Unit conversion

for Fun and Profit

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Public Unlimited Release

Why is this hard?

What do the following mean?

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Why is this hard?

What potential issues can you spot?

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Wall of Fail: Why we are rolling our own library

• udunits2
• "5 kg^1.5" parses as (5 kg^1) × (5) … and more.
• llnl units
• confusing parsing like udunits2, plus bit-vector math.
• boost::units
• compile-time type safety, but you must create a wrapper object for each unit you want to support at run time.
• pint
• Adds a dependency on python to core library; GIL issues.

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Mission statement

• SMTK needs a reliable method to ensure simulation input parameters have consistent units.
• Workflow designers specify units the simulation requires.
• Engineers specify values in convenient units.
• Conversion occurs when writing a simulation input deck.
• Engineers need a way to "check the work" of the unit library.

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What are units?

A dimension is a characteristic that can be quantified. Examples: length (L), mass (M), time (T).

A unit is a set of scales that lie along one or more dimensions. Examples: meter, Newton, Joule, Watt.

A measurement is a value that quantifies a characteristic on a particular scale (i.e., a unit plus a number).�Examples: 5 m, 12 in, 13.7 N

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What are units?

A prefix is a numeric base and exponent used to adjust a unit's scale for convenience.�Examples: milli- = 10^-3, kilo- = 10⁺³, kibi- = 2⁺¹⁰.

A conversion is an invertible transform that can be applied to a measurement.�Examples: 1 ft = 12 in, 1 N = 1 kg m s^-2, 1 N = 1 J / m

A unit system is a set of prefixes, dimensions, and units.

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What are units?

Conversions never change the dimension or character of something being measured; they change the scale(s) used to quantify the characteristic.

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Thus, we will never attempt to convert a measurement to units with a different underlying dimension.

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Why is this hard? part deux!

Testing whether units can be converted is easy... but how do we compute conversions?

We apply transforms to scales, but how do we choose which transforms to apply?

To convert lbf to N, we may need to apply:

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Why is this hard? part deux!

A conversion is not an arc between nodes in a graph of units; it is a family of arcs (i.e., it can apply to any unit that contains its source or target).

We can encode all units U and all conversions C into a UxC matrix T, choose a right-hand side u to generate our desired conversion, and solve

Tc = u

in a least squares sense to find conversions to apply.

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Solving conversions

The matrix T has columns representing conversions and rows representing units; each entry is an exponent of a unit the conversion transforms.

Tc = u

The right hand side, u, has

• exponents for the units we want and
• negated exponents of units we have.

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Solving conversions

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T

c

u

=

Solving conversions

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T

c

u

=

What does the units library do?

The units library provides

• preconfigured definitions of dimensions, prefixes, and units
• parsing of strings into dimensions, prefixes, units, and measurements;
• transformation of units according to conversions;
• identification of compatible units.

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How does the units library work?

A unit system is deserialized from JSON using nlohmann_json.

Strings are parsed via a simple PEGTL grammar and dimensions, units, or measurements are created.

Prefixes, dimensions, and units are all implemented using a common base class that holds a name, an optional symbol, optional name/symbol aliases, and an optional description.

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