for use in financial calculations.

An annuity is a recurring series of payments.  A "simple annuity" is one where equal payments are made at equal intervals, and the compounding of interest occurs at those same intervals.  The time between payments is called the "payment interval".  Where payments are made at the end of the payment interval, it is called an "ordinary annuity".  Where payments are made at the beginning of the payment interval, it is called an "annuity due".  Periods are numbered starting at 1.

6.12.2ACCRINT

Summary: Calculates the accrued interest for securities with periodic interest payments.

Syntax: ACCRINT( DateParam issue ; DateParam first ; DateParam settlement ; Number coupon ; Number par ; Integer frequency [ ; Basis basis = 0 [ ; Logical calc_method = TRUE() ] ] )

Returns: Currency

Constraints: issue < first < settlement ; coupon > 0; par > 0

frequency is one of the following values:

Table 9 - ACCRINT

frequency

Frequency of coupon payments

1

Annual

2

Semiannual

4

Quarterly

12

Monthly

Semantics: Calculates the accrued interest for securities with periodic interest payments. ACCRINT supports short, standard, and long coupon periods.

If calc_method is TRUE (the default) then ACCRINT returns the sum of the accrued interest in each coupon period from issue date until settlement date. If calc_method is FALSE then ACCRINT returns the sum of the accrued interest in each coupon period from first date until settlement date. For each coupon period, the interest is par*coupon*YEARFRAC(start-of-period;end-of-period; basis)

issue                The security's issue or dated date.
first                The security's first interest date.
settlement        The security's settlement date.
coupon                The security's annual coupon rate.
par                The security's par value, that is, the principal to be paid at maturity.
frequency        The number of coupon payments per year.
basis                The type of day-count basis to use; see section
4.11.6
calc_methodA logical value that specifies how to treat the case where settlement>first.

See also ACCRINTM 6.12.3

6.12.3ACCRINTM

Summary: Calculates the accrued interest for securities that pay at maturity.

Syntax: ACCRINT( DateParam issue ; DateParam settlement ; Number coupon ; Number par [ ; Basis basis = 0 ] )

Returns: Currency

Constraints: coupon > 0; par > 0

Semantics: Calculates the accrued interest for securities that pay at maturity.

issue                The security's issue or dated date.
settlement        The security's maturity date.
coupon                The security's annual coupon rate.
par                The security's par value, that is, the principal to be paid at maturity.
basis                The type of day-count basis to use; see section
4.11.6

See also ACCRINT 6.12.2

6.12.4AMORDEGRC

Summary: Calculates the amortization value for the French accounting system using degressive depreciation.

Syntax: AMORDEGRC( Number cost ; DateParam purchaseDate ; DateParam firstPeriodEndDate ; Number salvage ; Integer period ; Number rate [ ; Basis basis = 0 ] )

Returns: Currency

Constraints: cost > 0; purchaseDate <= firstPeriodEndDate; salvage >= 0; period >= 0; rate > 0

Semantics: Calculates the amortization value for the French accounting system using degressive depreciation.

cost                        The value of the asset at the date of aquisition.
purchaseDate                The date of aquisition.
firstPeriodEndDateThe end date of the first depreciation period.
salvage                        The value of the asset at the end of the depreciation life time.
period                        The period of interest.
rate                        The rate of depreciation.
basis                        The type of day-count basis to use; see section
4.11.6

The asset life time is the inverse of the rate,
. The depreciation factor is denoted by factor.
 

Table 10 - AMORDEGRC

Asset life time (
)
 
Depreciation factor (
)
 
 

1.0

 

1.5

 

2.0

 

2.5


The depreciation allowance for the period
is denoted by
and takes the following values:
 
 

See also AMORLINC 6.12.5 , DB 6.12.14, DDB 6.12.15, YEARFRAC 6.10.24

6.12.5AMORLINC

Summary: Calculates the amortization value for the French accounting system using linear depreciation (l'amortissement linéaire comptable) .

Syntax: AMORLINC( Number cost ; DateParam purchaseDate ; DateParam firstPeriodEndDate ; Number salvage ; Integer period ; Number rate [ ; Basis basis = 0 ] )

Returns: Currency

Constraints: cost > 0; purchaseDate <= firstPeriodEndDate; salvage >= 0; period >= 0; rate > 0

Semantics: Calculates the amortization value for the French accounting system using linear depreciation.

cost                        The value of the asset at the date of aquisition.
purchaseDate
                The date of aquisition.
firstPeriodEndDate       
The end date of the first depreciation period.
salvage                        The value of the asset at the end of the depreciation life time.
period                        Which period the depreciation should be calculated for.
rate                        The rate of depreciation.
basis                       
Indicates the day count basis to use; see section
4.11.6

When period = 0:

 

For full periods, where period > 0, the depreciation is cost * rate

 

For the last period, possibly a partial period, the depreciation = cost-salvage-accumulated-depreciation, where accumulated-depreciation is the sum of the depreciation in period 0 plus any full period depreciations.

 

When period > depreciated life of the asset, i.e., when period > (cost-salvage)/(cost*rate) then the depreciation is 0.

 

Note: The behavior of this function is implementation-defined in cases where purchaseDate = firstPeriodEndDate.

See also AMORDEGRC 6.12.4, DB 6.12.14, DDB 6.12.15, YEARFRAC 6.10.24

6.12.6COUPDAYBS

Summary: Calculates the number of days between the beginning of the coupon period that contains the settlement date and the settlement date.

Syntax: COUPDAYBS( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )

Returns: Number

Constraints: settlement < maturity

frequency is one of the following values:

Table 11 - COUPDAYBS

frequency

Frequency of coupon payments

1

Annual

2

Semiannual

4

Quarterly


Semantics: Calculate the number of days from the beginning of the coupon period to the settlement date.

settlementThe settlement date.
maturityThe maturity date.
frequencyThe number of coupon payments per year.
basisThe type of day-count basis; see section
4.11.6

See also COUPDAYS 6.12.7 , COUPDAYSNC 6.12.8 , COUPNCD 6.12.8 , COUPNUM 6.12.10 , COUPPCD 6.12.11

6.12.7COUPDAYS

Summary: Calculates the number of days in a coupon period that contains a settlement date.

Syntax: COUPDAYS( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )

Returns: Number

Constraints: settlement < maturity

frequency is one of the following values:

Table 12 - COUPDAYS

frequency

Frequency of coupon payments

1

Annual

2

Semiannual

4

Quarterly


Semantics: Calculates the number of days in the coupon period containing the settlement date.

settlementThe settlement date.
maturityThe maturity date.
frequencyThe number of coupon payments per year.
basisThe type of day-count basis; see section
4.11.6

See also COUPDAYBS 6.12.6 , COUPDAYSNC 6.12.8 , COUPNCD 6.12.8 , COUPNUM 6.12.10 , COUPPCD 6.12.11

6.12.8COUPDAYSNC

Summary: Calculates the number of days between a settlement date and the next coupon date.

Syntax: COUPDAYNC( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )

Returns: Number

Constraints: settlement < maturity

frequency is one of the following values:

Table 13 - COUPDAYSNC

frequency

Frequency of coupon payments

1

Annual

2

Semiannual

4

Quarterly


Semantics: Calculates the number of days between the settlement date and the next coupon date.

settlementThe settlement date.
maturityThe maturity date.
frequencyThe number of coupon payments per year.
basisThe type of day-count basis; see section
4.11.6

See also COUPDAYBS 6.12.6 , COUPDAYS 6.12.7 , COUPNCD 6.12.8 , COUPNUM 6.12.10 , COUPPCD 6.12.11

6.12.9COUPNCD

Summary: Calculates the next coupon date following a settlement.

Syntax: COUPNCD( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )

Returns: Date

Constraints: settlement < maturity

frequency is the number of coupon payments per year. frequency is one of the following values:

Table 14 - COUPNCD

frequency

Frequency of coupon payments

1

Annual

2

Semiannual

4

Quarterly


Semantics: Calculates the next coupon date after the settlement date based on the maturity (expiration) date of the asset, the frequency of coupon payments and the day-count basis.

6.12.10COUPNUM

Summary: Calculates the number of outstanding coupons between settlement and maturity dates.

Syntax: COUPNUM( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )

Returns: Number

Constraints: frequency is the number of coupon payments per year. frequency is one of the following values:

Table 15 - COUPNUM

frequency

Frequency of coupon payments

1

Annual

2

Semiannual

4

Quarterly


Semantics: Calculates the number of coupons in the interval between the settlement and the maturity (expiration) date of the asset, the frequency of coupon payments and the day-count basis.

See also COUPDAYBS 6.12.6, COUPDAYS 6.12.7, COUPDAYSNC 6.12.8, COUPNCD 6.12.8, COUPPCD 6.12.11

6.12.11COUPPCD

Summary: Calculates the next coupon date prior a settlement.

Syntax: COUPPCD( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )

Returns: Date

Constraints: settlement < maturity

frequency is the number of coupon payments per year. frequency is one of the following values:

Table 16 - COUPPCD

frequency

Frequency of coupon payments

1

Annual

2

Semiannual

4

Quarterly


Semantics: Calculates the next coupon date prior to the settlement date based on the maturity (expiration) date of the asset, the frequency of coupon payments and the day-count basis.

See also COUPDAYBS 6.12.6, COUPDAYS 6.12.7, COUPDAYSNC 6.12.8, COUPNCD 6.12.8, COUPNUM 6.12.10

6.12.12CUMIPMT

Summary: Calculates a cumulative interest payment.

Syntax: CUMIPMT( Number rate ; Number periods ; Number value ; Integer start ; Integer end ; Integer type )

Returns: Currency

Constraints: rate > 0; value > 0; 1 <= start <= end <= periods

type is one of the following values:

Table 17 - CUMIPMT

type

Maturity date

0

due at the end

1

due at the beginning

Semantics: Calculates the cumulative interest payment.

rateThe interest rate per period.
periodsThe number of periods.
valueThe current value of the loan.
startThe starting period.
endThe end period.
typeThe maturity date, the beginning or the end of a period.

 

See also IPMT 6.12.24, CUMPRINC 6.12.13

6.12.13CUMPRINC

Summary: Calculates a cumulative principal payment.

Syntax: CUMPRINC( Number rate ; Number periods ; Number value ; Integer start ; Integer end ; Integer type )

Returns: Currency

Constraints: type is one of the following values:

Table 18 - CUMPRINC

type

Maturity date

0

due at the end

1

due at the beginning

Semantics: Calculates the cumulative principal payment.

rateThe interest rate per period.
periodsThe number of periods.
valueThe current value of the loan.
startThe starting period.
endThe end period.
typeThe maturity date, the beginning or the end of a period.

 

See also PPMT 6.12.38 , CUMIPMT 6.12.12

6.12.14DB

Summary: Compute the depreciation allowance of an asset.

Syntax: DB( Number cost ; Number salvage ; Integer lifeTime ; Number period [ ; Number month = 12 ] )

Returns: Currency

Constraints: cost > 0, salvage >= 0, lifetime >0; period > 0; 0 < month < 13

Semantics: Calculate the depreciation allowance of an asset with an initial value of cost, an expected useful lifeTime, and a final salvage value at a specified period of time, using the fixed-declining balance method. The parameters are:

The rate is calculated as follows:

 

and is rounded to 3 decimals.

For the first period the residual value is

 

For all periods, where period <= lifeTime, the residual value is calculated by

 

If month was specified, the residual value for the period after lifeTime becomes

 

The depreciation allowance for the first period is

 

For all other periods the allowance is calculated by

 

For all periods, where period > lifeTime + 1 – INT(month/12), the depreciation allowance is zero.

See also DDB 6.12.15, SLN 6.12.46

6.12.15DDB

Summary: Compute the amount of depreciation at a given period of time.

Syntax: DDB( Number cost ; Number salvage ; Number lifeTime ; Number period [ ; Number declinationFactor = 2 ] )

Returns: Currency

Constraints: cost >= 0, salvage >= 0, salvage <= cost, 1 <= period <= lifeTime, declinationFactor > 0

Semantics: Compute the amount of depreciation of an asset at a given period of time. The parameters are:

To calculate depreciation, DDB uses a fixed rate. When declinationFactor = 2 this is the double-declining-balance method (because it is double the straight-line rate that would depreciate the asset to zero). The rate is given by:

 

The depreciation each period is calculated as

depreciation_of_period = MIN( book_value_at_start_of_ period * rate; book_value_at_start_of_ period - salvage )

Thus the asset depreciates at
rate until the book value is salvage value.

 

To allow also non-integer period values this algorithm may be used:

 

If period is an Integer number, the relation between DDB and VDB is:
DDB( cost ; salvage ; lifeTime ; period ; declinationFactor )
equals
VDB( cost ; salvage ; lifeTime ; period - 1 ; period ; declinationFactor ; TRUE() )

See also SLN 6.12.46, VDB 6.12.51

6.12.16DISC

Summary: Returns the discount rate of a security.

Syntax: DISC( DateParam settlement ; DateParam maturity ; Number price ; Number redemption [ ; Basis basis = 0 ] )

Returns: Percentage

Constraints: settlement < maturity

Semantics: Calculates the discount rate of a security.

settlementThe settlement date of the security.
maturityThe maturity date.
priceThe price of the security.
redemptionThe redemption value of the security.
basisThe day-count basis; see section
4.11.6

 

See also YEARFRAC 6.10.24

6.12.17DOLLARDE

Summary: Converts a fractional dollar representation into a decimal representation.

Syntax: DOLLARDE( Number fractional ; Integer denominator )

Returns: Number

Constraints: denominator > 0

Semantics: Converts a fractional dollar representation into a decimal representation.

fractional        Decimal fraction.
denominator        Denominator of the fraction.

 

See also DOLLARFR 6.12.18 , TRUNC 6.17.9

6.12.18DOLLARFR

Summary: Converts a decimal dollar representation into a fractional representation.

Syntax: DOLLARFR( Number decimal ; Integer denominator )

Returns: Number

Constraints: denominator > 0

Semantics: Converts a decimal dollar representation into a fractional representation.

decimal                Decimal number.
denominator        Denominator of the fraction.

 

See also DOLLARDE 6.12.17, TRUNC 6.17.9

6.12.19DURATION

Summary: Returns the Macaulay duration of a fixed interest security in years

Syntax: DURATION( Date Settlement ; Date Maturity ; Number Coupon ; Number Yield ; Number Frequency [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Yield >=0, Coupon >= 0, Settlement <= Maturity; Frequency = 1, 2, 4

Semantics: Computes the Macaulay duration, given:

See also MDURATION 6.12.27

6.12.20EFFECT

Summary: Returns the net annual interest rate for a nominal interest rate.

Syntax: EFFECT( Number rate ; Integer payments )

Returns: Number

Constraints: rate >= 0; payments > 0

Semantics: Nominal interest refers to the amount of interest due at the end of a calculation period. Effective interest increases with the number of payments made. In other words, interest is often paid in installments (for example, monthly or quarterly) before the end of the calculation period.

rateThe interest rate per period.
paymentsThe number of payments per period.

 

See also NOMINAL 6.12.29

6.12.21FV

Summary: Compute the future value (FV) of an investment.

Syntax: FV( Number Rate ; Number Nper ; Number Payment [ ; [ Number Pv = 0 ] [ ; Number PayType = 0 ] ] )

Returns: Currency

Constraints: None.

Semantics: Computes the future value of an investment. The parameters are:

See PV 6.12.42 for the equation this solves.

See also PV 6.12.42, NPER 6.12.30, PMT 6.12.37, RATE 6.12.43

6.12.22FVSCHEDULE

Summary: Returns the accumulated value given starting capital and a series of interest rates.

Syntax: FVSCHEDULE( Number Principal ; NumberSequence Schedule )

Returns: Currency

Constraints: None.

Semantics: Returns the accumulated value given starting capital and a series of interest rates, as follows:

 

See also PV 6.12.42, NPER 6.12.30, PMT 6.12.37, RATE 6.12.43

6.12.23INTRATE

Summary: Computes the interest rate of a fully vested security.

Syntax: INTRATE( Date Settlement ; Date Maturity ; Number Investment ; Number Redemption [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Settlement < Maturity

Semantics: Calculates the annual interest rate that results when an item is purchased at the investment price and sold at the redemption price. No interest is paid on the investment. The parameters are:

Settlement: the date of purchase of the security.

Maturity: the date on which the security is sold.

Investment: the purchase price.

Redemption: the selling price.

Basis: [optional] indicates the day count basis to use; see section 4.11.6.

The return value for this function is:

 

See also RECEIVED 6.12.44, YEARFRAC 6.10.24

6.12.24IPMT

Summary: Returns the amount of an annuity payment going towards interest.

Syntax: IPMT( Number Rate ; Number Period ; Number Nper ; Number PV [ ; Number FV = 0 [ ; Number Type = 0 ] ] )

Returns: Currency

Constraints: None.

Semantics: Computes the interest portion of an amortized payment for a constant interest rate and regular payments. The interest payment is the interest rate multiplied by the balance at the beginning of the period. The parameters are:

Rate: The periodic interest rate.

Period: The period for which the interest payment is computed.

Nper: The total number of periods for which the payments are made

PV: The present value (e.g. The initial loan amount).

FV: The future value (optional) at the end of the periods. Zero if omitted.

Type: the due date for the payments (optional). Zero if omitted. If type is 1, then payments are made at the beginning of each period. If type is 0, then payments are made at the end of each period.

See also PPMT 6.12.38, PMT 6.12.37

6.12.25IRR

Summary: Compute the internal rate of return for a series of cash flows.

Syntax: IRR( NumberSequence Values [ ; Number Guess = 0.1 ] )

Returns: Percentage

Constraints: None.

Semantics: Compute the internal rate of return for a series of cash flows.

If provided, Guess is an estimate of the interest rate to start the iterative computation. If omitted, the value 0.1 (10%) is assumed.

The result of IRR is the rate at which the NPV() function will return zero with the given values.

There is no closed form for IRR. Evaluators may return an approximate solution using an iterative method, in which case the Guess parameter may be used to initialize the iteration. If the evaluator is unable to converge on a solution given a particular Guess, it may return an Error.

See also NPV 6.12.31, RATE 6.12.43

6.12.26ISPMT

Summary: Compute the interest payment of an amortized loan for a given period.

Syntax: ISPMT( Number Rate ; Number Period ; Number Nper ; Number Pv )

Returns: Currency

Constraints: None.

Semantics: Computes the interest payment of an amortized loan for a given period. The parameters are:

See also PV 6.12.42, FV 6.12.21, NPER 6.12.30, PMT 6.12.37, RATE 6.12.43

6.12.27MDURATION

Summary: Returns the modified Macaulay duration of a fixed interest security in years

Syntax: MDURATION( Date Settlement ; Date Maturity ; Number Coupon ; Number Yield ; Number Frequency [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Yield >= 0, Coupon >= 0, Settlement <= Maturity; Frequency = 1, 2, 4

Semantics: Computes the modified Macaulay duration, given:

The modified duration is computed as follows:

 

See also DURATION 6.12.19

6.12.28MIRR

Summary: Returns the modified internal rate of return (IRR) of a series of periodic investments

Syntax: MIRR( Array Values ; Number Investment ; Number ReinvestRate )

Returns: Percentage

Constraints: Values shall contain at least one positive value and at least one negative value.

Semantics: Values is a series of periodic income (positive values) and payments (negative values) at regular intervals (Text and Empty cells are ignored). Investment is the rate of interest of the payments (negative values); ReinvestRate is the rate of interest of the reinvestment (positive values).

Computes the modified internal rate of return, which is:

 

where N is the number of incomes and payments in Values (total).

See also IRR 6.12.25

6.12.29NOMINAL

Summary: Compute the annual nominal interest rate.

Syntax: NOMINAL( Number EffectiveRate ; Integer CompoundingPeriods )

Returns: Number

Constraints: EffectiveRate >0 , CompoundingPeriods > 0

Semantics: Returns the annual nominal interest rate based on the effective rate and the number of compounding periods in one year. The parameters are:

Suppose that P is the present value, m is the compounding periods per year, the future value after one year is

 

The mapping between nominal rate and effective rate is

 

See also EFFECT 6.12.20

6.12.30NPER

Summary: Compute the number of payment periods for an investment.

Syntax: NPER( Number Rate ; Number Payment ; Number Pv [ ; [ Number Fv ] [ ; Number PayType ] ] )

Returns: Number

Constraints: None.

Semantics: Computes the number of payment periods for an investment. The parameters are:

If Rate is 0, then NPER solves this equation:

 

If Rate is non-zero, then NPER solves this equation:

 

Evaluators claiming to support the “Medium” or “Large” set shall support negative rates; evaluators only claiming to support the “Small” set need not.

See also FV 6.12.21, RATE 6.12.43, PMT 6.12.37, PV 6.12.42

6.12.31NPV

Summary: Compute the net present value (NPV) for a series of periodic cash flows.

Syntax: NPV( Number Rate ; { NumberSequenceList Value }+ )

Returns: Currency

Constraints: None.

Semantics: Computes the net present value for a series of periodic cash flows with the discount rate Rate. Values should be positive if they are received as income, and negative if the amounts are paid as outgo. Because the result is affected by the order of values, evaluators shall evaluate arguments in the order given and range reference and array arguments row-wise starting from top left.

If n is the number of values in the Values, the formula for NPV is:

 

See also FV 6.12.21, IRR 6.12.25, NPER 6.12.30, PMT 6.12.37, PV 6.12.42, XNPV 6.12.53

6.12.32ODDFPRICE

Summary: Compute the value of a security per 100 currency units of face value. The security has an irregular first interest date.

Syntax: ODDFPRICE( DateParam Settlement ; DateParam Maturity ; DateParam Issue ; DateParam First ; Number Rate ; Number Yield ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Rate, Yield, and Redemption should be greater than 0.

Semantics: The parameters are

See also ODDLPRICE 6.12.34 , ODDFYIELD 6.12.33

6.12.33ODDFYIELD

Summary: Compute the yield of a security per 100 currency units of face value. The security has an irregular first interest date.

Syntax: ODDFYIELD( DateParam Settlement ; DateParam Maturity ; DateParam Issue ; DateParam First ; Number Rate ; Number Price ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Rate, Price, and Redemption should be greater than 0. Maturity > First > Settlement > Issue.

Semantics: The parameters are

See also ODDLYIELD 6.12.35 , ODDFPRICE 6.12.32

6.12.34ODDLPRICE

Summary: Compute the value of a security per 100 currency units of face value. The security has an irregular last interest date.

Syntax: ODDLPRICE( DateParam Settlement ; DateParam Maturity ; DateParam Last ; Number Rate ; Number AnnualYield ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Rate, AnnualYield, and Redemption should be greater than 0. The Maturity date should be greater than the Settlement date, and the Settlement should be greater than the last interest date.

Semantics: The parameters are

See also ODDFPRICE 6.12.32

6.12.35ODDLYIELD

Summary: Compute the yield of a security which has an irregular last interest date.

Syntax: ODDLYIELD( DateParam Settlement ; DateParam Maturity ; DateParam Last ; Number Rate ; Number Price ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Rate, Price, and Redemption should be greater than 0.

Semantics: The parameters are

See also ODDLPRICE 6.12.34 , ODDFYIELD 6.12.33

6.12.36PDURATION

Summary: Returns the number of periods required by an investment to realize a specified value.

Syntax: PDURATION( Number rate ; Number currentValue ; Number specifiedValue )

Returns: Number

Constraints: rate > 0; currentValue > 0; specifiedValue > 0

Semantics: Calculates the number of periods for attaining a certain value specifiedValue, starting from currentValue and using the interest rate rate.

 

See also DURATION 6.12.19

6.12.37PMT

Summary: Compute the payment made each period for an investment.

Syntax: PMT( Number Rate ; Integer Nper ; Number Pv [ ; [ Number Fv = 0 ] [ ; Number PayType = 0 ] ] )

Returns: Currency

Constraints: Nper > 0

Semantics: Computes the payment made each period for an investment. The parameters are:

If Rate is 0, the following equation is solved:

 

If Rate is nonzero, then PMT solves this equation:

 

See also FV 6.12.21, NPER 6.12.30, PV 6.12.42, RATE 6.12.43

6.12.38PPMT

Summary: Calculate the payment for a given period on the principal for an investment at a given interest rate and constant payments.

Syntax: PPMT( Number Rate ; Integer Period ; Integer nPer ; Number Present [ ; Number Future = 0 [ ; Number Type = 0 ] ] )

Returns: Number

Constraints: Rate and Present should be greater than 0. 0<Period <nPer.

Semantics: The parameters are

See also PMT 6.12.37

6.12.39PRICE

Summary: Calculates a quoted price for an interest paying security, per 100 currency units of face value.

Syntax: PRICE( DateParam Settlement ; DateParam Maturity ; Number Rate ; Number AnnualYield ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Rate, AnnualYield, and Redemption should be greater than 0; Frequency = 1, 2 or 4.

Semantics: If A is the number of days from the Settlement date to next coupon date, B is the number of days of the coupon period that the Settlement is in, C is the number of coupons between Settlement date and Redemption date, D is the number of days from beginning of coupon period to Settlement date, then PRICE is calculated as

 

The parameters are

See also PRICEDISC 6.12.40, PRICEMAT 6.12.41

6.12.40PRICEDISC

Summary: Calculate the price of a security with a discount per 100 currency units of face value.

Syntax: PRICEDISC( DateParam Settlement ; DateParam Maturity ; Number Discount ; Number Redemption [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Discount and Redemption should be greater than 0.

Semantics: The parameters are

See also PRICE 6.12.39, PRICEMAT 6.12.41, YIELDDISC 6.12.55

6.12.41PRICEMAT

Summary: Calculate the price per 100 currency units of face value of the security that pays interest on the maturity date.

Syntax: PRICEMAT( DateParam Settlement ; DateParam Maturity ; DateParam Issue ; Number Rate ; Number AnnualYield [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Settlement < Maturity, Rate >= 0, AnnualYield >= 0

Semantics: The parameters are

If both, Rate and AnnualYield, are 0, the return value is 100.

See also PRICEDISC 6.12.40, PRICEMAT 6.12.41

6.12.42PV

Summary: Compute the present value (PV) of an investment.

Syntax: PV( Number Rate ; Number Nper ; Number Payment [ ; [ Number Fv = 0 ] [ ; Number PayType = 0 ] ] )

Returns: Currency

Constraints: None.

Semantics: Computes the present value of an investment. The parameters are:

If Rate is 0, then:

 

If Rate is nonzero, then PV solves this equation:

 

See also FV 6.12.21, NPER 6.12.30, PMT 6.12.37, RATE 6.12.43

6.12.43RATE

Summary: Compute the interest rate per period of an investment.

Syntax: RATE( Number Nper ; Number Payment ; Number Pv [ ; [ Number Fv = 0 ] [ ; [ Number PayType = 0 ] [ ; Number Guess = 0.1 ] ] ] )

Returns: Percentage

Constraints: If Nper is 0 or less than 0, the result is an Error.

Semantics: Computes the interest rate of an investment. The parameters are:

RATE solves this equation:

 

See also FV 6.12.21, NPER 6.12.30, PMT 6.12.37, PV 6.12.42

6.12.44RECEIVED

Summary: Calculates the amount received at maturity for a zero coupon bond.

Syntax: RECEIVED( DateParam Settlement ; DateParam Maturity ; Number Investment ; Number Discount [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Investment and Discount should be greater than 0.

Semantics:

The parameters are

The return value is:

 

See also YEARFRAC 6.10.24

6.12.45RRI

Summary: Returns an equivalent interest rate when an investment increases in value.

Syntax: RRI( Number N ; Number Pv ; Number Fv )

Returns: Percentage

Constraints: N > 0

Semantics: Returns the interest rate given N (the number of periods), Pv (present value), and Fv (future value), calculated as follows:

 

See also FV 6.12.21, NPER 6.12.30, PMT 6.12.37, PV 6.12.42, RATE 6.12.43

6.12.46SLN

Summary: Compute the amount of depreciation at a given period of time using the straight-line depreciation method.

Syntax: DDB( Number Cost ; Number Salvage ; Number LifeTime )

Returns: Currency

Constraints: None.

Semantics: Compute the amount of depreciation of an asset at a given period of time using straight-line depreciation. The parameters are:

For alternative methods to compute depreciation, see DDB 6.12.15.

See also DDB 6.12.15

6.12.47SYD

Summary: Compute the amount of depreciation at a given period of time using the Sum-of-the-Years'-Digits method.

Syntax: SYD( Number Cost ; Number Salvage ; Number LifeTime ; Number Period )

Returns: Currency

Constraints: None.

Semantics: Compute the amount of depreciation of an asset at a given period of time using the Sum-of-the-Years'-Digits method. The parameters are:

 

For other methods of computing depreciation, see DDB 6.12.15.

See also SLN 6.12.46, DDB 6.12.15

6.12.48TBILLEQ

Summary: Compute the bond-equivalent yield for a treasury bill.

Syntax: TBILLEQ( DateParam Settlement ; DateParam Maturity ; Number Discount )

Returns: Number

Constraints: The maturity date should be less than one year beyond settlement date. Discount is any positive value.

Semantics: The parameters are defined as,

TBILLEQ is calculated as

 

where DSM is the number of days between settlement and maturity computed according to the 360 days per year basis (basis 2, 4.11.6)

See also TBILLPRICE 6.12.49, TBILLYIELD 6.12.50

6.12.49TBILLPRICE

Summary: Compute the price per 100 face value for a treasury bill.

Syntax: TBILLPRICE( DateParam Settlement ; DateParam Maturity ; Number Discount )

Returns: Number

Constraints: The maturity date should be less than one year beyond settlement. Discount is any positive value.

Semantics: The parameters are:

See also TBILLEQ 6.12.48, TBILLYIELD 6.12.50

6.12.50TBILLYIELD

Summary: Compute the yield for a treasury bill.

Syntax: TBILLYIELD( DateParam Settlement ; DateParam Maturity ; Number Price )

Returns: Number

Constraints: The maturity date should be less than one year beyond settlement. Price is any positive value.

Semantics: The parameters are:

See also TBILLEQ 6.12.48, TBILLPRICE 6.12.49

6.12.51VDB

Summary: Calculates the depreciation allowance of an asset with an initial value, an expected useful life, and a final value of salvage for a period specified, using the variable-rate declining balance method..

Syntax: VDB( Number cost ; Number salvage ; Number lifeTime ; Number startPeriod ; Number endPeriod [ ; Number depreciationFactor = 2 [ ; Logical noSwitch = FALSE() ] ] )

Returns: Number

Constraints: salvage < cost, lifeTime > 0, 0 ≤ startPeriod ≤ lifeTime, startPeriod ≤ endPeriod ≤ lifeTime, depreciationFactor ≥ 0

Semantics: cost is the amount paid for the asset. cost can be any value greater than salvage.

salvage is the value of the asset at the end of its life. salvage can be any value.

lifeTime is the number of periods the asset takes to depreciate to its salvage value. lifeTime can be any value greater than 0.

startPeriod is the point in the asset's life when you want to begin calculating depreciation. start-Period can be any value greater than or equal to 0, but cannot be greater than lifeTime.

endPeriod is the point in the asset's life when you want to stop calculating depreciation. end-Period can be any value greater than startPeriod.

startPeriod and endPeriod correspond to the asset's life, relative to the fiscal period. For example, if you want to find the first year's depreciation of an asset purchased at the beginning of the second quarter of a fiscal year, start-period would be 0 and end-period would be 0.75 (1 minus 0.25 of a year).

VDB allows for the use of an initialPeriod option to calculate depreciation for the period the asset is placed in service. VDB uses the fractional part of startPeriod and endPeriod to determine the initialPeriod option. If both startPeriod and endPeriod have fractional parts, then VDB uses the fractional part of startPeriod.

depreciationFactor is an optional argument that specifies the percentage of straight-line depreciation you want to use as the depreciation rate. If you omit this argument, VDB uses 2, which is the double-declining balance rate. depreciation-factor can be any value greater than or equal to 0; commonly used rates are 1.25, 1.50, 1.75, and 2.

noSwitch is an optional argument that you include if you do not want VDB to switch to straight-line depreciation for the remaining useful life. Normally, declining-balance switches to such a straight-line calculation when it is greater than the declining-balance calculation.

If noSwitch is FALSE() or omitted, VDB automatically switches to straight-line depreciation when that is greater than declining-balance depreciation. If noSwitch is TRUE(), VDB never switches to straight-line depreciation.

See also DDB 6.12.15, SLN 6.12.46

6.12.52XIRR

Summary: Compute the internal rate of return for a non-periodic series of cash flows.

Syntax: XIRR( NumberSequence Values ; DateSequence Dates [ ; Number Guess = 0.1 ] )

Returns: Number

Constraints: The size of Values and Dates are equal. Values contains at least one positive and one negative cash flow.

Semantics: Compute the internal rate of return for a series of cash flows which is not necessarily periodic. The parameters are

See also IRR 6.12.25

6.12.53XNPV

Summary: Compute the net present value of a series of cash flows.

Syntax: XNPV( Number Rate ; Reference|Array Values ; Reference| Array Dates )

Returns: Number

Constraints:

Number of elements in Values equals number of elements in Dates.

All elements of Values are of type Number.

All elements of Dates are of type Number.

All elements of Dates >= Dates[1]

Semantics: Compute the net present value for a series of cash flows which is not necessarily periodic. The parameters are

With N being the number of elements in Values and Dates each, the formula is:

 

See also NPV 6.12.31

6.12.54YIELD

Summary: Calculate the yield of a bond.

Syntax: YIELD( DateParam Settlement ; DateParam Maturity ; Number Rate ; Number Price ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Rate, Price, and Redemption should be greater than 0.

Semantics: The parameters are

See also PRICE 6.12.39, YIELDDISC 6.12.55, YIELDMAT 6.12.56

6.12.55YIELDDISC

Summary: Calculate the yield of a discounted security per 100 currency units of face value.

Syntax: YIELDDISC( DateParam Settlement ; DateParam Maturity ; Number Price ; Number Redemption [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Price and Redemption should be greater than 0.

Semantics: The parameters are

The return value is

 

See also PRICEDISC 6.12.40, YEARFRAC 6.10.24

6.12.56YIELDMAT

Summary: Calculate the yield of the security that pays interest on the maturity date.

Syntax: YIELDMAT( DateParam Settlement ; DateParam Maturity ; DateParam Issue ; Number Rate ; Number Price [ ; Basis Basis = 0 ] )

Returns: Number

Constraints: Rate and Price should be greater than 0.

Semantics: The parameters are

See also PRICE 6.12.39, YIELD 6.12.54, YIELDDISC 6.12.55

6.13Information Functions

6.13.1General

Information functions provide information about a data value, the spreadsheet, or underlying environment, including special functions for converting between data types.

6.13.2AREAS

Summary: Returns the number of areas in a given reference

Syntax: AREAS( ReferenceList R )

Returns: Number

Constraints: None

Semantics: Returns the number of areas in the reference list.

See also Infix Operator Reference Concatenation 6.4.13, INDEX 6.14.6

6.13.3CELL

Summary: Returns information about position, formatting or contents in a reference.

Syntax: CELL( Text Info_Type [ ; Reference R ] )

Returns: Information about position, formatting properties or content

Constraints: None

Semantics: The parameters are

Table 19 - CELL

Info_Type

Comment

COL

Returns the column number of the cell.

ROW

Returns the row number of the cell.

SHEET

Returns the sheet number of the cell.

ADDRESS

Returns the absolute address of the cell. The sheet name is included if given in the reference. For an external reference a Source as specified in the syntax rules for References 5.8 is included.

FILENAME

Returns the file name of the file that contains the cell as an IRI. If the file is newly created and has not yet been saved, the file name is empty text “”.

CONTENTS

Returns the contents of the cell, without formatting properties.

COLOR

Returns 1 if color formatting is set for negative value in this cell; otherwise returns 0

FORMAT

Returns a text string which shows the number format of the cell.

,(comma) = number with thousands separator

F = number without thousands separator

C = currency format

S = exponential representation

P = percentage

To indicate the number of decimal places after the decimal separator, a number is given right after the above characters.

D1 = MMM-D-YY, MM-D-YY and similar formats

D2 = DD-MM

D3 = MM-YY

D4 = DD-MM-YYYY HH:MM:SS

D5 = MM-DD

D6 = HH:MM:SS AM/PM

D7 = HH:MM AM/PM

D8 = HH:MM:SS

D9 = HH:MM

G = All other formats

- (Minus) at the end = negative numbers in the cell have color setting

() (brackets) at the end = this cell has the format settings with parentheses for positive or all values

TYPE

Returns the text value corresponding to the type of content in the cell:

“b” : blank or empty cell content

“l” : label or text cell content

“v” : number value cell content

WIDTH

Returns the column width of the cell.

The unit is the width of one zero (0) character in default font size.

PROTECT

Returns the protection status of the cell:

1 = cell is protected

0 = cell is unprotected

PARENTHESES

Returns 1 if the cell has the format settings with parentheses for positive or all values, otherwise returns 0

PREFIX

Returns single character text strings corresponding to the alignment of the cell.

“'” (APOSTROPHE, U+0027) = left alignment

'"' (QUOTATION MARK, U+0022) = right alignment

^(caret) = centered alignment

\(back slash) = filled alignment

otherwise, returns empty string "".

6.13.4COLUMN

Summary: Returns the column number(s) of a reference

Syntax: COLUMN( [ Reference R ] )

Returns: Number

Constraints: AREAS(R) = 1

Semantics: Returns the column number of a reference, where “A” is 1, “B” is 2, and so on. If no parameter is given, the current cell is used. If a reference has multiple columns, an array of numbers is returned with all of the columns in the reference.

See also ROW 6.13.29, SHEET 6.13.31

6.13.5COLUMNS

Summary: Returns the number of columns in a given range

Syntax: COLUMNS( Reference|Array R )

Returns: Number

Constraints: None

Semantics: Returns the number of columns in the range or array specified. The result is not dependent on the cell content in the range.

See also ROWS 6.13.30

6.13.6COUNT

Summary: Count the number of Numbers provided

Syntax: COUNT( { NumberSequenceList N }+ )

Returns: Number

Constraints: One or more parameters.

Semantics: Counts the numbers in the list of NumberSequences provided. Only numbers in references are counted; all other types are ignored. Errors are not propagated. It is implementation-defined what happens if 0 parameters are passed, but it should be an Error or 0.

See also COUNTA 6.13.7

6.13.7COUNTA

Summary: Count the number of non-empty values

Syntax: COUNTA( { Any A }+ )

Returns: Number

Constraints: None.

Semantics: Counts the number of non-blank values in the list of Any sequences provided. A value is non-blank if it contains any content of any type, including an Error. In a reference, every cell that is not empty is included in the count. An empty string value ("") is not considered blank. Errors contained in a range are considered a non-blank value for purposes of the count; errors do not propagate. Constant expressions or formulas are allowed; these are evaluated and if they produce an Error value the Error value is counted as one non-blank value (and not propagated as an Error). It is implementation-defined what happens if 0 parameters are passed, but it should be an Error or 0. Any A may be a ReferenceList.

See also COUNT 6.13.6, ISBLANK 6.13.14

6.13.8COUNTBLANK

Summary: Count the number of blank values

Syntax: COUNTBLANK( ReferenceList R )

Returns: Number

Constraints: None.

Semantics: Counts the number of blank cells in the Reference provided. A cell is blank if the cell is empty for purposes of COUNTBLANK. If ISBLANK(R) is true, then it is blank. A cell with numeric value zero ('0') is not blank. It is implementation-defined whether or not a cell returning the empty string ("") is considered blank; because of this, there is a (potential) subtle difference between COUNTBLANK and ISBLANK.

Evaluators shall support one Reference as a parameter and may support a ReferenceList as a parameter.

See also COUNT 6.13.6, COUNTA 6.13.7, COUNTIF 6.13.9, ISBLANK 6.13.14

6.13.9COUNTIF

Summary: Count the number of cells in a range that meet a criteria.

Syntax: COUNTIF( ReferenceList R ; Criterion C )

Returns: Number

Constraints: Does not accept constant values as the reference parameter.

Semantics: Counts the number of cells in the reference range R that meet the Criterion C (4.11.7).

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also COUNT 6.13.6, COUNTA 6.13.7, COUNTBLANK 6.13.8, COUNTIFS 6.13.10, SUMIF 6.16.62, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9

6.13.10COUNTIFS

Summary: Count the number of cells that meet multiple criteria in multiple ranges.

Syntax: COUNTIFS( Reference R1 ; Criterion C1 [ ; Reference R2 ; Criterion C2 ]... )

Returns: Number

Constraints: Does not accept constant values as the reference parameter.

Semantics: Counts the number of cells that meet the Criterion C1 in the reference range R1 and the Criterion C2 in the reference range R2, and so on (4.11.7). All reference ranges shall have the same dimension and size, else an Error is returned. A logical AND is applied between each array result of each selection; an entry is counted only if the same position in each array is the result of a Criterion match.

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also COUNT 6.13.6, COUNTA 6.13.7, COUNTBLANK 6.13.8, COUNTIF 6.13.9, SUMIF 6.16.62, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9

6.13.11ERROR.TYPE

Summary: Returns Number representing the specific Error type.

Syntax: ERROR.TYPE( Error E )

Returns: Number

Constraints: None.

Semantics: Returns a number representing what kind of Error has occurred. Note that unlike most functions, this function does not propagate Error values. Receiving a non-Error value returns an Error. In particular, ERROR.TYPE(NA()) returns 7, and ERROR.TYPE applied to a non-Error returns an Error.

See also NA 6.13.27

6.13.12FORMULA

Summary: Returns formula at given reference as text

Syntax: FORMULA( Reference X )

Returns: String

Constraints: Reference X shall contain a formula

Semantics: Returns the formula in reference X as a string. The specific syntax of this returned string is implementation-defined. This function is intended to aid debugging by simplifying display of formulas in other cells. Error results of the referred formula cell are not propagated.

See also ISFORMULA 6.13.18

6.13.13INFO

Summary: Returns information about the environment

Syntax: INFO( Text Category )

Returns: Any (see below)

Constraints: Category shall be valid

Semantics: Returns information about the environment in the given category.

Evaluators shall support at least the following categories:

Table 20 - INFO

Category

Meaning

Type

"directory"

Current directory. This shall be formatted so file names can be appended to the result (e.g., on POSIX and Windows systems it shall end with the separator “/” or “\” respectively).

Text

"memavail"

Amount of memory “available”, in bytes. On many modern (virtual memory) systems this value is not really available, but a system should return 0 if it is known that there is no more memory available, and greater than 0 otherwise

Number

"memused"

Amount of memory used, in bytes, by the data

Number

"numfile"

Number of active worksheets in files

Number

"osversion"

Operating system version

Text

"origin"

The top leftmost visible cell's absolute reference prefixed with “$A:”. In locales where cells are ordered right-to-left, the top rightmost visible cell is used instead.

Text

"recalc"

Current recalculation mode. If the locale is English, this is either "Automatic" or "Manual" (the exact text depends on the locale)

Text

"release"

The version of the implementation.

Text

"system"

The type of the operating system.

Text

"totmem"

Total memory available in bytes, including the memory already used.

Number

Evaluators may support other categories.

See also CELL 6.13.3

6.13.14ISBLANK

Summary: Return TRUE if the referenced cell is blank, else return FALSE

Syntax: ISBLANK( Scalar X )

Returns: Logical

Constraints: None

Semantics: If X is of type Number, Text, or Logical, return FALSE. If X is a reference to a cell, examine the cell; if it is blank (has no value), return TRUE, but if it has a value, return FALSE. A cell with the empty string is not considered blank.

See also ISNUMBER 6.13.22, ISTEXT 6.13.25

6.13.15ISERR

Summary: Return True if the parameter has type Error and is not NA, else return False.

Syntax: ISERR( Scalar X )

Returns: Logical

Constraints: None

Semantics: If X is of type Error, and ISNA(X) is not true, returns TRUE. Otherwise it returns FALSE. Note that this function returns False if given NA(); if this is not desired, use ISERROR 6.13.16. Note that this function does not propagate Error values.

ISERR(X) is the same as:

IF(ISNA(X),FALSE(),ISERROR(X))

See also ERROR.TYPE 6.13.11, ISERROR 6.13.16, ISNUMBER 6.13.22, ISTEXT 6.13.25, NA 6.13.27

6.13.16ISERROR

Summary: Return TRUE if the parameter has type Error, else return FALSE

Syntax: ISERROR( Scalar X )

Returns: Logical

Constraints: None

Semantics: If X is of type Error, returns TRUE, else returns FALSE. Note that this function returns True if given NA(); if this is not desired, use ISERR 6.13.15. Note that this function does not propagate Error values.

See also ERROR.TYPE 6.13.11, ISERR 6.13.15, ISNA 6.13.20, ISNUMBER 6.13.22, ISTEXT 6.13.25, NA 6.13.27

6.13.17ISEVEN

Summary: Return TRUE if the value is even, else return FALSE

Syntax: ISEVEN( Number X )

Returns: Logical

Constraints: None

Semantics: First, compute X1=TRUNC(X). Then, if X1 is even (a division by 2 has a remainder of 0), return True, else return False. The result is implementation-defined if given a Logical value; an evaluator may return either an Error or the result of converting the Logical value to a Number (per Conversion to Number 6.3.5 ).

See also ISODD 6.13.23

6.13.18ISFORMULA

Summary: Return TRUE if the reference refers to a formula, else return FALSE

Syntax: ISFORMULA( Reference X )

Returns: Logical

Constraints: None

Semantics: If X refers to a cell whose value is computed by a formula, return TRUE(), else return FALSE(). A formula itself may compute a constant; in that case it will still return TRUE() since it is still a formula. Passing a non-reference, or a reference to more than one cell, is implementation-defined.

See also ISTEXT 6.13.25, ISNUMBER 6.13.22

6.13.19ISLOGICAL

Summary: Return TRUE if the parameter has type Logical, else return FALSE

Syntax: ISLOGICAL( Scalar X )

Returns: Logical

Constraints: None

Semantics: If X is of type Logical, returns TRUE, else FALSE. Evaluators that do not have a distinct Logical type will return the same value ISNUMBER(X) would return.

See also ISTEXT 6.13.25, ISNUMBER 6.13.22

6.13.20ISNA

Summary: Return True if the parameter is of type NA, else return False.

Syntax: ISERR( Scalar X )

Returns: Logical

Constraints: None

Semantics: If X is NA, return True, else return False. Note that if X is a reference, the value being referenced is considered. This function does not propagate Error values.

See also ERROR.TYPE 6.13.11, ISERROR 6.13.16, ISERR 6.13.15, ISNUMBER 6.13.22, ISTEXT 6.13.25, NA 6.13.27

6.13.21ISNONTEXT

Summary: Return TRUE if the parameter does not have type Text, else return FALSE

Syntax: ISNONTEXT( Scalar X )

Returns: Logical

Constraints: None

Semantics: If X is of type Text, returns FALSE, else TRUE. If X is a reference, examines what X references. References to empty cells are NOT considered Text, so a reference to an empty cell will return TRUE. Empty Cell 4.7

ISNONTEXT(X) is equivalent to NOT(ISTEXT(X))

See also ISNUMBER 6.13.22, ISLOGICAL 6.13.19, ISTEXT 6.13.25

6.13.22ISNUMBER

Summary: Return TRUE if the parameter has type Number, else return FALSE

Syntax: ISNUMBER( Scalar X )

Returns: Logical

Constraints: None

Semantics: If X is of type Number, returns TRUE, else FALSE. Evaluators may not have a distinguished Logical type; in such evaluators, ISNUMBER(TRUE()) is TRUE.

See also ISTEXT 6.13.25, ISLOGICAL 6.13.19

6.13.23ISODD

Summary: Return TRUE if the value is even, else return FALSE

Syntax: ISODD( Number X )

Returns: Logical

Constraints: None

Semantics: First, compute X1=TRUNC(X). Then, if X1 is odd (a division by 2 has a remainder of 1), return True, else return False. The result is implementation-defined if given a Logical value; an evaluator may return either an Error or the result of converting the Logical value to a Number (per Conversion to Number 6.3.5 ).

See also ISEVEN 6.13.17

6.13.24ISREF

Summary: Return True if the parameter is of type reference, else return False.

Syntax: ISREF( Any X )

Returns: Logical

Constraints: None

Semantics: If X is of type Reference or ReferenceList, return True, else return False. Note that unlike nearly all other functions, when given a reference this function does not then examine the value being referenced. Some functions and operators return references, and thus ISREF will return True when given their results. X may be a ReferenceList, in which case ISREF returns True.

See also ISNUMBER 6.13.22, ISTEXT 6.13.25

6.13.25ISTEXT

Summary: Return TRUE if the parameter has type Text, else return FALSE. If X is a reference, examines what X references. References to empty cells are NOT considered Text, so a reference to a empty cell will return FALSE. Empty Cell 4.7

ISTEXT(X) is equivalent to NOT(ISNONTEXT(X)).

Syntax: ISTEXT( Scalar X )

Returns: Logical

Constraints: None

Semantics: If X is of type Text, returns TRUE, else FALSE. References to blank cells are NOT considered Text.

See also ISNONTEXT 6.13.21, ISNUMBER 6.13.22, ISLOGICAL 6.13.19

6.13.26N

Summary: Return the number of a value.

Syntax: N( Any X )

Returns: Text

Constraints: None

Semantics: If X is a Reference, it is first dereferenced to a scalar. Then its type is examined. If it is of type Number, it is returned. If it is of type Logical, 1 is returned if TRUE else 0 is returned. It is implementation-defined what happens if it is provided a Text value.

See also T 6.20.22, VALUE 6.13.34

6.13.27NA

Summary: Return the constant Error value #N/A.

Syntax: NA()

Returns: Error

Constraints: Shall have 0 parameters

Semantics: This function takes no arguments and returns the Error NA

See also ERROR.TYPE 6.13.11, ISERROR 6.13.16

6.13.28NUMBERVALUE

Summary: Convert text to number, in a locale-independent way

Syntax: NUMBERVALUE( Text X [ ; Text DecimalSeparator [ ; Text GroupSeparator ] ] )

Returns: Number

Constraints: LEN(DecimalSeparator) = 1, DecimalSeparator shall not appear in GroupSeparator

Semantics: Converts given Text value X into Number. If X is a Reference, it is first dereferenced.

DecimalSeparator defines the character used as the decimal separator, for example "." (period) or "," (comma). If this parameter is not given, only integer numbers are parsed.

GroupSeparator defines the character(s) used as grouping separator, for example "," (comma) or "." (period). If this parameter is not given, only integer or decimal numbers containing the DecimalSeparator are parsed. If this parameter is given, all characters contained are ignored in T if each is surrounded by a digit on each side. If GroupSeparator contains " " U+0020 (SPACE), U+0020 and U+00A0 (NO-BREAK SPACE) shall be equally treated.

If the supplied text X cannot be converted into a Number, an Error is returned.

Regardless of the current locale, the evaluator shall accept text representations that match this regular expression when DecimalSeparator is "." (a period) and GroupSeparator is "," (a comma):

[+|-]?([0-9]+(,[0-9])*)?(\.[0-9]+)?(([eE][+-]?[0-9]+)|%)?

If, for example, DecimalSeparator is "," (a comma) and GroupSeparator is "." (a period), use the expression above but swapping the comma for the period (so "." is ignored).

See also N 6.13.26, T 6.20.22, DATEVALUE 6.10.4, TIMEVALUE 6.10.18, VALUE 6.13.34

6.13.29ROW

Summary: Returns the row number(s) of a reference

Syntax: ROW( [ Reference R ] )

Returns: Number

Constraints: AREAS(R) = 1

Semantics: Returns the row number of a reference. If no parameter is given, the current cell is used. If a reference has multiple rows, an array of numbers is returned with all of the rows in the reference.

See also COLUMN 6.13.4, SHEET 6.13.31

6.13.30ROWS

Summary: Returns the number of rows in a given range

Syntax: ROWS( Reference|Array R )

Returns: Number

Constraints: None

Semantics: Returns the number of rows in the range or array specified. The result is not dependent on the cell content in the range.

See also COLUMNS 6.13.5

6.13.31SHEET

Summary: Returns the sheet number of the reference or the string representing a sheet name.

Syntax: SHEET( [ Text|Reference R ] )

Returns: Number >= 1

Constraints: R shall not contain a Source Location (5.8 References)

Semantics: Returns the 1 based sheet number of the given reference or sheet name.

Hidden sheets are not excluded from the sheet count.

If no parameter is given, the result is the sheet number of the sheet containing the formula.

If a Reference is given it is not dereferenced.

If the reference encompasses more than one sheet, the result is the number of the first sheet in the range.

If a reference does not contain a sheet reference, the result is the sheet number of the sheet containing the formula.

See also COLUMN 6.13.4, ROW 6.13.29, SHEETS 6.13.32

6.13.32SHEETS

Summary: Returns the number of sheets in a reference or current document

Syntax: SHEETS( [ Reference R ] )

Returns: Number >= 1

Constraints: R shall not contain a Source Location (5.8 References)

Semantics: Returns the number of sheets in the given reference.

If no parameter is given, the number of sheets in the document is returned.

Hidden sheets are not excluded from the sheet count.

See also COLUMNS 6.13.5, ROWS 6.13.30, SHEET 6.13.31

6.13.33TYPE

Summary: Returns a number indicating the type of the provided value.

Syntax: TYPE( Any value )

Returns: Number

Constraints: None

Semantics: Returns a number indicating the type of the value given:

Table 21 - TYPE

Value's Type

TYPE Return

Number

1

Text

2

Logical

4

Error

16

Array

64

If a Reference is provided, the reference is first dereferenced, and any formulas are evaluated.

Note: Reliance on the return of 4 for TYPE() will impair the interoperability of a document containing an expression that relies on that value.

See also ERROR.TYPE 6.13.11

6.13.34VALUE

Summary: Convert text to number

Syntax: VALUE( Text X )

Returns: Number

Constraints: None

Semantics: Converts given text value X into Number. If X is a Reference, it is first dereferenced. VALUE is only specified if it is given a Text value or a Reference to a single cell containing a Text value; it is implementation-defined what happens if VALUE is given neither a Text value nor a Reference to a Text value. If the Text has a date, time, or datetime format, it is converted into a serial Number. In many cases the conversion of a date or datetime format is locale-dependent.

If the supplied text X cannot be converted into a Number, an Error is returned.

Regardless of the current locale, an evaluator shall accept numbers matching this regular expression (which does not include a decimal point character) and convert it into a Number. If the value ends in %, it shall divide the number by 100:

[+-]? [0-9]+([eE][+-]?[0-9]+)?)%?

VALUE shall accept text representations of numbers in the current locale. In the en_US locale, an evaluator shall accept decimal numbers matching this regular expression and convert it into a Number (the leading “$” is ignored; commas are ignored if they match the rule of a thousands separator; if the value ends in %, it shall divide the number by 100):

[+-]?\$?([0-9]+(,[0-9]{3})*)?(\.[0-9]+)?(([eE][+-]?[0-9]+)|%)?

Evaluators shall accept accept fractional values matching the regular expression:

[+-]? [0-9]+ \ [0-9]+/[1-9][0-9]?

A leading minus sign is considered identifying a negative number for the entire value. There is a space between the integer and the fractional portion; values between 0 and 1 can be represented by using 0 for the integer part.

Evaluators shall support time values in at least the HH:MM and HH:MM:SS formats, where HH is a 1-2 digit value from 0 to 23, MM is a 1-2 digit value from 0 to 59, and SS is a 1-2 digit value from 0 to 59. The hour may be one or two digits when it is less than 10. VALUE converts time values into Numbers ranging from 0 to 1, which is percentage of day that has elapsed by that time. Thus, VALUE("2:00") is the same as 2/24. Evaluators should accept times with fractional seconds as well when expressed in the form HH:MM:SS.ssss...

Evaluators shall accept textual dates in ISO 8601 format (YYYY-MM-DD), converting them into serial numbers based on the current epoch. Evaluators shall, when running in the en_US locale, accept the format MM/DD/YYYY .

In addition, in locale en_US, evaluators shall support the following formats (where YYYY is a 4-digit year, YY a 2-digit year, MM a numerical month, DD a numerical day, mmm a 3-character abbreviated alphabetical name, and mmmmm a full name):

Table 22 - VALUE

Format

Example

Comment

MM/DD/YYYY

5/21/2006

LOCALE-DEPENDENT; Long year format with slashes.

MM/DD/YY

5/21/06

LOCALE-DEPENDENT; Short year format with slashes

MM-DD-YYYY

5-21-2006

LOCALE-DEPENDENT; Long year format with dashes (short year may be supported, but it may also be used for years less than 100 .

mmm DD, YYYY

Oct 29, 2006

LOCALE-DEPENDENT; Short alphabetic month day, year. Note: mmm depends on the locale's language.

DD mmm YYYY

29 Oct 2006

LOCALE-DEPENDENT; Short alphabetic day month year

mmmmm DD, YYYY

October 29, 2006

LOCALE-DEPENDENT; Long alphabetic month day, year

DD mmmmm YYYY

29 October 2006

LOCALE-DEPENDENT; Long alphabetic day month year

Evaluators should support other locales. Many conversions will vary by locale, including the decimal point (comma or period), names of months, date formats (MM/DD vs. DD/MM), and so on. Dates in particular vary by locale.

Evaluators shall support the datetime format, which is a date followed by a time, using either the space character or the literal “T” character as the separator (the “T” is from ISO 8601). Evaluators shall support at least the ISO date format in a datetime format; they may support other date formats in a datetime format as well. Formats such as “YYYY-MM-DD HH:MM” and “YYYY-MM-DDTHH:MM:SS” (where “T” is the literal character T) shall be accepted. The result of accepting a datetime format shall be a representation of that specific time (without removing either the date or the time of day, unlike DATEVALUE or TIMEVALUE).

Evaluators may accept other formats that will convert to numbers, and those conversions may be locale-dependent, as long as they do not conflict with the above. Where no conversion is determined, an Error is returned.

See also N 6.13.26, T 6.20.22, DATEVALUE 6.10.4, TIMEVALUE 6.10.18, NUMBERVALUE 6.13.28

6.14Lookup Functions

6.14.1General

These functions look up information. Note that IF() can be considered a trivial lookup function, but it is listed as a logical function instead.

6.14.2ADDRESS

Summary: Returns a cell address (reference) as text

Syntax: ADDRESS( Integer Row ; Integer Column [ ; Integer Abs = 4 [ ; Logical A1 = TRUE() [ ; Text Sheet ] ] ] )

Returns: Text

Constraints: Row >= 1, Column >= 1, 1 <= Abs <= 4; A1 = TRUE(). Evaluators may evaluate expressions that do not meet the constraint A1 = TRUE().

Semantics: Returns a cell address (reference) as text. The text does not include the surrounding [...] of a reference. If a Sheet name is given, the sheet name in the text returned is followed by a “.” and the column/row reference if A1 is TRUE, or a “!” and the column/row reference if A1 is FALSE; otherwise no “.” respectively “!” is included. Columns are identified using uppercase letters. The value of Abs determines if the column and/or row is absolute or relative. The value of A1 determines if A1 reference style or R1C1 reference style is used.

Table 23 - ADDRESS

Abs

Meaning

A1 = TRUE()

A1 = FALSE()

1

fully absolute

$A$1

R1C1

2

row absolute, column relative

A$1

R1C[1]

3

row relative, column absolute

$A1

R[1]C1

4

fully relative

A1

R[1]C[1]

Note that the INDIRECT function accepts this format.

See also INDIRECT 6.14.7

6.14.3CHOOSE

Summary: Uses an index to return a value from a list of values.

Syntax: CHOOSE( Integer Index ; { Any Value }+ )

Returns: Any

Constraints: Returns an Error if Index < 1 or if there is no corresponding value in the list of Values.

Semantics: Uses Index to determine which value, from a list of values, to return. If Index is 1, CHOOSE returns the first Value; if Index is 2, CHOOSE returns the second value, and so on. Note that the Values may be formula expressions. Expression paths of parameters other than the one chosen are not calculated or evaluated for side effects.

See also IF 6.15.4

6.14.4GETPIVOTDATA

Summary: Return a value from a data pilot table.

Syntax: GETPIVOTDATA( Text DataField ; Reference Table { ; Text Field ; Scalar Member }* )

Note: This function knows two different syntaxes. This version of the syntax is distinguished by the second parameter Table being a Reference.

Returns: Any

Semantics: Returns a single result from the calculation of a data pilot table.

The data pilot table is selected by Table, which is a reference to a cell or cell range that's within a data pilot table or contains a data pilot table. If the cell range contains several data pilot tables, the last one in the order of <table:data-pilot-table> elements in the file is used.

DataField selects one of the data pilot table's data fields. It can be the name of the source column, or the given name of the data field (such as “Sum of Sales”).

If no Field/Member pairs are given, the grand total is returned. Otherwise, each pair adds a constraint that the result shall satisfy. Field is the name of a field from the data pilot table. Member is the name of a member (item) from that field. If a member is a number, Member can alternatively be its numerical value.

If the data pilot table contains only a single result value that fulfills all of the constraints, or a subtotal result that summarizes all matching values, that result is returned. If there is no matching result, or several ones without a subtotal for them, an Error is returned. These conditions apply to results that are included in the data pilot table. If the source data contains entries that are hidden by settings of the data pilot table, they are ignored. The order of the Field/Member pairs is not significant. Field and member names are case-insensitive.

If no constraint for a page field is given, the field's selected value is implicitly used. If a constraint for a page field is given, it shall match the field's selected value, or an Error is returned.

Subtotal values from the data pilot table are only used if they use the function “auto” (except when specified in the constraint, see below).

Alternative syntax: GETPIVOTDATA( Reference Table ; Text Constraints )

For compatibility, a second syntax is allowed. Table has the same meaning as above. This version of the syntax is distinguished by the first parameter Table being a Reference.

Constraints is a space-separated list. Entries can be quoted (single quotes). One of the entries can be the data field name. The data field name can be left out if the data pilot table contains only one data field, otherwise it shall be present. Each of the other entries specifies a constraint in the form Field[Member] (with literal characters [ and ]), or only Member if the member name is unique within all fields that are used in the data pilot table. A function name can be added in the form Field[Member;Function], which will cause the constraint to match only subtotal values which use that function. The possible function names are the same as in the table:function attribute of the <table:data-pilot-subtotal> element, case-insensitive.

6.14.5HLOOKUP

Summary: Look for a matching value in the first row of the given table, and return the value of the indicated row.

Syntax: HLOOKUP( Any Lookup ; Reference|Array DataSource ; Integer Row [ ; Logical RangeLookup = TRUE() ] )

Returns: Any

Constraints: Row >= 1; Searched portion of DataSource shall not include Logical values. Evaluators may evaluate expressions that do not meet the constraint that the searched portion of a DataSource not include Logical values.

Semantics:

If RangeLookup is omitted or TRUE or not 0, the first row of DataSource is assumed to be sorted in ascending order, with smaller numbers before larger ones, smaller text values before larger ones (e.g., "A" before "B", and "B" before "BA"), and False before True. If the types are mixed, Numbers are sorted before Text, and Text before Logicals; evaluators without a separate Logical type may include a Logical as a Number. The lookup will try to match an entry of value Lookup. If none is found the largest entry less than Lookup is taken as a match. From a sequence of identical values <= Lookup the last entry is taken. If there is no data less than or equal to Lookup, the #N/A Error is returned. If Lookup is of type Text and the value found is of type Number, the #N/A Error is returned. If DataSource is not sorted, the result is undetermined and implementation-dependent. In most cases it will be arbitrary and just plain wrong due to binary search algorithms.

If RangeLookup is FALSE or 0, DataSource does not need to be sorted and an exact match is searched. Each value in the first row of DataSource is examined in order (starting at the left) until its value matches Lookup.

Both methods, if there is a match, return the corresponding value in row Row, relative to the DataSource, where the topmost row in DataSource is 1.

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also INDEX 6.14.6, MATCH 6.14.9, OFFSET 6.14.11, VLOOKUP 6.14.12

6.14.6INDEX

Summary: Returns a value using a row and column index value (and optionally an area index).

Syntax: INDEX( ReferenceList|Array DataSource ; [ Integer Row ] [ ; [ Integer Column ] ] [ ; Integer AreaNumber = 1 ] )

Returns: Any

Constraints: Row >= 0, Column >= 0,
1 <= AreaNumber <= number of references in DataSource if that is a ReferenceList, else AreaNumber = 1

Semantics:

Given a DataSource, returns the value at the given Row and Column (starting numbering at 1, relative to the top left of the DataSource) of the given area AreaNumber. If AreaNumber is not given, it defaults to 1 (the first and possibly only area). This function is essentially a two-dimensional version of CHOOSE, which does not accept range parameters.

If Row is omitted or an empty parameter (two consecutive ;; semicolons) or 0, an entire column of the given area AreaNumber in DataSource is returned. If Column is omitted or an empty parameter (two consecutive ;; semicolons) or 0, an entire row of the given area AreaNumber in DataSource is returned. If both, Row and Column, are omitted or empty or 0, the entire given area AreaNumber is returned.

If DataSource is a one-dimensional column vector, Column is optional or can be omitted as an empty parameter (two consecutive ;; semicolons). If DataSource is a one-dimensional row vector, Row is optional, which effectively makes Row act as the column offset into the vector, or can be omitted as an empty parameter (two consecutive ;; semicolons).

If Row or Column have a value greater than the dimension of the corresponding given area AreaNumber, an Error is returned.

See also AREAS 6.13.2, CHOOSE 6.14.3

6.14.7INDIRECT

Summary: Return a reference given a string representation of a reference

Syntax: INDIRECT( Text Ref [ ; Logical A1 = TRUE() ] )

Returns: Reference

Constraints: Ref is valid reference

Semantics: Given text for a reference (such as “A3”), returns a reference. If A1 is False, it is interpreted as an R1C1 reference style. For interoperability, if the Ref text includes a sheet name, evaluators should be able to parse both, the “.” dot and the “!” exclamation mark, as the sheet name separator. If evaluators support the A1=FALSE() case of the ADDRESS 6.14.2 function and include the “!” exclamation mark as the sheet name separator, evaluators shall correctly parse that in the A1=FALSE() case of this INDIRECT function. Evaluators shall correctly parse the “.” dot as the sheet name separator in the A1=TRUE() case.

See also ADDRESS 6.14.2

6.14.8LOOKUP

Summary: Look for criterion in an already-sorted array, and return a corresponding result

Syntax: LOOKUP( Any Find ; ForceArray Reference|Array Searched [ ; ForceArray Reference|Array Results ] )

Returns: Any

Constraints: The searched portion of Searched shall be sorted in ascending order; if provided, Results shall have the same length as Searched. The searched portion of Searched shall not include Logical values. Evaluators may evaluate expressions that do not meet the constraint that the searched portion of a Searched not include Logical values.

Semantics: This function searches for Find in a row or column of the previously-sorted array Searched and returns a corresponding value. The match is the largest value in the row/column of Searched that is less than or equal to Find (so an exact match is always preferred over inexact ones). From a sequence of identical values <= Find the last entry is taken. If Find is smaller than the smallest value in the first row or column (depending on the array dimensions), LOOKUP returns the #N/A Error. If Find is of type Text and the value found is of type Number, the #N/A Error is returned.

The searched portion of Searched shall be sorted in ascending order, and so that values of type Number precede values of type Text if both types are included (e.g., -2, 0, 2, “A”, “B”).

There are two major uses for this function; the 3-parameter version (vector) and the 2-parameter version (non-vector array).

Note: Interoperability is improved by use of HLOOKUP or VLOOKUP in expressions over LOOKUP.

When given two parameters, Searched is first examined:

When given 3 parameters, Results shall be a vector (either a row or a column) or an Error is raised. The function determines the index of the match in the first column respectively row of Searched, and returns the value in Results with the same index.

Searched is first examined:

The lengths of the search vector and the result vector do not need to be identical. When the match position falls outside the length of the result vector, an Error is returned if the result vector is given as an array object. If it is a cell range, it gets automatically extended to the length of the searched vector, but in the direction of the result vector. If just a single cell reference was passed, a column vector is generated. If the cell range cannot be extended due to the sheet's size limit, then the #N/A Error is returned.

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also HLOOKUP 6.14.5, INDEX 6.14.6, MATCH 6.14.9, OFFSET 6.14.11, VLOOKUP 6.14.12

6.14.9MATCH

Summary: Finds a Search item in a sequence, and returns its position (starting from 1).

Syntax: MATCH( Scalar Search ; Reference|Array SearchRegion [ ; Integer MatchType = 1 ] )

Returns: Any

Constraints: -1 <= MatchType <= 1; The searched portion of SearchRegion shall not include Logical values. Evaluators may evaluate expressions that do not meet the constraint that the searched portion of a SearchRegion not include Logical values.

SearchRegion shall be a vector (a single row or column)

Semantics:

If a match is found, MATCH returns the relative position (starting from 1). For Text the comparison is case-insensitive. MatchType determines the type of search; if MatchType is 0, the SearchRegion shall be considered unsorted, and the first match is returned. If MatchType is 1, the SearchRegion may be assumed to be sorted in ascending order, with smaller Numbers before larger ones, smaller Text values before larger ones (e.g., "A" before "B", and "B" before "BA"), and False before True. If the types are mixed, Numbers are sorted before Text, and Text before Logicals; evaluators without a separate Logical type may include a Logical as a Number. If MatchType is -1, then SearchRegion may be assumed to be sorted in descending order (the opposite of the above). If MatchType is 1 or -1, evaluators may use binary search or other techniques so that they do not need to examine every value in linear order. MatchType defaults to 1.

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also HLOOKUP 6.14.5, OFFSET 6.14.11, VLOOKUP 6.14.12

6.14.10MULTIPLE.OPERATIONS

Summary: Executes a formula expression while substituting a row reference and a column reference.

Syntax: MULTIPLE.OPERATIONS( Reference FormulaCell ; Reference RowCell ; Reference RowReplacement [ ; Reference ColumnCell ; Reference ColumnReplacement ] )

Returns: Any

Semantics:

MULTIPLE.OPERATIONS executes the formula expression pointed to by FormulaCell and all formula expressions it depends on while replacing all references to RowCell with references to RowReplacement respectively all references to ColumnCell with references to ColumnReplacement.

If calls to MULTIPLE.OPERATIONS are encountered in dependencies, replacements of target cells shall occur in queued order, with each replacement using the result of the previous replacement.

Note: The function may be used to create tables of expressions that depend on two input parameters.

Example: FormulaCell is B5, RowCell is B3, ColumnCell is B2

Table 24 - MULTIPLE.OPERATIONS

 

col_B

col_C

col_D

col_E

col_F

row_2

1

 

1

2

3

row_3

1

1

=MULTIPLE.OPERATIONS($B$5;$B$3;$C3;$B$2;D$2)

=MULTIPLE.OPERATIONS($B$5;$B$3;$C3;$B$2;E$2)

=MULTIPLE.OPERATIONS($B$5;$B$3;$C3;$B$2;F$2)

row_4

=B2+B3

2

=MULTIPLE.OPERATIONS($B$5;$B$3;$C4;$B$2;D$2)

=MULTIPLE.OPERATIONS($B$5;$B$3;$C4;$B$2;E$2)

=MULTIPLE.OPERATIONS($B$5;$B$3;$C4;$B$2;F$2)

row_5

=B2*B3+B4

3

=MULTIPLE.OPERATIONS($B$5;$B$3;$C5;$B$2;D$2)

=MULTIPLE.OPERATIONS($B$5;$B$3;$C5;$B$2;E$2)

=MULTIPLE.OPERATIONS($B$5;$B$3;$C5;$B$2;F$2)

 

 

4

=MULTIPLE.OPERATIONS($B$5;$B$3;$C6;$B$2;D$2)

=MULTIPLE.OPERATIONS($B$5;$B$3;$C6;$B$2;E$2)

=MULTIPLE.OPERATIONS($B$5;$B$3;$C6;$B$2;F$2)

Result:

Table 25 - MULTIPLE.OPERATIONS

 

col_B

col_C

col_D

col_E

col_F

row_2

1

 

1

2

3

row_3

1

1

3

5

7

row_4

2

2

5

8

11

row_5

3

3

7

11

15

 

 

4

9

14

19

Note that although only cell B5 is passed as the FormulaCell parameter, also the references to B2 and B3 of the formula in cell B4 are replaced, because B5 depends on B4.

6.14.11OFFSET

Summary: Modifies a reference's position and dimension.

Syntax: OFFSET( Reference reference ; Integer rowOffset ; Integer columnOffset [ ; [ Integer newHeight ] [ ; [ Integer newWidth ] ] ] )

Returns: Reference

Constraints: newWidth > 0; newHeight > 0
The modified reference shall be in a valid range, starting from column/row one to the maximum column/row.

Semantics: Shifts reference by rowOffset rows and by columnOffset columns. Optionally, the dimension can be set to newWidth and/or newHeight, if omitted the width/height of the original reference is taken. Note that newHeight may be empty (two consecutive semicolons ;;) followed by a given newWidth argument. Returns the modified reference.

See also COLUMN 6.13.4, COLUMNS 6.13.5, ROW 6.13.29, ROWS 6.13.30

6.14.12VLOOKUP

Summary: Look for a matching value in the first column of the given table, and return the value of the indicated column.

Syntax: VLOOKUP( Any Lookup ; Reference|Array DataSource ; Integer Column [ ; Logical RangeLookup = TRUE() ] )

Returns: Any

Constraints: Column >= 1; The searched portion of DataSource shall not include Logical values. Evaluators may evaluate expressions that do not meet the constraint that the searched portion of a DataSource not include Logical values.

Semantics:

If RangeLookup is omitted or TRUE or not 0, the first column of DataSource is assumed to be sorted in ascending order, with smaller Numbers before larger ones, smaller Text values before larger ones (e.g., "A" before "B", and "B" before "BA"), and False before True. If the types are mixed, Numbers are sorted before Text, and Text before Logicals; evaluators without a separate Logical type may include a Logical as a Number. The lookup will try to match an entry of value Lookup. From a sequence of identical values <= Lookup the last entry is taken. If none is found the largest entry less than Lookup is taken as a match. If there is no data less than or equal to Lookup, the #N/A Error is returned. If Lookup is of type Text and the value found is of type Number, the #N/A Error is returned. If DataSource is not sorted, the result is undetermined and implementation-dependent. In most cases it will be arbitrary and just plain wrong due to binary search algorithms.

If RangeLookup is FALSE or 0, DataSource does not need to be sorted and an exact match is searched. Each value in the first column of DataSource is examined in order (starting at the top) until its value matches Lookup. If no value matches, the #N/A Error is returned.

Both methods, if there is a match, return the corresponding value in column Column, relative to the DataSource, where the leftmost column in DataSource is 1.

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also HLOOKUP 6.14.5, INDEX 6.14.6, MATCH 6.14.9, OFFSET 6.14.11

6.15Logical Functions

6.15.1General

The logical functions are the constants TRUE() and FALSE(), the functions that compute Logical values NOT(), AND(), and OR(), and the conditional function IF(). The OpenDocument specification mentions "logical operators"; these are another name for the logical functions.

Note that because of Error values, any logical function that accepts parameters can actually produce TRUE, FALSE, or an Error value, instead of TRUE or FALSE.

These are not bitwise operations, e.g., AND(12;10) produces TRUE(), not 8. See the bit operation functions for bitwise operations.

6.15.2AND

Summary: Compute logical AND of all parameters.

Syntax: AND( { Logical|NumberSequenceList L }+ )

Returns: Logical

Constraints: Shall have 1 or more parameters

Semantics: Computes the logical AND of the parameters. If all parameters are True, returns True; if any are False, returns False. When given one parameter, this has the effect of converting that one parameter into a Logical value. When given zero parameters, evaluators may return a Logical value or an Error.

Also in array context a logical AND of all arguments is computed, range or array parameters are not evaluated as a matrix and no array is returned. This behavior is consistent with functions like SUM. To compute a logical AND of arrays per element use the * operator in array context.

See also OR 6.15.8, IF 6.15.4

6.15.3FALSE

Summary: Returns constant FALSE

Syntax: FALSE()

Returns: Logical

Constraints: Shall have 0 parameters

Semantics: Returns logical constant FALSE. This may be a Number or a distinct type.

See also TRUE 6.15.9, IF 6.15.4

6.15.4IF

Summary: Return one of two values, depending on a condition

Syntax: IF( Logical Condition [ ; [ Any IfTrue ] [ ; [ Any IfFalse ] ] ] )

Returns: Any

Constraints: None.

Semantics: Computes Condition. If it is TRUE, it returns IfTrue, else it returns IfFalse. If there is only 1 parameter, IfTrue is considered to be TRUE(). If there are less than 3 parameters, IfFalse is considered to be FALSE(). Thus the 1 parameter version converts Condition into a Logical value. If there are 2 or 3 parameters but the second parameter is null (two consecutive ;; semicolons), IfFalse is considered to be 0. If there are 3 parameters but the third parameter is null, IfFalse is considered to be 0. This function only evaluates IfTrue, or ifFalse, and never both; that is to say, it short-circuits.

See also AND 6.15.2, OR 6.15.8

6.15.5IFERROR

Summary: Return X unless it is an Error, in which case return an alternative value

Syntax: IFERROR( Any X ; Any Alternative )

Returns: Any

Constraints: None.

Semantics: Computes X. If ISERROR(X) is true, return Alternative, else return X. Thus this is semantically equivalent to IF(ISERROR(X); Alternative; X), except that X is only computed once. If X or Alternative is a cell reference to an empty cell, it is treated as the empty string "".

See also IF 6.15.2

6.15.6IFNA

Summary: Return X unless it is an NA, in which case return an alternative value

Syntax: IFNA( Any X ; Any Alternative )

Returns: Any

Constraints: None.

Semantics: Computes X. If ISNA(X) is true, return Alternative, else return X. Thus this is semantically equivalent to IF(ISNA(X); Alternative; X), except that X is only computed once. If X or Alternative is a cell reference to an empty cell, it is treated as the empty string "".

See also IF 6.15.2

6.15.7NOT

Summary: Compute logical NOT

Syntax: NOT( Logical L )

Returns: Logical

Constraints: Shall have 1 parameter

Semantics: Computes the logical NOT. If given TRUE, returns FALSE; if given FALSE, returns TRUE.

See also AND 6.15.2, IF 6.15.4

6.15.8OR

Summary: Compute logical OR of all parameters.

Syntax: OR( { Logical|NumberSequenceList L }+ )

Returns: Logical

Constraints: Shall have 1 or more parameters

Semantics: Computes the logical OR of the parameters. If all parameters are False, it shall return False; if any are True, it shall returns True. When given one parameter, this has the effect of converting that one parameter into a Logical value. When given zero parameters, evaluators may return a Logical value or an Error.

Also in array context a logical OR of all arguments is computed, range or array parameters are not evaluated as a matrix and no array is returned. This behavior is consistent with functions like SUM. To compute a logical OR of arrays per element use the + operator in array context.

See also AND 6.15.2, IF 6.15.4

6.15.9TRUE

Summary: Returns constant TRUE

Syntax: TRUE()

Returns: Logical

Constraints: Shall have 0 parameters

Semantics: Returns logical constant TRUE. The result of this function may or may not be equal to 1 when compared using “=”. It always has the value of 1 if used in a context requiring Number (because of the automatic conversions), so if ISNUMBER(TRUE()), then it shall have the value 1.

See also FALSE 6.15.3, IF 6.15.4

6.15.10XOR

Summary: Compute a logical XOR of all parameters.

Syntax: XOR( { Logical L }+ )

Returns: Logical

Constraints: Shall have 1 or more parameters.

Semantics: Computes the logical XOR of the parameters such that the result is an addition modulo 2. If an even number of parameters is True it returns False, if an odd number of parameters is True it returns True. When given one parameter, this has the effect of converting that one parameter into a Logical value.

See also AND 6.15.2, OR 6.15.8

6.16Mathematical Functions

6.16.1General

This section describes functions for various mathematical functions, including trigonometric functions like SIN 6.16.55). Note that the constraint text presumes that a value of type Number is a real number (no imaginary component). Unless noted otherwise, all angle measurements are in radians.

6.16.2ABS

Summary: Return the absolute (nonnegative) value.

Syntax: ABS( Number N )

Returns: Number

Constraints: None

Semantics: If N < 0, returns -N, otherwise returns N.

See also Prefix Operator “-” 6.4.16

6.16.3ACOS

Summary: Returns the principal value of the arc cosine of a number. The angle is returned in radians.

Syntax: ACOS( Number N )

Returns: Number

Constraints: -1.0 <= N <= 1.0.

Semantics: Computes the arc cosine of a number, in radians.

 

Returns a principal value 0 result PI.

See also COS 6.16.19, RADIANS 6.16.49, DEGREES 6.16.25

6.16.4ACOSH

Summary: Return the principal value of the inverse hyperbolic cosine

Syntax: ACOSH( Number N )

Returns: Number

Constraints: N >= 1

Semantics: Computes the principal value of the inverse hyperbolic cosine.

 

See also COSH 6.16.20, ASINH 6.16.8

6.16.5ACOT

Summary: Return the principal value of the arc cotangent of a number. The angle is returned in radians.

Syntax: ACOT( Number N )

Returns: Number

Semantics: Computes the arc cotangent of a number, in radians.

Returns a principal value 0 < result < PI.

See also COT 6.16.21, ATAN 6.16.9, TAN 6.16.69, RADIANS 6.16.49, DEGREES 6.16.25

6.16.6ACOTH

Summary: Return the hyperbolic arc cotangent

Syntax: ACOTH( Number N )

Returns: Number

Constraints: ABS(N) > 1

Semantics: Computes the hyperbolic arc cotangent. The hyperbolic arc cotangent is an analog of the ordinary (circular) arc cotangent.

 

See also COSH 6.16.20, ASINH 6.16.8

6.16.7ASIN

Summary: Return the principal value of the arc sine of a number. The angle is returned in radians.

Syntax: ASIN( Number N )

Returns: Number

Constraints: -1 <= N <= 1.

Semantics: Computes the arc sine of a number, in radians.

 

Returns a principal value -PI/2 result PI/2.

See also SIN 6.16.55, RADIANS 6.16.49, DEGREES 6.16.25

6.16.8ASINH

Summary: Return the principal value of the inverse hyperbolic sine

Syntax: ASINH( Number N )

Returns: Number

Constraints: None

Semantics: Computes the principal value of the inverse hyperbolic sine.

 

See also SINH 6.16.56, ACOSH 6.16.4

6.16.9ATAN

Summary: Return the principal value of the arc tangent of a number. The angle is returned in radians.

Syntax: ATAN( Number N )

Returns: Number

Semantics: Computes the arc tangent of a number, in radians.

Returns a principal value -PI/2 < result < PI/2.

See also ATAN2 6.16.10, TAN 6.16.69, RADIANS 6.16.49, DEGREES 6.16.25

6.16.10ATAN2

Summary: Returns the principal value of the arc tangent given a coordinate of two numbers.

The angle is returned in radians.

Syntax: ATAN2( Number x ; Number y )

Returns: Number

Constraints: x<>0 or y<>0

Semantics: Computes the arc tangent of two numbers (the x and y coordinates of a point), in radians. This is similar to ATAN(y/x), but the signs of the two numbers are taken into account so that the result covers the full range from -PI() to +PI(). ATAN2(0;0) is implementation-defined, evaluators may return 0 or an Error.

Returns a principal value -PI < result ≤ PI.

See also ATAN 6.16.9, TAN 6.16.69, RADIANS 6.16.49, DEGREES 6.16.25

6.16.11ATANH

Summary: Return the principal value of the inverse hyperbolic tangent

Syntax: ATANH( Number N )

Returns: Number

Constraints: -1 < N < 1

Semantics: Computes the principal value of the inverse hyperbolic tangent.

 

See also COSH 6.16.20, SINH 6.16.56, ASINH 6.16.8, ACOSH 6.16.4, ATAN 6.16.9, ATAN2 6.16.10, FISHER 6.18.26

6.16.12BESSELI

Summary: Returns the modified Bessel function of integer order In(x).

Syntax: BESSELI( Integer X ; Number N )

Returns: Number

Constraints: N >= 0, INT(N)=N; Evaluators may evaluate expressions where N >= 0 returns a non-error value.

Semantics: Computes the modified Bessel function of integer order In(x). N is also known as the order.

See also BESSELJ 6.16.13, BESSELK 6.16.14, BESSELY 6.16.15

6.16.13BESSELJ

Summary: Returns the Bessel function of integer order Jn(x) (cylinder function)

Syntax: BESSELJ( Integer X ; Number N )

Returns: Number

Constraints: N >= 0, INT(N)=N; Evaluators may evaluate expressions where N >= 0 returns a non-error value.

Semantics: Computes the Bessel function of integer order Jn(x). N is also known as the order.

See also BESSELI 6.16.12, BESSELK 6.16.14, BESSELY 6.16.15

6.16.14BESSELK

Summary: Returns the modified Bessel function of integer order Kn(x).

Syntax: BESSELK( Integer X ; Number N )

Returns: Number

Constraints: N >= 0, INT (N)=N; Evaluators may evaluate expressions where N >= 0 returns a non-error value.

Semantics: Computes the Bessel function of integer order Kn(x). N is also known as the order.

See also BESSELI 6.16.12, BESSELJ 6.16.13, BESSELY 6.16.15

6.16.15BESSELY

Summary: Returns the Bessel function of integer order Yn(x), also known as the Neumann function.

Syntax: BESSELY( Integer X ; Number N )

Returns: Number

Constraints: N >= 0, INT(N)=N; Evaluators may evaluate expressions where N >= 0 returns a non-error value.

Semantics: Computes Bessel function of integer order Yn(x), also known as the Neumann function. N is also known as the order.

See also BESSELI 6.16.12, BESSELJ 6.16.13, BESSELK 6.16.14

6.16.16COMBIN

Summary: Returns the number of different R-length sets that can be selected from N items.

Syntax: COMBIN( Integer N ; Integer R )

Returns: Number

Constraints: N >= 0, R >= 0, R <= N

Semantics: COMBIN returns the binomial coefficient, which is the number of different R-length sets that can be selected from N items. Since they are sets, order in the sets is not relevant. The parameters are truncated (using INT) before use. For example, if a jar contains five marbles, each one a distinct color, the number of different three-marble groups COMBIN(5;3) = 10. The result is

 

Note that if order is important, use PERMUT instead.

See also PERMUT 6.18.59

6.16.17COMBINA

Summary: Returns the number of combinations with repetitions.

Syntax: COMBINA( Integer N ; Integer M )

Returns: Number

Constraints: N >= 0, M >= 0, N >= M; Evaluators may evaluate expressions where N >= 0, M >= 0 returns a non-error value.

Semantics: Returns the number of possible combinations of M objects out of N possible ones, with repetitions allowed. Actual arguments that are not integers are truncated (using INT) before use. The result is

 

See also COMBIN 6.16.16

6.16.18CONVERT

Summary: Returns a number converted from one unit system into another

Syntax: CONVERT( Number N ; Text From ; Text Into )

Returns: Number

Constraints: From and Into shall be legal units, and shall be in the same unit group.

Semantics: Returns the number converted from the unit identified by From into the unit identified by Into. A unit is a unit symbol , optionally preceded by a unit prefix (either a decimal prefix or a binary prefix). Units (including both the unit symbol and the optional unit prefix) are case-sensitive.

Evaluators claiming to implement this function shall support at least the following unit symbols (with conversions between them and other units in the same group):

Table 26 - Unit names

Unit group

Unit symbol

Description

Area

"uk_acre"

International acre (using international feet), exactly 4046.8564224 m2; normally not used for U.S. land areas

"us_acre"

U.S. survey/statute acre (using U.S. survey/statute feet), exactly 4046+13525426/15499969 m 2

"ang2" or "ang^2" *

Square angstrom (an Angstrom is exactly 10-10 m)

"ar" *

are, 100 m2 (not abbreviated as “a”)

"ft2" or "ft^2"

Square international feet (1 foot is exactly 0.3048 m)

"ha"

hectare, 10 000 m2

"in2" or "in^2"

Square international inches (1 inch is exactly 2.54 cm)

"ly" or "ly2"

Square light-year (where year=365.25 days)

"m2" or "m^2" *

Square meters

"Morgen"

Morgen, 2500 m2

"mi2" or "mi^2"

Square international miles

"Nmi2" or "Nmi^2"

Square nautical miles (1 nautical mile is 1852 m)

"Pica2" or "Pica^2"

Square Pica (one Pica is 1/72 in.)

"yd2" or "yd^2"

Square international yards (1 yard is 0.9144 m)

 

 

Distance (Length)

"ang" *

Angstrom, exactly 10-10 m

"ell"

Ell, exactly 45 international inches

"ft"

International Foot, exactly 0.3048 m and also exactly 12 international inches.

"in"

International Inch, exactly 2.54 cm.

"ly" *

Light-year, the distance light travels, in a vacuum, in a Julian year of 365.25 days

"m" *

Meter

"mi"

International Mile, exactly 1609.344 m and exactly 5280 international feet. This is not a U.S. survey/statute mile (see “smi”) nor a nautical mile (see “Nmi”), but this is the mile normally used in the U.S. customary system

"Nmi"

International nautical mile, exactly 1852 m. Note that this is not the obsolete U.S. nautical mile nor the Admiralty mile.

"parsec" or "pc" *

Distance from sun to a point having heliocentric parallax of one second (used for stellar distance)*

"Pica"

Pica (1/72 in.)

"survey_mi"

U.S. survey mile, aka U.S. statute mile, exactly 6336000/3937 m; used in some U.S. maps. This is not the mile (see “mi”) normally used in the U.S.

"yd"

International yard, exactly 0.9144 m and exactly 3 international feet.

 

 

Energy

"BTU" ("btu")

International Table British Thermal Unit

"c" *

Thermodynamic calorie, 4.184 J. This is not a dietary Calorie (kilocalorie). For high accuracy, use Joule, due to the many conflicting definitions of calorie.

"cal" *

International Table (IT) calorie, 4.1868 J. This is not a dietary Calorie (kilocalorie). For high accuracy, use Joule, due to the many conflicting definitions of calorie.

"e" *

Erg

"eV" ("ev") *

Electron volt (eV preferred)

"flb"

Foot-pound (international foot, avoirdupois pound)

"HPh" ("hh")

Horsepower-hour (HPh preferred)

"J" *

Joule

"Wh" ("wh") *

Watt-hour

 

 

Force (Weight)

"dyn" ("dy") *

Dyne

"N" *

Newton

"lbf"

Pound force (see “lbm” for pound mass)

"pond" *

Pond, gravitational force on a mass of one gram

 

 

Information

"bit" *

bit

"byte" *

byte = 8 bits

 

 

Magnetic Flux Density

"ga" *

Gauss

"T" *

Tesla

 

 

Mass

"g" *

Gram

"grain"

Grain, 1/7000 international pound mass (avoirdupois) (U.S. usage).

"cwt" ("shweight")

U.S. (short) hundredweight, 100 lbm

"uk_cwt" or "lcwt" ("hweight")

Imperial hundredweight, aka long hundredweight; 112 lbm

"lbm"

International pound mass (avoirdupois), exactly 453.59237 g (see “lbf” for pound force)

"stone"

14 international pound mass (avoirdupois)

"ton"

2000 international pound mass (avoirdupois) (U.S. usage). Note that there are many other measures also called “ton”; in particular, this is not a metric ton (tonne).

"ozm"

Ounce mass (avoirdupois), exactly 1/16 of an international pound mass (avoirdupois) (see “oz” for fluid ounce)

"sg"

Slug; 32.174 international pound mass (avoirdupois)

"u" *

U (atomic mass unit)

"uk_ton" or "LTON" ("brton")

Imperial ton, aka “long ton”, "deadweight ton", or "weight ton". 2240 lbm.

 

 

Power

"HP" ("h")

Horsepower. The unit “h” is deprecated and should be replaced with “HP”.

"PS"

Pferdestärke (German “horse strength”, close but not identical to “HP”)

"W" ("w") *

Watt

 

 

Pressure

"atm" ("at") *

Atmosphere

"mmHg" *

mm of Mercury

"Pa" *

Pascal; Pa preferred, as it is the standard abbreviation. Note that “P” or “p” may not be accepted.

"psi"

Pounds per square inch, using avoirdupois pounds and international inches.

"Torr"

Torr, exactly 101325/760 Pa (this is close but not equal to mmHg)

 

 

Speed

"admkn"

Admiralty knot, exactly 6080 international feet/hour.

"kn"

Knot, exactly one Nautical mile per hour or exactly 1852/3600 m/s. Note that this is not an Admiralty knot (“admkn”).

"m/h" or "m/hr" *

Meters per hour

"m/s" or "m/sec" *

Meters per second

"mph"

Miles per hour (international miles)

 

 

Temperature

"C" ("cel")

degrees Celsius

"F" ("fah")

degrees Fahrenheit

"K" ("kel") *

Kelvin

"Rank"

degrees Rankine

"Reau"

degrees Réaumur; °C = °Ré · 5/4.

 

 

Time

"day" or "d"

Day (exactly 24 hours)

"hr"

Hour (exactly 60 minutes)

"mn" or "min"

Minute (exactly 60 seconds)

"sec" or "s" *

Second (“s” is the official abbreviation of this SI base unit, while “sec” is its traditional abbreviation in the CONVERT function) *

"yr"

Year (exactly 365.25 days, for purposes of this function)

 

 

Volume

"ang3" or "ang^3" *

Cubic angstrom

"barrel"

U.S. oil barrel, exactly 42 U.S. customary gallons (liquid). Note that many other units are also called barrels (e.g., a beer barrel in the U.K. is 36 Imperial gallons)

"bushel"

U.S. bushel (not Imperial bushel), interpreted as volume

"cup"

Cup (U.S. customary liquid measure)

"ft3" or "ft^3"

Cubic international feet

"gal"

Gallon (U.S. customary liquid measure)

"GRT" ("regton")

Gross Registered Ton, 100 cubic (international) feet

"in3" or "in^3"

Cubic international inch

"l" or "L" ("lt") *

Liter

"ly3" or "ly^3"

Cubic light-year

"m3" or "m^3" *

Cubic meter

"mi3" or "mi^3"

Cubic international mile

"MTON"

Measurement ton aka “freight ton”, 40 cubic feet

"Nmi3" or "Nmi^3"

Cubic nautical mile

"oz"

Fluid ounce (U.S. customary liquid measure; see “ozm” for ounce mass)

"Pica3" or "Pica^3"

Cubic Pica

"pt" or "us_pt"

U.S. Pint (liquid measure)

"qt"

Quart (U.S. customary liquid measure). This is 0.946352946 liters, and thus not the same as the U.S. dry quart (1.101220 liters), nor is this the same as the Imperial quart (as used in the U.K. and Canada, which is 1.1365225 liters exactly)

"tbs"

Tablespoon (U.S. customary, traditional meaning). This shall be 0.5 U.S. fluid ounce, not 15mL (common in U.S.) or 20mL (common in Australia).

"tsp"

Teaspoon (U.S. customary, traditional meaning), 1/6 fluid ounce in U.S. customary measure. This is not the 1/8 Imperial fl. oz. per Imperial units nor the modern teaspoon of 5 mL currently used in the U.S.; see “tspm”

"tspm"

Modern teaspoon, 5mL

"uk_gal"

U.K. / Imperial gallon

"uk_pt"

U.K. / Imperial pint

"uk_qt"

U.K. / Imperial quart

"yd3" or "yd^3"

Cubic international yard

 

 

Evaluators shall support decimal prefixes for unit symbols marked with * and binary prefixes for unit symbols marked with †. Evaluators should not support prefixes for other unit symbols.

The unit symbols in parentheses are deprecated unit symbols; evaluators shall support these unit symbols.

Evaluators should use internationally-standardized unit name abbreviations for such additions where possible. Evaluators may support the obsolete symbols “p” and “P” as unit names for Pascals.

For purposes of this function, a year is exactly 365.25 days long.

Evaluators claiming to support this function shall permit the following unit decimal prefixes to be prepended to any unit symbol marked with “*” in the unit table cell above. Adding a unit prefix indicates multiplication of the (scalar) unit by the given prefix value; for example km indicates kilometres, and km2 or km^2 indicate square kilometres.

Table 27 - Decimal Prefixes for use in CONVERT

Unit Prefix

Description

Prefix Value

"Y"

yotta

1E+24

"Z"

zetta

1E+21

"E"

exa

1E+18

"P"

peta

1E+15

"T"

tera

1E+12

"G"

giga

1E+09

"M"

mega

1E+06

"k"

kilo

1E+03

"h"

hecto

1E+02

“da” or "e"

deka (note: “e” is not a standard SI prefix)

1E+01

"d"

deci

1E-01

"c"

centi

1E-02

"m"

milli

1E-03

"u"

micro (note: this is “u”, not the standard SI µ)

1E-06

"n"

nano

1E-09

"p"

pico

1E-12

"f"

femto

1E-15

"a"

atto

1E-18

"z"

zepto

1E-21

"y"

yocto

1E-24

The prefix “e” for 10 1 is nonstandard and included for backward compatibility with legacy applications and documents.

The unit names marked with † in the unit symbol table above (see the Information group) shall also support the following binary prefixes per IEC 60027-2:

Table 28 - Binary prefixes for use in CONVERT

Binary Unit Prefix

Description

Prefix Value

Derived from

"Yi"

yobi

2^80 = 1 208 925 819 614 629 174 706 176

yotta

"Zi"

zebi

2^70 = 1 180 591 620 717 411 303 424

zetta

"Ei"

exbi

2^60 = 1 152 921 504 606 846 976

exa

"Pi"

pebi

2^50 = 1 125 899 906 842 624

peta

"Ti"

tebi

2^40 = 1 099 511 627 776

tera

"Gi"

gibi

2^30 = 1 073 741 824

giga

"Mi"

mebi

2^20 = 1 048 576

mega

"ki"

kibi

2^10 = 1024

kilo

 

In the case where there is a naming conflict (a unit name with a prefix is the same as an unprefixed name), the unprefixed name shall take precedence.

Evaluators may implement this conversion by first converting to some SI unit (e.g., meter and kilogram), and then convert again to the final unit.

See also EUROCONVERT 6.16.29

6.16.19COS

Summary: Return the cosine of an angle specified in radians.

Syntax: COS( Number N )

Returns: Number

Constraints: None

Semantics: Computes the cosine of an angle specified in radians.

 

See also ACOS 6.16.3, RADIANS 6.16.49, DEGREES 6.16.25

6.16.20COSH

Summary: Return the hyperbolic cosine of the given hyperbolic angle

Syntax: COSH( Number N )

Returns: Number

Constraints: None

Semantics: Computes the hyperbolic cosine of a hyperbolic angle. The hyperbolic cosine is an analog of the ordinary (circular) cosine. The points (cosh t, sinh t) define the right half of the equilateral hyperbola, just as the points (cos t, sin t) define the points of a circle.

 

See also ACOSH 6.16.4, SINH 6.16.56, TANH 6.16.70

6.16.21COT

Summary: Return the cotangent of an angle specified in radians

Syntax: COT( Number N )

Returns: Number

Constraints: None

Semantics: Computes the cotangent of an angle specified in radians.

COT(x) = 1 / TAN(x)

See also ACOT 6.16.5, TAN 6.16.69, RADIANS 6.16.49, DEGREES 6.16.25, SIN 6.16.55, COS 6.16.19

6.16.22COTH

Summary: Return the hyperbolic cotangent of the given hyperbolic angle

Syntax: COTH( Number N )

Returns: Number

Constraints: N<>0

Semantics: Computes the hyperbolic cotangent of a hyperbolic angle. The hyperbolic cotangent is an analog of the ordinary (circular) cotangent.

 

See also ACOSH 6.16.4, SINH 6.16.56, TANH 6.16.70

6.16.23CSC

Summary: Return the cosecant of an angle specified in radians.

Syntax: CSC( Number N )

Returns: Number

Constraints: None

Semantics: Computes the cosecant cosine of an angle specified in radians. Equivalent to:

1/SIN(N)

See also SIN 6.16.55

6.16.24CSCH

Summary: Return the hyperbolic cosecant of the given angle specified in radians

Syntax: CSCH( Number N )

Returns: Number

Constraints: None

Semantics: Computes the hyperbolic cosecant of a hyperbolic angle. This is equivalent to:

1/SINH(N)

See also SINH 6.16.56, CSCH

6.16.25DEGREES

Summary: Convert radians to degrees.

Syntax: DEGREES( Number N )

Returns: Number

Constraints: None

Semantics: Converts a number in radians into a number in degrees. DEGREES(N) is equal to N*180/PI().

See also RADIANS 6.16.49, PI 6.16.45

6.16.26DELTA

Summary: Report if two numbers are equal, returns 1 if they are equal.

Syntax: DELTA( Number X [ ; Number Y = 0 ] )

Returns: Number

Constraints: None

Semantics: If X and Y are equal, return 1, else 0. Y is set to 0 if omitted.

See also Infix operator “=” 6.4.7

6.16.27ERF

Summary: Calculates the error function.

Syntax: ERF( Number z0 [ ; Number z1 ] )

Returns: Number

Constraints: None

Semantics: With a single argument, returns the error function of z0:

 

With two arguments, returns

 

See also ERFC 6.16.28

6.16.28ERFC

Summary: Calculates the complementary error function.

Syntax: ERFC( Number z )

Returns: Number

Constraints: None

Semantics: returns the complementary error function of z: ERFC(z) = 1 – ERF(z)

See also ERF 6.16.27

6.16.29EUROCONVERT

Summary: Converts a Number, representing a value in one European currency, to an equivalent value in another European currency, according to the fixed conversion rates defined by the Council of the European Union.

Syntax: EUROCONVERT( Number N ; Text From ; Text To [ ; Logical FullPrecision = FALSE() [ ; Integer TriangulationPrecision ] ] )

Returns: Currency

Constraints: From and To shall be known to the evaluator. TriangulationPrecision shall be >= 3, if not omitted.

If an evaluator does not support the parameters FullPrecision and TriangulationPrecision, FullPrecision should be assumed to be false.

Semantics: Returns the given money value of a conversion from From currency into To currency. Both From and To shall be the official ISO 4217 abbreviation for the given currency; note that these are in upper case, but the function accepts lower case or mixed case as well. If From and To are equal currencies, the value N is returned, no precision or triangualation is applied.

The function shall use the rates of exchange as set by the European Commission, as follows:

Table 29 - EUROCONVERT

From

To

Rate

Currency

Decimals

"EUR"

"ATS"

13.7603

Austrian Schilling

2

"EUR"

"BEF"

40.3399

Belgian Franc

0

"EUR"

"DEM"

1.95583

German Mark

2

"EUR"

"ESP"

166.386

Spanish Peseta

0

"EUR"

"FIM"

5.94573

Finnish Markka

2

"EUR"

"FRF"

6.55957

French Franc

2

"EUR"

"IEP"

0.787564

Irish Pound

2

"EUR"

"ITL"

1936.27

Italian Lira

0

"EUR"

"LUF"

40.3399

Luxembourg Franc

0

"EUR"

"NLG"

2.20371

Dutch Guilder

2

"EUR"

"PTE"

200.482

Portuguese Escudo

2

"EUR"

"GRD"

340.750

Greek Drachma

2

"EUR"

"SIT"

239.640

Slovenian Tolar

2

“EUR”

“MTL”

0.429300

Maltese Lira

2

“EUR”

“CYP”

0.585274

Cypriot Pound

2

"EUR"

"SKK"

30.1260

Slovak Koruna

2

As new member countries adopt the Euro, new conversion rates will become active and evaluators may add them using the respective ISO 4217 codes and fixed rates as defined by the European Council, on the basis of a European Commission proposal.

Note:
The European Commission's Euro entry page is
http://ec.europa.eu/euro/
The conversion rates and triangulation rules are available at http://ec.europa.eu/economy_finance/euro/adoption/conversion/index_en.htm with links to the European Council Regulation legal documents at the http://eur-lex.europa.eu/ European Union law database server.

If FullPrecision is omitted or False, the result is rounded according to the decimals of the To currency. If FullPrecision is True the result is not rounded.

If TriangulationPrecision is given and >=3, the intermediate result of a triangular conversion (currency1,EUR,currency2) is rounded to that precision. If TriangulationPrecision is omitted, the intermediate result is not rounded. Also if To currency is “EUR”, TriangulationPrecision precision is used as if triangulation was needed and conversion from EUR to EUR was applied.

See also CONVERT

6.16.30EVEN

Summary: Rounds a number up to the nearest even integer. Rounding is away from zero.

Syntax: EVEN( Number N )

Returns: Number

Constraints: None

Semantics: Returns the even integer whose sign is the same as N's and whose absolute value is greater than or equal to the absolute value of N.

See also ODD 6.16.44

6.16.31EXP

Summary: Returns e raised by the given number.

Syntax: EXP( Number X )

Returns: Number

Constraints: None

Semantics: Computes

 

See also LOG 6.16.40, LN 6.16.39

6.16.32FACT

Summary: Return factorial (!).

Syntax: FACT( Integer F )

Returns: Number

Constraints: F >= 0

Semantics: Return the factorial

 

F(0)=F(1)=1.

See also Infix Operator "*" 6.4.4, GAMMA 6.16.34

6.16.33FACTDOUBLE

Summary: Returns double factorial (!!).

Syntax: FACTDOUBLE( Integer F )

Returns: Number

Constraints: F >= 0

Semantics: Return

 

Double factorial is computed by multiplying every other number in the 1..N range, with N always being included.

See also Infix Operator "*" 6.4.4, GAMMA 6.16.34, FACT 6.16.32

6.16.34GAMMA

Summary: Return gamma function value.

Syntax: GAMMA( Number N )

Returns: Number

Constraints: N<>0 and N not a negative integer.

Semantics: Return

 

with Γ(N+1) = N * Γ(N). Note that for non-negative integers N, Γ(N+1) = N! = FACT(N). Note that GAMMA can accept non-integers.

See also FACT 6.16.32

6.16.35GAMMALN

Summary: Returns the natural logarithm of the GAMMA function.

Syntax: GAMMALN( Number X )

Returns: Number

Constraints: For each X, X > 0

Semantics: Returns the same value as =LN(GAMMA(X))

See also GAMMA 6.16.34, FACT 6.16.32

6.16.36GCD

Summary: Returns the greatest common divisor (GCD)

Syntax: GCD( { NumberSequenceList X }+ )

Returns: Number

Constraints: For all a in X: INT(a) >= 0 and for at least one a in X: INT(a)>0

Semantics: Return the largest integer N such that for every a in X: INT(a) is a multiple of N.

Note: If for all a in X: INT(a)=0 the return value is implementation-defined but is either an Error or 0.

See also LCM 6.16.38

6.16.37GESTEP

Summary: Returns 1 if a number is greater than or equal to another number, else returns 0.

Syntax: GESTEP( Number X [ ; Number Step = 0 ] )

Returns: Number

Semantics: Number X is tested against number Step. If greater or equal 1 is returned, else 0. The second parameter is assumed 0 if omitted. If one of the parameters is not a Number, the function results in an Error.

See also

6.16.38LCM

Summary: Returns the least common multiplier

Syntax: LCM( { NumberSequenceList X }+ )

Returns: Number

Constraints: For all in X: INT(X)=X, X >= 0

Semantics: Return the smallest integer that is the multiple of the given values. Each value has INT applied to it first. Note that if given two numbers, ABS(a*b)=LCM(a;b)*GCD(a;b).

See also GCD 6.16.36

6.16.39LN

Summary: Return the natural logarithm of a number.

Syntax: LN( Number X )

Returns: Number

Constraints: X>0

Semantics: Computes the natural logarithm (base e) of the given number.

 

See also LOG 6.16.40, LOG10 6.16.41, POWER 6.16.46, EXP 6.16.31

6.16.40LOG

Summary: Return the logarithm of a number in a specified base.

Syntax: LOG( Number N [ ; Number Base = 10 ] )

Returns: Number

Constraints: N > 0

Semantics: Computes the logarithm of a number in the specified base. Note that if the base is not specified, the logarithm base 10 is returned.

See also LOG10 6.16.41, LN 6.16.39, POWER 6.16.46, EXP 6.16.31

6.16.41LOG10

Summary: Return the base 10 logarithm of a number.

Syntax: LOG10( Number N )

Returns: Number

Constraints: N > 0

Semantics: Computes the base 10 logarithm of a number.

See also LOG 6.16.40, LN 6.16.39, POWER 6.16.46, EXP 6.16.31

6.16.42MOD

Summary: Return the remainder when one number is divided by another number.

Syntax: MOD( Number a ; Number b )

Returns: Number

Constraints: b != 0

Semantics: Computes the remainder of a/b. The remainder has the same sign as b.

See also Infix Operator "/" 6.4.5, QUOTIENT 6.16.48

6.16.43MULTINOMIAL

Summary: Returns the multinomial for the given values.

Syntax: MULTINOMIAL( { NumberSequence A }+ )

Returns: Number

Constraints: None

Semantics: Returns the multinomial of the sequence A = (a1, a2, ..., an). Multinomial is defined as FACT(a1+a2+...+an) / (FACT(a1)*FACT(a2)*...*FACT(an))

See also FACT 6.16.32

6.16.44ODD

Summary: Rounds a number up to the nearest odd integer, where "up" means "away from 0".

Syntax: ODD( Number N )

Returns: Number

Constraints: None

Semantics: Returns the odd integer whose sign is the same as N's and whose absolute value is greater than or equal to the absolute value of N. In other words, any "rounding" is away from zero. By definition, ODD(0) is 1.

See also EVEN 6.16.30

6.16.45PI

Summary: Return the approximate value of Pi.

Syntax: PI()

Returns: Number

Constraints: None.

Semantics: This function takes no arguments and returns the (approximate) value of pi. Evaluators should use the closest possible numerical representation that is possible in their representation of numbers.

See also SIN 6.16.55, COS 6.16.19

6.16.46POWER

Summary: Return the value of one number raised to the power of another number.

Syntax: POWER( Number a ; Number b )

Returns: Number

Constraints: None

Semantics: Computes a raised to the power b.

See also LOG 6.16.40, LOG10 6.16.41, LN 6.16.39, EXP 6.16.31

6.16.47PRODUCT

Summary: Multiply the set of numbers, including all numbers inside ranges

Syntax: PRODUCT( { NumberSequence N }+ )

Returns: Number

Constraints: None

Semantics: Returns the product of the Numbers (and only the Numbers, i.e., not Text inside ranges). This is equivalent to SUM except that it uses the * operator instead of +.

See also SUM 6.16.61

6.16.48QUOTIENT

Summary: Return the integer portion of a division.

Syntax: QUOTIENT( Number A ; Number B )

Returns: Number

Constraints: B <> 0

Semantics: Return the integer portion of a division.

See also MOD 6.16.42

6.16.49RADIANS

Summary: Convert degrees to radians.

Syntax: RADIANS( Number N )

Returns: Number

Constraints: None

Semantics: Converts a number in degrees into a number in radians. RADIANS(N) is equal to N*PI()/180.

See also DEGREES 6.16.25, PI 6.16.45

6.16.50RAND

Summary: Return a random number between 0 (inclusive) and 1 (exclusive).

Syntax: RAND()

Returns: Number

Semantics: This function takes no arguments and returns a random number between 0 (inclusive) and 1 (exclusive). Note that unlike most functions, this function will typically return different values when called each time with the same (empty set of) parameters.

See also RANDBETWEEN 6.16.51

6.16.51RANDBETWEEN

Summary: Return a random integer number between A and B.

Syntax: RANDBETWEEN( Integer A ; Integer B )

Returns: Integer

Constraints: A <= B

Semantics: The function returns a random integer number between A and B inclusive. Note that unlike most functions, this function will often return different values when called each time with the same parameters.

See also RAND 6.16.50

6.16.52SEC

Summary: Return the secant of an angle specified in radians.

Syntax: SEC( Number N )

Returns: Number

Constraints: None

Semantics: Computes the secant cosine of an angle specified in radians. Equivalent to:

1/COS(N)

See also SIN 6.16.55

6.16.53SERIESSUM

Summary: Returns the sum of a power series.

Syntax: SERIESSUM( Number X ; Number N ; Number M ; Array Coefficients )

Returns: Number

Constraints:

All elements of Coefficients are of type Number.

X < > 0 if any of the exponents, which are generated from N and M, are negative.

Semantics: Returns a sum of powers of the number X.

With C being the number of coefficients the function is computed as:

 
If X=0 and all of the exponents are non-negative then
shall be set to 1 and
shall be set to 0.
 

6.16.54SIGN

Summary: Return the sign of a number

Syntax: SIGN( Number N )

Returns: Number

Constraints: None

Semantics: If N < 0, returns -1; if N > 0, returns +1; if N == 0, returns 0.

See also ABS 6.16.2

6.16.55SIN

Summary: Return the sine of an angle specified in radians

Syntax: SIN( Number N )

Returns: Number

Constraints: None

Semantics: Computes the sine of an angle specified in radians.

 

See also ASIN 6.16.7, RADIANS 6.16.49, DEGREES 6.16.25

6.16.56SINH

Summary: Return the hyperbolic sine of the given hyperbolic angle

Syntax: SINH( Number N )

Returns: Number

Constraints: None

Semantics: Computes the hyperbolic sine of a hyperbolic angle. The hyperbolic sine is an analog of the ordinary (circular) sine. The points (cosh t, sinh t) define the right half of the equilateral hyperbola, just as the points (cos t, sin t) define the points of a circle.

 

See also ASINH 6.16.8, COSH 6.16.20, TANH 6.16.70

6.16.57SECH

Summary: Return the hyperbolic secant of the given angle specified in radians

Syntax: SECH( Number N )

Returns: Number

Constraints: None

Semantics: Computes the hyperbolic secant of a hyperbolic angle. This is equivalent to:

1/COSH(N)

See also SINH 6.16.56, CSCH

6.16.58SQRT

Summary: Return the square root of a number

Syntax: SQRT( Number N )

Returns: Number

Constraints: N>=0

Semantics: Returns the square root of a non-negative number. This function shall produce an Error if given a negative number; for producing complex numbers, see IMSQRT.

See also POWER 6.16.46, IMSQRT 6.8.22, SQRTPI 6.16.59

6.16.59SQRTPI

Summary: Return the square root of a number multiplied by pi.

Syntax: SQRTPI( Number N )

Returns: Number

Constraints: N>=0

Semantics: Returns the square root of a non-negative number after it was first multiplied by PI, that is, SQRT(N*PI()). This function shall produce an Error if given a negative number; for producing complex numbers, see IMSQRT.

See also POWER 6.16.46, SQRT 6.16.58, PI 6.16.45, IMSQRT 6.8.22

6.16.60SUBTOTAL

Summary: Evaluates a function on a range.

Syntax: SUBTOTAL( Integer function ; NumberSequence sequence )

Returns: Number

Constraints: None

Semantics: Computes a given function on a number sequence. Function is denoted by the first parameter: The difference from standard functions is that all members of the sequence are excluded which:

Function

Exclude hidden by filter

Exclude hidden by filter or collapsed

AVERAGE

1

101

COUNT

2

102

COUNTA

3

103

MAX

4

104

MIN

5

105

PRODUCT

6

106

STDEV

7

107

STDEVP

8

108

SUM

9

109

VAR

10

110

VARP

11

111

See also SUM 6.16.61, AVERAGE 6.18.3

6.16.61SUM

Summary: Sum (add) the set of numbers, including all numbers in ranges

Syntax: SUM( { NumberSequenceList N }+ )

Returns: Number

Constraints: N != {}; Evaluators may evaluate expressions that do not meet this constraint.

Semantics: Adds Numbers (and only Numbers) together (see the text on conversions).

See also AVERAGE 6.18.3

6.16.62SUMIF

Summary: Sum the values of cells in a range that meet a criteria.

Syntax: SUMIF( ReferenceList|Reference R ; Criterion C [ ; Reference S ] )

Returns: Number

Constraints: Does not accept constant values as the range parameter.

Semantics: Sums the values of type Number in the range R or S that meet the Criterion C (4.11.7).

If S is not given, R may be a reference list. If S is given, R shall not be a reference list with more than 1 references and an Error be generated if it was.

If the optional range S is included, then the values of S starting from the top left cell and matching the geometry of R (same number of rows and columns) are summed if the corresponding value in R meets the Criterion. The actual range S is not considered. If the resulting range exceeds the sheet bounds, column numbers larger than the maximum column and row numbers larger than the maximum row are silently ignored, no Error is generated for this case.

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also COUNTIF 6.13.9, SUM 6.16.61, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9

6.16.63SUMIFS

Summary: Sum the values of cells in a range that meet multiple criteria in multiple ranges.

Syntax: SUMIFS( Reference R ; Reference R1 ; Criterion C1 [ ; Reference R2 ; Any C2 ]... )

Returns: Number

Constraints: Does not accept constant values as the reference parameter.

Semantics: Sums the value of cells in range R that meet the Criterion C1 in the reference range R1 and the Criterion C2 in the reference range R2, and so on (4.11.7). All reference ranges shall have the same dimension and size, else an Error is returned. A logical AND is applied between each array result of each selection; an entry is counted only if the same position in each array is the result of a criteria match.

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also COUNTIFS 6.13.10, SUMIF 6.16.62, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9

6.16.64SUMPRODUCT

Summary: Returns the sum of the products of the matrix elements.

Syntax: SUMPRODUCT( { ForceArray Array A }+ )

Returns: Number

Constraints: All matrices shall have the same dimensions.

Semantics: Multiplies the corresponding elements of all matrices and returns the sum of them.

 
where
denotes an element of the matrix
.
 

6.16.65SUMSQ

Summary: Sum (add) the set of squares of numbers, including all numbers in ranges

Syntax: SUMSQ( { NumberSequence N }+ )

Returns: Number

Constraints: N != {}; Evaluators may evaluate expressions that do not meet this constraint.

Semantics: Adds squares of Numbers (and only Numbers) together. See the text on conversions.

6.16.66SUMX2MY2

Summary: Returns the sum of the difference between the squares of the matrices A and B.

Syntax: SUMX2MY2( ForceArray Array A ; ForceArray Array B )

Returns: Number

Constraints: Both matrices shall have the same dimensions.

Semantics: Sums up the differences of the corresponding elements squares for two matrices.

 

6.16.67SUMX2PY2

Summary: Returns the total sum of the squares of the matrices A and B.

Syntax: SUMX2PY2( ForceArray Array A ; ForceArray Array B )

Returns: Number

Constraints: Both matrices shall have the same dimensions.

Semantics: Sums up the squares of each element of the two matrices.

 

6.16.68SUMXMY2

Summary: Returns the sum of the squares of the differences between matrix A and B.

Syntax: SUMXMY2( ForceArray Array A ; ForceArray Array B )

Returns: Number

Constraints: Both matrices shall have the same dimensions.

Semantics: Sums up the squares of the differences of the corresponding elements for two matrices.

 

6.16.69TAN

Summary: Return the tangent of an angle specified in radians

Syntax: TAN( Number N )

Returns: Number

Constraints: None

Semantics: Computes the tangent of an angle specified in radians.

TAN(x) = SIN(x) / COS(x)

See also ATAN 6.16.9, ATAN2 6.16.10, RADIANS 6.16.49, DEGREES 6.16.25, SIN 6.16.55, COS 6.16.19, COT 6.16.21

6.16.70TANH

Summary: Return the hyperbolic tangent of the given hyperbolic angle

Syntax: TANH( Number N )

Returns: Number

Constraints: None

Semantics: Computes the hyperbolic tangent of a hyperbolic angle. The hyperbolic tangent is an analog of the ordinary (circular) tangent. The points (cosh t, sinh t) define the right half of the equilateral hyperbola, just as the points (cos t, sin t) define the points of a circle.

 

See also ATANH 6.16.11, SINH 6.16.56, COSH 6.16.20, FISHERINV 6.18.27

6.17Rounding Functions

6.17.1General

Rounding functions convert an arbitrary Number into an Integer.

 

6.17.2CEILING

Summary: Round a number N up to the nearest multiple of the second parameter, significance.

Syntax: CEILING( Number N [ ; [ Number significance ] [ ; Number mode ] ] )

Returns: Number

Constraints: Both N and significance shall be numeric and have the same sign if not 0.

Semantics: Rounds a number up to a multiple of the second number. If significance is omitted or an empty parameter (two consecutive ;; semicolons) it is assumed to be -1 if N is negative and +1 if N is non-negative, making the function act like the normal mathematical ceiling function if mode is not given or zero. If mode is given and not equal to zero, the amount of N is rounded away from zero to a multiple of significance and then the sign applied. If mode is omitted or zero, rounding is toward positive infinity; the number is rounded to the smallest multiple of significance that is equal-to or greater than N. If any of the two parameters N or significance is zero, the result is zero.

Note: Many application user interfaces have a CEILING function with only two parameters, and somewhat different semantics than given here (e.g., they operate as if there was a non-zero mode value). These CEILING functions are inconsistent with the standard mathematical definition of CEILING.

See also FLOOR 6.17.4, INT 6.17.3

6.17.3INT

Summary: Rounds a number down to the nearest integer.

Syntax: INT( Number N )

Returns: Number

Constraints: None

Semantics: Returns the nearest integer whose value is less than or equal to N. Rounding is towards negative infinity.

See also ROUND 6.17.6, TRUNC 6.17.9

6.17.4FLOOR

Summary: Round a number N down to the nearest multiple of the second parameter, significance.

Syntax: FLOOR( Number N [ ; [ Number significance ] [ ; Number mode ] ] )

Returns: Number

Constraints: Both N and significance shall be numeric and have the same sign.

Semantics: Rounds a number down to a multiple of the second number. If significance is omitted or an empty parameter (two consecutive ;; semicolons) it is assumed to be -1 if N is negative and +1 if N is non-negative, making the function act like the normal mathematical floor function if mode is not given or zero. If mode is given and not equal to zero, the amount of N is rounded toward zero to a multiple of significance and then the sign applied. Otherwise, it rounds toward negative infinity, and the result is the largest multiple of significance that is less than or equal to N. If any of the two parameters N or significance is zero, the result is zero.

Note: Many application user interfaces have a FLOOR function with only two parameters, and somewhat different semantics than given here (e.g., they operate as if there was a non-zero mode value). These FLOOR functions are inconsistent with the standard mathematical definition of FLOOR.

See also CEILING 6.17.2, INT 6.17.3

6.17.5MROUND

Summary: Rounds the number to given multiple.

Syntax: MROUND( Number a ; Number b )

Returns: Number

Constraints: None

Semantics: Returns the number X, for which the following holds: X/b=INT(X/b) (b divides X), and for any other Y with the same property, ABS(Y-a)>=ABS(X-a). In case that two such X exist, the greater one is the result. In less formal language, this function rounds the number a to multiples of b.

See also ROUND 6.17.6

6.17.6ROUND

Summary: Rounds the value X to the nearest multiple of the power of 10 specified by Digits.

Syntax: ROUND( Number X [ ; Number Digits = 0 ] )

Returns: Number

Constraints: None

Semantics: Round number X to the precision specified by Digits. The number X is rounded to the nearest power of 10 given by 10Digits. If Digits is zero, or absent, round to the nearest decimal integer. If Digits is non-negative, round to the specified number of decimal places. If Digits is negative, round to the left of the decimal point by -Digits places. If X is halfway between the two nearest values, the result shall round away from zero. Note that if X is a Number, and Digits <= 0, the results will always be an integer (without a fractional component).

See also TRUNC 6.17.9, INT 6.17.3

6.17.7ROUNDDOWN

Summary: Rounds the value X towards zero to the number of digits specified by Digits

Syntax: ROUNDDOWN( Number X [ ; Integer Digits = 0 ] )

Returns: Number

Constraints: None

Semantics: Round X towards zero, to the precision specified by Digits. The number returned is a multiple of 10−Digits. If Digits is zero, or absent, round to the largest decimal integer smaller or equal to X. If Digits is positive, round towards zero to the specified number of decimal places. If Digits is negative, round towards zero to the left of the decimal point by -Digits places.

See also TRUNC 6.17.9, INT 6.17.3, ROUND 6.17.6, ROUNDUP 6.17.8

6.17.8ROUNDUP

Summary: Rounds the value X away from zero to the number of digits specified by Digits

Syntax: ROUNDUP( Number X [ ; Integer Digits = 0 ] )

Returns: Number

Constraints: None

Semantics: Round X away from zero, to the precision specified by Digits. The number returned is a multiple of 10−Digits. If Digits is zero, or absent, round to the smallest decimal integer larger or equal to X. If Digits is positive, round away from zero to the specified number of decimal places. If Digits is negative, round away from zero to the left of the decimal point by -Digits places.

See also TRUNC 6.17.9, INT 6.17.3, ROUND 6.17.6, ROUNDDOWN 6.17.7

6.17.9TRUNC

Summary: Truncate a number to a specified number of digits.

Syntax: TRUNC( Number a ; Number b )

Returns: Number

Constraints: None

Semantics: Truncate number a to the number of digits specified by b. If b is zero, or absent, truncate to a decimal integer. If b is positive, truncate to the specified number of decimal places. If b is negative, truncate to the left of the decimal point. If b is not an integer, it is truncated.

See also ROUND 6.17.6, INT 6.17.3

6.18Statistical Functions

6.18.1General

The following are statistical functions (functions that report information on a set of numbers). Some functions that could also be considered statistical functions, such as SUM, are listed elsewhere.

6.18.2AVEDEV

Summary: Calculates the average of the absolute deviations of the values in list.

Syntax: AVEDEV( { NumberSequenceList N }+ )

Returns: Number

Constraints: None.

Semantics:

 

See also SUM, AVERAGE

6.18.3AVERAGE

Summary: Average the set of numbers

Syntax: AVERAGE( { NumberSequence N }+ )

Returns: Number

Constraints: At least one Number included. Returns an Error if no Numbers provided.

Semantics: Computes SUM(List) / COUNT(List).

See also SUM 6.16.61, COUNT 6.13.6

6.18.4AVERAGEA

Summary: Average values, including values of type Text and Logical.

Syntax: AVERAGEA( { Any N }+ )

Returns: Number

Constraints: At least one value included. Returns an Error if no value provided.

Semantics: A variant of the AVERAGE function that includes values of type Text and Logical. Text values are treated as number 0. Logical True is treated as 1 and False is treated as 0. Empty cells are not included. Any N may be of type ReferenceList.

See also AVERAGE 6.18.3

6.18.5AVERAGEIF

Summary: Average the values of cells in a range that meet a criteria.

Syntax: AVERAGEIF( Reference R ; Criterion C [ ; Reference A ] )

Returns: Number

Constraints: Does not accept constant values as reference parameters.

Semantics: If reference A is omitted, averages the values of cells in the reference range R that meet the Criterion C (4.11.7). If reference A is given, averages the values of cells of a range that is constructed using the top left cell of reference A and applying the dimensions, shape and size, of reference R. If no cell in range R matches the Criterion C, an Error is returned. If no Numbers are in the range to be averaged, an Error is returned.

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also AVERAGEIFS 6.18.6, COUNTIF 6.13.9, SUMIF 6.16.62, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9

6.18.6AVERAGEIFS

Summary: Average the values of cells that meet multiple criteria in multiple ranges.

Syntax: AVERAGEIFS( Reference A ; Reference R1 ; Criterion C1 [ ; Reference R2 ; Criterion C2 ]... )

Returns: Number

Constraints: Does not accept constant values as reference parameters.

Semantics: Averages the values of cells in the reference range A that meet the Criterion C1 in the reference range R1 and the Criterion C2 in the reference range R2, and so on (4.11.7). All reference ranges shall have the same dimension and size, else an Error is returned. A logical AND is applied between each array result of each selection; a cell of reference range A is evaluated only if the same position in each array is the result of a Criterion match. If no numbers are in the result set to be averaged, an Error is returned.

The values returned may vary depending upon the HOST-USE-REGULAR-EXPRESSIONS or HOST-USE-WILDCARDS properties. 3.4

See also AVERAGEIF 6.18.5, COUNTIFS 6.13.10, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9

6.18.7BETADIST

Summary: returns the value of the probability density function or the cumulative distribution function for the beta distribution.

Syntax: BETADIST( Number x ; Number a ; Number b [ ; Number a = 0 [ ; Number b = 1 [ ; Logical Cumulative = TRUE() ] ] ] )

Returns: Number

Constraints: a > 0, b > 0, a < b,
If a < 1, then the density function has a pole at x = a.
If b < 1, then the density function has a pole at x = b.
In both cases, if x=a respectively x=b and Cumulative=FALSE(), an Error is returned.

Semantics: If Cumulative is FALSE(), BETADIST returns 0 if x < a or x > b and the value

 

otherwise.

If Cumulative is TRUE(), BETADIST returns 0 if x < a, 1 if x > b, and the value

 

otherwise.

Note: With substitution

 

the term can be written as

 

See also BETAINV 6.18.8

6.18.8BETAINV

Summary: returns the inverse of BETADIST(x;a;b;a;b;TRUE()).

Syntax: BETAINV( Number p ; Number a ; Number b [ ; Number a = 0 [ ; Number b = 1 ] ] )

Returns: Number

Constraints:
, a > 0, b > 0, a < b
 

Semantics: BETAINV returns the unique number x in the closed interval from a to b such that BETADIST(x;a;b;a;b) = p.

See also BETADIST 6.18.7

6.18.9BINOM.DIST.RANGE

Summary: Returns the probability of a trial result using binomial distribution.

Syntax: BINOM.DIST.RANGE( Integer N ; Number P ; Integer S [ ; Integer S2 ] )

Returns: Number

Constraints: 0<=P<=1, 0<=S<=S2<=N

Semantics: Let N be a total number of independent trials, and P be a probability of success for each trial. This function returns the probability that the number of successful trials shall be exactly S. If the optional parameter S2 is provided, this function returns the probability that the number of successful trials shall lie between S and S2 inclusive.

This function is computed as follows:

If S2 is not given, let S2:=S. Then the function returns the value of

 

See also BINOMDIST 6.18.10

Note: This describes how the function works in OOo. KSpread has a similar function, called BINO, which takes the arguments in a different order, and doesn't have the 4th argument. Gnumeric doesn't have this function. Excel doesn't have this function.

6.18.10BINOMDIST

Summary: Returns the binomial distribution.

Syntax: BINOMDIST( Integer S ; Integer N ; Number P ; Logical Cumulative )

Returns: Number

Constraints: 0 <= P <= 1; 0 <= S <= N

Semantics: If Cumulative is FALSE(), this function returns the same result as BINOM.DIST.RANGE(N;P;S). If Cumulative is TRUE(), it is equivalent to calling BINOM.DIST.RANGE(N;P;0;S).

See also BINOM.DIST.RANGE 6.18.9

6.18.11LEGACY.CHIDIST

Summary: returns the right-tail probability for the c2-distribution.

Syntax: LEGACY.CHIDIST( Number x ; Number DegreesOfFreedom )

Returns: Number

Constraints: DegreesOfFreedom is a positive integer.

Semantics: In the following n is DegreesOfFreedom. LEGACY.CHIDIST returns 1 for
and the value
 
 
for
.
 

See also CHISQDIST 6.18.12, LEGACY.CHITEST 6.18.15

6.18.12CHISQDIST

Summary: returns the value of the probability density function or the cumulative distribution function for the c2-distribution.

Syntax: CHISQDIST( Number x ; Number DegreesOfFreedom [ ; Logical Cumulative = TRUE() ] )

Returns: Number

Constraints: DegreesOfFreedom is a positive integer.

Semantics: In the following n is DegreesOfFreedom.

If Cumulative is FALSE(), CHISQDIST returns 0 for
and the value
 
 
for
.
 
If Cumulative is TRUE(), CHISQDIST returns 0 for
and the value
 
 
for
.
 

See also LEGACY.CHIDIST 6.18.11

6.18.13LEGACY.CHIINV

Summary: returns the inverse of LEGACY.CHIDIST(x; DegreesOfFreedom).

Syntax: LEGACY.CHIINV( Number p ; Number DegreesOfFreedom )

Returns: Number

Constraints: DegreesOfFreedom is a positive integer and
.
 

Semantics: LEGACY.CHIINV returns the unique number x such that LEGACY.CHIDIST(x; DegreesOfFreedom) = p.

See also LEGACY.CHIDIST 6.18.11

6.18.14CHISQINV

Summary: returns the inverse of CHISQDIST(x; DegreesOfFreedom; TRUE()).

Syntax: CHISQINV( Number p ; Number DegreesOfFreedom )

Returns: Number

Constraints: DegreesOfFreedom is a positive integer and
.
 
Semantics: CHISQINV returns the unique number
such that CHISQDIST(x; DegreesOfFreedom;TRUE()) = p.
 

See also CHISQDIST 6.18.12

6.18.15LEGACY.CHITEST

Summary: Returns some Chi square goodness-for-fit test.

Syntax: LEGACY.CHITEST( ForceArray Array A ; ForceArray Array E )

Returns: Number

Constraints:
ROWS(A) == ROWS(E)
COLUMNS(A) == COLUMNS(E)
COLUMNS(A) * ROWS(A) > 1

Semantics:

For an empty element or an element of type Text or Boolean in A the element at the corresponding position of E is ignored, and vice versa.

First a Chi square statistic is calculated:

 

Then LEGACY.CHIDIST is called with the Chi-square value and a degree of freedom (df):

 

See also LEGACY.CHIDIST 6.18.11

6.18.16CONFIDENCE

Summary: Returns the confidence interval for a population mean.

Syntax: CONFIDENCE( Number alpha ; Number stddev ; Number size )

Returns: Number

Constraints: 0 < alpha < 1; stddev > 0, size >= 1

Semantics: Calling this function is equivalent to calling NORMINV(1 - alpha / 2; 0; 1) * stddev / SQRT (size)

6.18.17CORREL

Summary: Calculates the correlation coefficient of values in N1 and N2.

Syntax: CORREL( ForceArray Array N1 ; ForceArray Array N2 )

Returns: Number

Constraints: COLUMNS(N1) = COLUMNS(N2), ROWS(N1) = ROWS(N2), both sequences shall contain at least one number at corresponding positions each.

Semantics: Has the same value as COVAR(N1;N2)/STDEVP(N1)*(STDEVP(N2)). The CORREL function actually is identical to the PEARSON function.

For an empty element or an element of type Text or Boolean in N1 the element at the corresponding position of N2 is ignored, and vice versa.

See also PEARSON 6.18.56

6.18.18COVAR

Summary: Calculates covariance of two cell ranges.

Syntax: COVAR( ForceArray Array n1 ; ForceArray Array n2 )

Returns: Number

Constraints: COLUMNS(n1) = COLUMNS(n2), ROWS(n1) = ROWS(n2), both sequences shall contain at least one number at corresponding positions each.

Semantics: returns

 
where
is the result of calling AVERAGE(n1), and
is the result of calling AVERAGE(n2).
 

For an empty element or an element of type Text or Boolean in n1 the element at the corresponding position of n2 is ignored, and vice versa.

6.18.19CRITBINOM

Summary: Returns the smallest value for which the cumulative binomial distribution is greater than or equal to a criterion value.

Syntax: CRITBINOM( Number Trials ; Number SP ; Number Alpha )

Returns: Number

Constraints:  Trials >=0, 0 <= SP <= 1, Alpha >= 1

Semantics:
Trials is the total number of trials.
SP is the probability of success for one trial.
Alpha is the threshold probability to be reached or exceeded.

6.18.20DEVSQ

Summary: Calculates sum of squares of deviations.

Syntax: DEVSQ( { NumberSequence n }+ )

Returns: Number

Semantics: returns

 

where a is the result of calling AVERAGE(n).

6.18.21EXPONDIST

Summary: returns the value of the probability density function or the cumulative distribution function for the exponential distribution.

Syntax: EXPONDIST( Number x ; Number l [; Logical Cumulative = TRUE() ] )

Returns: Number

Constraints: l > 0

Semantics: If Cumulative is FALSE(), EXPONDIST returns 0 if x < 0 and the value

 

otherwise.

If Cumulative is TRUE(), EXPONDIST returns 0 if x < 0 and the value

 

otherwise.

6.18.22FDIST

Summary: returns the value of the probability density function or the cumulative distribution function for the F-distribution.

Syntax: FDIST( Number x ; Number r1 ; Number r2 [ ; Logical Cumulative = TRUE() ] )

Returns: Number

Constraints: r1 and r2 are positive integers

Semantics:

r1 is the degrees of freedom in the numerator of the F distribution.
r2 is the degrees of freedom in the denominator of the F distribution.

If Cumulative is FALSE(), FDIST returns 0 if x < 0, an Error if the numerator degrees of freedom r1 = 1 and x = 0, and the value

 

otherwise.


If the numerator degrees of freedom r1 = 1, then the density function has a pole at x=0, the subterm
is not defined.
 

If Cumulative is TRUE(), FDIST returns 0 if x < 0 and the value

 

otherwise.

See also LEGACY.FDIST 6.18.23

6.18.23LEGACY.FDIST

Summary: returns the area of the right tail of the probability density function for the F-distribution.

Syntax: LEGACY.FDIST( Number x ; Number r1 ; Number r2 )

Returns: Number

Constraints: r1 and r2 are positive integers

Semantics:

LEGACY.FDIST returns Error if x < 0 and the value

 

otherwise.

Note that the latter is (1-FDIST(x; r1; r2;TRUE())).

See also FDIST 6.18.22

6.18.24FINV

Summary: returns the inverse of FDIST(x;r1;r2;TRUE()).

Syntax: FINV( Number p ; Number r1 ; Number r2 )

Returns: Number

Constraints:
, r1 and r2 are positive integers
 

Semantics: FINV returns the unique non-negative number x such that FDIST(x;r1;r2) = p.

See also FDIST 6.18.22, LEGACY.FDIST 6.18.23, LEGACY.FINV 6.18.25

6.18.25LEGACY.FINV

Summary: returns the inverse of LEGACY.FDIST(x;r1;r2).

Syntax: LEGACY.FINV( Number p ; Number r1 ; Number r2 )

Returns: Number

Constraints:
, r1 and r2 are positive integers
 

Semantics: LEGACY.FINV returns the unique non-negative number x such that LEGACY.FDIST(x;r1;r2) = p.

See also FDIST 6.18.22, LEGACY.FDIST 6.18.23, FINV 6.18.24

6.18.26FISHER

Summary: returns the Fisher transformation.

Syntax: FISHER( Number r )

Returns: Number

Constraints: -1 < r < 1

Semantics: Returns the Fisher transformation with a sample correlation r. This function computes