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# Developing Formula Evaluation

## Introduction

This document is for developers wishing to contribute to the FormulaEvaluator API functionality.

When evaluating workbooks you may encounter a org.apache.poi.ss.formula.eval.NotImplementedException which indicates that a function is not (yet) supported by POI. Is there a workaround? Yes, the POI framework makes it easy to add implementation of new functions. Prior to POI-3.8 you had to checkout the source code from svn and make a custom build with your function implementation. Since POI-3.8 you can register new functions in run-time.

Currently, contribution is desired for implementing the standard MS excel functions. Place holder classes for these have been created, contributors only need to insert implementation for the individual "evaluate()" methods that do the actual evaluation.

## Overview of FormulaEvaluator

Briefly, a formula string (along with the sheet and workbook that form the context in which the formula is evaluated) is first parsed into RPN tokens using the FormulaParser class . (If you don't know what RPN tokens are, now is a good time to read this.)

### The big picture

RPN tokens are mapped to Eval classes. (Class hierarchy for the Evals is best understood if you view the class diagram in a class diagram viewer.) Depending on the type of RPN token (also called as Ptgs henceforth since that is what the FormulaParser calls the classes) a specific type of Eval wrapper is constructed to wrap the RPN token and is pushed on the stack.... UNLESS the Ptg is an OperationPtg. If it is an OperationPtg, an OperationEval instance is created for the specific type of OperationPtg. And depending on how many operands it takes, that many Evals are popped of the stack and passed in an array to the OperationEval instance's evaluate method which returns an Eval of subtype ValueEval.Thus an operation in the formula is evaluated.

Note
An Eval is of subinterface ValueEval or OperationEval. Operands are always ValueEvals, Operations are always OperationEvals.

OperationEval.evaluate(Eval[]) returns an Eval which is supposed to be of type ValueEval (actually since ValueEval is an interface, the return value is instance of one of the implementations of ValueEval). The valueEval resulting from evaluate() is pushed on the stack and the next RPN token is evaluated.... this continues till eventually there are no more RPN tokens at which point, if the formula string was correctly parsed, there should be just one Eval on the stack - which contains the result of evaluating the formula.

Of course I glossed over the details of how AreaPtg and ReferencePtg are handled a little differently, but the code should be self explanatory for that. Very briefly, the cells included in AreaPtg and RefPtg are examined and their values are populated in individual ValueEval objects which are set into the AreaEval and RefEval (ok, since AreaEval and RefEval are interfaces, the implementations of AreaEval and RefEval - but you'll figure all that out from the code)

OperationEvals for the standard operators have been implemented and tested.

## What functions are supported?

As of September 2017, POI supports about 176 built-in functions, see Appendix A for the full list. You can programmatically list supported / unsupported functions using the following helper methods:

// list of functions that POI can evaluate
Collection<String> supportedFuncs = WorkbookEvaluator.getSupportedFunctionNames();
// list of functions that are not supported by POI
Collection<String> unsupportedFuncs = WorkbookEvaluator.getNotSupportedFunctionNames();

## Two base interfaces to start your implementation

All Excel formula function classes implement either org.apache.poi.hssf.record.formula.functions.Function or org.apache.poi.hssf.record.formula.functions.FreeRefFunction interface. Function is a common interface for the functions defined in the binary Excel format (BIFF8): these are "classic" Excel functions like SUM, COUNT, LOOKUP, etc. FreeRefFunction is a common interface for the functions from the Excel Analysis Toolpack and for User-Defined Functions. In the future these two interfaces are expected be unified into one, but for now you have to start your implementation from two slightly different roots.

## Which interface to start from?

You are about to implement a function XXX and don't know which interface to start from: Function or FreeRefFunction. Use the following code to check whether your function is from the excel Analysis Toolpack:

if(AnalysisToolPack.isATPFunction(functionName)){
// the function implements org.apache.poi.hssf.record.formula.functions.Function
} else {
// the function implements org.apache.poi.hssf.record.formula.functions.FreeRefFunction
}

## Walkthrough of an "evaluate()" implementation.

Here is the fun part: lets walk through the implementation of the excel function SQRT()

AnalysisToolPack.isATPFunction("SQRTPI") returns false so the base interface is Function. There are sub-interfaces that make life easier when implementing numeric functions or functions with fixed number of arguments, 1-arg, 2-arg and 3-arg function:

- org.apache.poi.hssf.record.formula.functions.NumericFunction
- org.apache.poi.hssf.record.formula.functions.Fixed1ArgFunction
- org.apache.poi.hssf.record.formula.functions.Fixed2ArgFunction
- org.apache.poi.hssf.record.formula.functions.Fixed3ArgFunction
- org.apache.poi.hssf.record.formula.functions.Fixed4ArgFunction

Since SQRTPI takes exactly one argument we start our implementation from org.apache.poi.hssf.record.formula.functions.Fixed1ArgFunction:

Function SQRTPI = new Fixed1ArgFunction() {
public ValueEval evaluate(int srcRowIndex, int srcColumnIndex, ValueEval arg0) {
try {
// Retrieves a single value from a variety of different argument types according to standard
// Excel rules. Does not perform any type conversion.
ValueEval ve = OperandResolver.getSingleValue(arg0, srcRowIndex, srcColumnIndex);
// Applies some conversion rules if the supplied value is not already a number.
// Throws EvaluationException(#VALUE!) if the supplied parameter is not a number
double arg = OperandResolver.coerceValueToDouble(ve);
// this where all the heavy-lifting happens
double result = Math.sqrt(arg*Math.PI);
// Excel uses the error code #NUM! instead of IEEE
nity
// so when a numeric function evaluates to Double.NaN or Double.Infinity,
// be sure to translate the result to the appropriate error code
if (Double.isNaN(result) || Double.isInfinite(result)) {
throw new EvaluationException(ErrorEval.NUM_ERROR);
}
return new NumberEval(result);
} catch (EvaluationException e){
return e.getErrorEval();
}
}
}

Now when the implementation is ready we need to register it in the formula evaluator:

WorkbookEvaluator.registerFunction("SQRTPI", SQRTPI);

Voila! The formula evaluator now recognizes SQRTPI!

## Floating-point Arithmetic in Excel

Excel uses the IEEE Standard for Double Precision Floating Point numbers except two cases where it does not adhere to IEEE 754:

1. Positive/Negative Infinities: Infinities occur when you divide by 0. Excel does not support infinities, rather, it gives a #DIV/0! error in these cases.
2. Not-a-Number (NaN): NaN is used to represent invalid operations (such as infinity/infinity, infinity-infinity, or the square root of -1). NaNs allow a program to continue past an invalid operation. Excel instead immediately generates an error such as #NUM! or #DIV/0!.

Be aware of these two cases when saving results of your scientific calculations in Excel: “where are my Infinities and NaNs? They are gone!”

## Testing Framework

Automated testing of the implemented Function is easy. The source code for this is in the file: o.a.p.h.record.formula.GenericFormulaTestCase.java This class has a reference to the test xls file (not /a/ test xls, /the/ test xls :) which may need to be changed for your environment. Once you do that, in the test xls, locate the entry for the function that you have implemented and enter different tests in a cell in the FORMULA row. Then copy the "value of" the formula that you entered in the cell just below it (this is easily done in excel as: [copy the formula cell] > [go to cell below] > Edit > Paste Special > Values > "ok"). You can enter multiple such formulas and paste their values in the cell below and the test framework will automatically test if the formula evaluation matches the expected value (Again, hard to put in words, so if you will, please take time to quickly look at the code and the currently entered tests in the patch attachment "FormulaEvalTestData.xls" file).

## Appendix A

Functions supported by POI (as of September 2017)

ABS
ACOS
ACOSH
ADDRESS
AND
ASIN
ASINH
ATAN
ATAN2
ATANH
AVEDEV
AVERAGE
BIN2DEC
CEILING
CHAR
CHOOSE
CLEAN
CODE
COLUMN
COLUMNS
COMBIN
COMPLEX
CONCATENATE
COS
COSH
COUNT
COUNTA
COUNTBLANK
COUNTIF
COUNTIFS
DATE
DAY
DAYS360
DEC2BIN
DEC2HEX
DEGREES
DELTA
DEVSQ
DGET
DMIN
DOLLAR
EDATE
EOMONTH
ERROR.TYPE
EVEN
EXACT
EXP
FACT
FACTDOUBLE
FALSE
FIND
FIXED
FLOOR
FV
HEX2DEC
HLOOKUP
HOUR
HYPERLINK
IF
IFERROR
IMAGINARY
IMREAL
INDEX
INDIRECT
INT
INTERCEPT
IPMT
IRR
ISBLANK
ISERR
ISERROR
ISEVEN
ISLOGICAL
ISNA
ISNONTEXT
ISNUMBER
ISODD
ISREF
ISTEXT
LARGE
LEFT
LEN
LN
LOG
LOG10
LOOKUP
LOWER
MATCH
MAX
MAXA
MDETERM
MEDIAN
MID
MIN
MINA
MINUTE
MINVERSE
MIRR
MMULT
MOD
MODE
MONTH
MROUND
NA
NETWORKDAYS
NOT
NOW
NPER
NPV
OCT2DEC
ODD
OFFSET
OR
PERCENTILE
PI
PMT
POISSON
POWER
PPMT
PRODUCT
PROPER
PV
QUOTIENT
RADIANS
RAND
RANDBETWEEN
RANK
RATE
REPLACE
REPT
RIGHT
ROMAN
ROUND
ROUNDDOWN
ROUNDUP
ROW
ROWS
SEARCH
SECOND
SIGN
SIN
SINH
SLOPE
SMALL
SQRT
STDEV
SUBSTITUTE
SUBTOTAL
SUM
SUMIF
SUMIFS
SUMPRODUCT
SUMSQ
SUMX2MY2
SUMX2PY2
SUMXMY2
T
TAN
TANH
TEXT
TIME
TODAY
TRANSPOSE
TRIM
TRUE
TRUNC
UPPER
VALUE
VAR
VARP
VLOOKUP
WEEKDAY
WEEKNUM
WORKDAY
YEAR
YEARFRAC

by Amol Deshmukh, Yegor Kozlov