This document discusses sheet-defined functions in spreadsheets as a way to define custom functions without using VBA. It describes how sheet-defined functions work, providing examples of triangle area and normal distribution functions. The document also outlines a new book on spreadsheet implementation technology that will cover sheet-defined functions in more detail. Higher-order functions and linking sheet-defined functions to Excel are briefly discussed as areas for future work.

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High-performance
sheet-defined functions
in spreadsheets
Peter Sestoft
IT University of Copenhagen
SEMS 2014-07-02
With thanks to Thomas S Iversen, Daniel Cortes, Morten Hansen,
Poul Serek, Morten Poulsen, Hui Xu, Mainul Liton, Poul Brønnum,
Tim Garbos, Kasper Videbæk, Jens Hamann, Jonas Druedahl Rask,
Simon Eikeland Timmermann

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The trouble with functions
• One cannot define functions in a spreadsheet
• To define new functions, ”experts” use VBA
• Often very poorly, witness newsgroup
microsoft.public.excel.programming
• Many (Excel) built-in functions are bad:
– Week numbers: two kinds, but not ISO standard
• Possible answers to this mess:
– ”People should not use spreadsheets”
– ”Only computer scientists should define functions”
– ”All necessary functions should be built in”
– Or: Functions within the spreadsheet metaphor
(Nuñez 2000, Peyton-Jones et al 2003)

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Problem example: Area of triangles
• Area of triangle with sides a, b, c is
SQRT(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2
Either (1) compute s in column D:
or (2) try to inline s in the area formula:
Annoying intermediate result
Horrible and error-prone

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A solution:
Sheet-defined function TRIAREA
Function
sheet
Ordinary
sheet
Input
cells
Output
cell

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How use sheet-defined functions
• Assumptions
– End-users understand spreadsheet models
– End-users do not understand VBA, C#, VB.NET, …
• Sheet-defined functions in the organization
– Models are developed in ordinary spreadsheets
– After a while functions are factored out of models
– Functions can be further developed interactively
– An organization can develop and share libraries
– Without preventing further evolution by users
• Works only if
– Sheet-defined functions are fast enough

6. Dual implementation
• Ordinary sheets, interpretive evaluation
– Frequently edited, rarely evaluated (at "recalculation")
• Function sheets, compiled evaluation
– Rarely edited, frequently evaluated (at function calls)
– Run-time code generation permits interactive editing

7. Runtime code generation
=SQRT(a1*a1+a2*a2)
ldloc 2
ldloc 2
mul
ldloc 3
ldloc 3
mul
add
call Math.Sqrt
fldl 0xfffffff0(%ebp)
fldl 0xfffffff0(%ebp)
fmulp %st,%st(1)
fldl 0xffffffe8(%ebp)
fldl 0xffffffe8(%ebp)
fmulp %st,%st(1)
faddp %st,%st(1)
fsqrt
Spreadsheet
formula
.NET
bytecode
x86 machine
code
My
compiler
JIT
compiler
Result: A very
fast, portable
spreadsheet
implementation

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New book (next month)
• Spreadsheet Implementation Technology,
MIT Press, August 2014
8
Peter Sestoft
Spreadsheet
Implementation
Technology
Basics and Extensions
Version 0.99.5 of 2014-05-10
The MIT Press
Cambridge, Massachusetts
London, England
• A standard spreadsheet
implementation
• Sheet-defined functions
• Examples
• Design choices
• Scalability and speed
• Implementation details
• Funcalc user manual

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Example function: NORMDISTCDF
• Normal distribution N(0,1) cumulative distribution function
• As accurate as Excel’s built-in NORMSDIST(z), and faster
Input cell Output cell

10. NORMDISTCDF generated code
• Approximately 118 ns/call on 2.66 GHz Intel Core 2
• VBA: 1760 ns; Excel built-in: 1140 ns; C#: 64 ns; C: 54 ns
0000 ldarg V_0 0068 ldloc.0 0198 div
0004 call ValueToDoubleOrNan 0069 call Double.IsInfinity 0199 add
0009 stloc.s V_6 006e brtrue IL_01a0 019a div
000b ldloc.s V_6 0073 ldloc.0 019b br IL_01a1
000d call Math.Abs 0074 call Double.IsNaN 01a0 ldloc.0
0012 stloc.3 0079 brtrue IL_01a0 01a1 br IL_01a7
0013 ldc.r8 -1 007e ldloc.0 01a6 ldloc.0
001c ldloc.3 007f ldc.r8 7.071 01a7 stloc.s V_5
001d mul 0088 bge IL_0144 01a9 ldloc.s V_6
001e ldloc.3 008d ldloc.s V_4 01ab stloc.0
001f mul 008f ldc.r8 220.206867912376 01ac ldloc.0
0020 ldc.r8 2 0098 ldloc.3 01ad call Double.IsInfinity
0029 div 0099 ldc.r8 221.213596169931 01b2 brtrue IL_01f3
002a call Math.Exp 00a2 ldloc.3 01b7 ldloc.0
002f stloc.s V_4 00a3 ldc.r8 112.07929149787 01b8 call Double.IsNaN
0031 ldloc.3 00ac ldloc.3 01bd brtrue IL_01f3
0032 stloc.0 00ad ldc.r8 33.912866078383 01c2 ldloc.0
0033 ldloc.0 00b6 ldloc.3 01c3 ldc.r8 0
0034 call Double.IsInfinity 00b7 ldc.r8 6.37396220353165 01cc bge IL_01dd
0039 brtrue IL_01a6 00c0 ldloc.3 01d1 ldloc.s V_5
003e ldloc.0 00c1 ldc.r8 0.700383064443688 01d3 call NumberValue.Make
003f call Double.IsNaN 00ca ldloc.3 01d8 br IL_01ee
0044 brtrue IL_01a6 00cb ldc.r8 0.035262496599891 01dd ldc.r8 1
0049 ldloc.0 00d4 mul 01e6 ldloc.s V_5
004a ldc.r8 37 00d5 add 01e8 sub
0053 ble IL_0066 00d6 mul 01e9 call NumberValue.Make
0058 ldc.r8 0 00d7 add 01ee br IL_01f9
0061 br IL_01a1 00d8 mul 01f3 ldloc.0
0066 ldloc.3 00d9 add 01f4 call NumberValue.Make
0067 stloc.0 ... 61 lines left out ... 01f9 ret
Asingle
unwrapping
WrappingWrappingWrapping

11. Examples: Calendrical functions
• Excel’s calendar functions are poor
– Wrong before 1900, no ISO week numbers,
cannot easily find first Monday of month, Easter, …
• Easy to implement as sheet-defined functions
• Example: Easter in a given year (1400 ns/call):
By MSc students Xu and
Liton, following
Dershowitz & Reingold
(3rd ed, Cambridge UP)
Input: year
Output:
Easter
fixdate
• Some other functions:
– Fixdate to/from day-month-year
– Fixdate to/from ISO week and ISO year
– Last/nth Monday (etc) before given date
– First/nth Monday (etc) after given date

12. Higher-order functions:
Sheet-defined functions as values
• New built-ins to manipulate functions
– CLOSURE(“name”, a1, …) evaluates to a closure:
a partially applied sheet-defined function
– APPLY(f, b1, …) applies a function value
• Example function “ndie”, a general n-side die
• Defining & rolling 6-sided and 20-sided dice
Input cell
Output cell

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Funsheet: Linking Excel and Funcalc
• Sheet-defined functions in Excel!
• Eikeland and Timmermann MSc, June 2014
• Via Excel DNA, an Excel-.NET bridge
• Generated code is as fast as Funcalc
• Call speed Excel -> Funcalc suffers from
general Excel slowness, 11 us/call or so
• Complete Funcalc functionality: DEFINE,
CLOSURE, APPLY, SPECIALIZE, BENCHMARK
• Prototype, so still a number of defects
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TO DO: Validation
• Improve the Excel <-> Funcalc link
• Demonstrate one application area
• Fix obvious problems
• Perform development experiments
• Perform maintenance experiments
• ...
• But experiments is not my area of expertise
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