debkeepr: Analysis of Non-Decimal Currencies
debkeepr integrates non-decimal currencies that use the tripartite
system of pounds, shillings, and pence into the methodologies of Digital
Humanities and the practices of reproducible research. The package makes
it possible for historical non-decimal currencies to behave like
decimalized numeric values through the implementation of the
deb_decimal vector classes or types. These types are based on the
infrastructure provided by the vctrs
debkkeepr simplifies the process
of performing arithmetic calculations with non-decimal currencies — such
as adding £3 13s. 4d. sterling to £8 15s. 9d. sterling — and also
provides a basis for analyzing account books with thousands of
transactions recorded in non-decimal currencies. The name of the
debkeepr package derives from this latter capability of analyzing
historical account books that often used double-entry
You can install
debkeepr from GitHub with
# install.packages("remotes") remotes::install_github("jessesadler/debkeepr")
Please open an issue if you have any questions, comments, or requests.
debkeepr package uses the nomenclature of l, s, and
d to represent pounds,
shillings, and pence units in non-decimal currencies. The abbreviations
derive from the Latin terms
denarius. The libra was a
Roman measurement of weight, while the solidus and denarius were both
Roman coins. The denarius was a silver coin from the era of the
Republic, in contrast to the golden solidus that was issued in the Late
Empire. As the production of silver coins overtook that of gold by the
8th century, a solidus came to represent 12 silver denarii coins, and
240 denarii were — for a time — made from one libra or pound of silver.
The custom of counting coins in dozens (solidi) and scores of dozens
(librae) spread throughout the Carolingian Empire and became engrained
in much of Europe. However, a variety of currencies or monies of account
used other bases
for the solidus and denarius units.
debkeepr provides a consistent
manner for dealing with any set of bases within a tripartite system
bases attribute of
deb_decimal vectors and
unit attribute of
Translations of libra, solidus, and denarius units:
- English: pounds, shillings, pence
- French: livres, sols or sous, deniers
- Italian: lire, soldi, denari
- Flemish: ponden, schellingen, groten
- Dutch: guilders, stuivers, penningen
- Getting Started with debkeepr
An introduction to the
deb_decimaltypes and their use as vectors and as columns in data frames.
- Transactions in Richard Dafforne’s Journal vignette: Examples of financial and arithmetic calculations dealing with various currencies taken from the practice journal in Richard Dafforne’s Merchant’s Mirrour (1660), a 17th-century textbook for learning accounting practices.
- Analysis of Richard Dafforne’s Journal and Ledger
An analysis of the practice journal and ledger in Dafforne’s
Merchant’s Mirrour using the
dafforne_accountsdata provided in
- A PDF copy of Dafforne’s practice journal can be consulted to further investigate the practices of early modern double-entry bookkeeping.
deb_decimal types are implemented to deal with two
interrelated problems inherent in historical currencies.
- Historical currencies consist of three separate non-decimal units: pounds, shillings, and pence.
- The bases of the shillings and pence units differed by region, coinage, and era.
deb_lsd type maintains the tripartite structure of non-decimal
currencies and provides a
bases attribute to record the bases for the
shillings and pence units. The
deb_decimal type also contains a
bases attribute, as well as a
unit attribute to track which unit the
decimalized value represents (pounds, shillings, or pence). The print
methods for both types show the
bases attribute, and
vectors include the
Let’s see how this works in practice, beginning with
Note that all of the functions in
debkeepr begin with the prefix
deb_, which is short for double-entry bookkeeping.
library(debkeepr) # Create deb_lsd vectors with standard bases of 20s. 12d. lsd1 <- deb_lsd(l = 3, s = 13, d = 4) lsd2 <- deb_lsd(l = 8, s = 15, d = 9) # Combine multiple values together c(lsd1, lsd2) #> <deb_lsd> #>  3:13s:4d 8:15s:9d #> # Bases: 20s 12d
A primary reason for the creation of the
deb_lsd type is to simplify
arithmetic calculations with non-decimal currency. Doing calculations by
hand requires the use of compound unit
All implemented arithmetic calculations with
deb_lsd vectors —
-, etc. — automatically normalize the values
according to the
bases attribute. In addition, you can manually
normalize non-standard values with
# Perform arithmetic lsd1 + lsd2 #> <deb_lsd> #>  12:9s:1d #> # Bases: 20s 12d lsd2 - lsd1 #> <deb_lsd> #>  5:2s:5d #> # Bases: 20s 12d lsd2 * 2 - lsd1 #> <deb_lsd> #>  13:18s:2d #> # Bases: 20s 12d # Normalize a non-standard value to default bases deb_normalize(deb_lsd(132, 53, 35)) #> <deb_lsd> #>  134:15s:11d #> # Bases: 20s 12d
Both types allow the user to define the solidus and denarius units of values, enabling integration of currencies that do not use the standardized bases. For example, the Polish florin found in Dafforne’s practice journal used the non-standard bases of 30 gros of 18 denars.
# Create deb_lsd vector with standard bases of 20s. 12d. (lsd3 <- deb_lsd(l = c(28, 32, 54, 18), s = c(15, 8, 18, 12), d = c(8, 11, 7, 9))) #> <deb_lsd> #>  28:15s:8d 32:8s:11d 54:18s:7d 18:12s:9d #> # Bases: 20s 12d # Same numerical values as Polish florins (florins <- deb_lsd(l = c(28, 32, 54, 18), s = c(15, 8, 18, 12), d = c(8, 11, 7, 9), bases = c(30, 18))) #> <deb_lsd> #>  28:15s:8d 32:8s:11d 54:18s:7d 18:12s:9d #> # Bases: 30s 18d # Different outcome with sum due to the different bases sum(lsd3) #> <deb_lsd> #>  134:15s:11d #> # Bases: 20s 12d sum(florins) #> <deb_lsd> #>  133:24s:17d #> # Bases: 30s 18d # Vectors with different bases cannot be combined since # their relationship is unknown. Doing so results in an error. sum(lsd3, florins) #> Error: `bases` attributes must be equal to combine <deb_lsd> or <deb_decimal> vectors.
In contrast to the tripartite structure of
deb_decimal vectors represent non-decimal currencies in the more
familiar decimal form. Internally,
deb_decimal vectors are built on
double() vectors. These decimalized vectors are linked to their
non-decimal form through the
# Create deb_decimal from numeric vector (dec1 <- deb_decimal(c(5.525, 12.235, 8.45))) #> <deb_decimal> #>  5.525 12.235 8.450 #> # Unit: libra #> # Bases: 20s 12d # Same currency values in solidus unit (dec2 <- deb_decimal(c(110.5, 244.7, 169), unit = "s")) #> <deb_decimal> #>  110.5 244.7 169.0 #> # Unit: solidus #> # Bases: 20s 12d # Equality between different units dec1 == dec2 #>  TRUE TRUE TRUE # Equality between deb_lsd and deb_decimal vectors # £5 10s. 6d. is equal to 1,326 pence deb_lsd(5, 10, 6) == deb_decimal(1326, unit = "d") #>  TRUE
When working with decimalized data is preferable, the
makes casting from and to
deb_lsd possible without losing any metadata
bases and therefore the actual value being represented.
deb_decimal vectors can also be combined with numeric
vectors or cast from and to numeric vectors.
debkeepr uses an internal
# Combining deb_lsd and deb_decimal gives a deb_lsd vector c(dec1, lsd1, lsd2) #> <deb_lsd> #>  5:10s:6d 12:4s:8.4d 8:9s:0d 3:13s:4d 8:15s:9d #> # Bases: 20s 12d c(dec1, lsd1, 8.25) #> <deb_lsd> #>  5:10s:6d 12:4s:8.4d 8:9s:0d 3:13s:4d 8:5s:0d #> # Bases: 20s 12d # Cast between deb_lsd and deb_decimal vectors deb_as_lsd(dec1) #> <deb_lsd> #>  5:10s:6d 12:4s:8.4d 8:9s:0d #> # Bases: 20s 12d deb_as_decimal(lsd3) #> <deb_decimal> #>  28.78333 32.44583 54.92917 18.63750 #> # Unit: libra #> # Bases: 20s 12d deb_as_decimal(florins) #> <deb_decimal> #>  28.51481 32.28704 54.61296 18.41667 #> # Unit: libra #> # Bases: 30s 18d # Represented by solidus/shillings unit deb_as_decimal(lsd3, unit = "s") #> <deb_decimal> #>  575.6667 648.9167 1098.5833 372.7500 #> # Unit: solidus #> # Bases: 20s 12d # Represented by denarius/pence unit deb_as_decimal(lsd3, unit = "d") #> <deb_decimal> #>  6908 7787 13183 4473 #> # Unit: denarius #> # Bases: 20s 12d # Either type can be cast to base numeric, which, # of course, leads to the loss of all metadata as.numeric(lsd3) #>  28.78333 32.44583 54.92917 18.63750 as.numeric(dec1) #>  5.525 12.235 8.450
See the Getting Started with debkeepr vignette for an in depth discussion of the similarities and differences between the two types.
deb_lsdtype has the advantage of maintaining the structure and values used by non-decimal currencies, making it easier to identify and present such values.
deb_decimalimplements a wider array of mathematical functions and arithmetic operations than
- You can move between the two types without losing any data through
deb_decimalare based on the vctrs package, both types act as expected in data frames or tibbles columns. From dplyr 1.0.0 — which is the minimal version used by debkeepr — all dplyr functions work on both
- ggplot2 does not know how to pick a
deb_lsdvectors. In contrast,
deb_decimalvectors work properly with
ggplot2, though explicitly identifying the scale as continuous — with
scale_x_continuous()— is needed to avoid the appearance of a message.
deb_decimalvectors cannot be combined in a single function if their
basesdiffer. The only way to transform the bases of
deb_decimalvectors is explicitly with
deb_convert_bases(). This prevents mistakenly combining two different currencies together without properly converting their values.