A few years ago at CppCon, an engineer who works with electrical power systems every day
stopped me after a talk. He told me that his team confuses active power, reactive
power, apparent power, and complex power all the time, and that the mistake is easy
to make and expensive to find. Then he said the sentence that has stuck with me since: a
units library that will not make those four incompatible types is of no use in his
industry.
How do units and linear algebra fit together? We get that question often. The honest
answer is that two different questions hide inside it, and they have different solutions.
The occasion for answering now is concrete: mp-units ships opt-in integrations that let
mainstream linear algebra libraries (Eigen,
GLM, and Blaze)
act directly as the representation type of a quantity.
The Brno 2026 ISO C++ Committee meeting has just finished. It was the first
meeting of the C++29 cycle, and a surprising amount already landed in the working
draft. Below I share the highlights voted in during the closing plenary, followed
by an update on the quantities and units standardization effort.
Integers overflow. That is not a controversial statement. What is surprising
is how easily overflow can hide behind the abstraction of a units library.
Most developers immediately think of explicit or implicit scaling operations —
calling .in(unit) to convert a quantity, constructing a quantity from a different
unit, or assigning between quantities with different units. These are indeed
places where overflow can occur, and the library cannot prevent it at compile time
when the values are only known at runtime. But at least these operations are
visible in your code: you wrote the conversion, you asked for the scaling,
and you can reason about whether the multiplication or division might overflow
your integer type.
The far more insidious problem is what happens when you don't ask for a conversion.
When you write 1 * m + 1 * ft, the library must automatically convert both
operands to a common unit before performing the addition. That conversion —
which you never explicitly requested — involves multiplication or division by
scaling factors. With integer representations, those scaling operations can
overflow silently, producing garbage results that propagate through your
calculations undetected.
No compile-time programming can prevent this. The values are only known at
runtime. But very few libraries provide proper tools to detect it.
This article explains why that limitation is real, how other libraries have
tried to work around it, and what mp-units provides to close the gap as
tightly as the language allows.
Physical units libraries have always been very good at preventing dimensional
errors and unit mismatches. But there is a category of correctness that they have
universally ignored: domain constraints on quantity point values.
A latitude is not just a length divided by a radius. It is a value that lives in
\([-90°, +90°]\); anything outside that range is physically meaningless. An angle
used in bearing navigation wraps cyclically around a circle; treating it as an
unbounded real number ignores a fundamental property of the domain. A clinical
body-temperature sensor should reject a reading of \(44\ \mathrm{°C}\) at the API
boundary, not silently pass it downstream.
Type-level constraint enforcement for quantity points with this level of
flexibility is a relatively unexplored area in mainstream physical units libraries.
The approach we present here is novel and experimental — we are certain there are
edge cases and design considerations we haven't yet discovered.
This article describes the motivation in depth, the design we arrived at, and
the open questions we would love the community's help to answer.
It has been 1.5 years since the last major update on the ISO C++ standardization
progress here. It is not that I got lazy , but there was really not much
to share.
This time, things were different. We achieved a nearly unprecedented
success — one probably not even expected by most, definitely not by me! 🎉
Physical quantities and units libraries exist primarily to prevent errors at compile time.
However, not all libraries provide the same level of safety. Some focus only on dimensional
analysis and unit conversions, while others go further to prevent representation errors,
semantic misuse of same-dimension quantities, and even errors in the mathematical structure
of equations.
This article explores six distinct safety levels that a comprehensive quantities and units
library can provide. We'll examine each level in detail with practical examples, then compare
how leading C++ libraries and units libraries from other languages perform across these
safety dimensions. Finally, we'll analyze the performance and memory costs associated
with different approaches, helping you understand the trade-offs between safety guarantees
and runtime efficiency.
We'll pay particular attention to the upper safety levels—especially quantity kind
safety (distinguishing dimensionally equivalent concepts such as work vs. torque, or
Hz vs. Bq) and quantity safety (enforcing correct quantity hierarchies and
scalar/vector/tensor mathematical rules)—which are well-established concepts in metrology
and physics, yet remain widely overlooked in the C++ ecosystem. Most units library authors
and users simply do not realize these guarantees are achievable, or how much they matter
in practice. These levels go well beyond dimensional analysis, preventing subtle semantic
errors that unit conversions alone cannot catch, and are essential for realizing truly
strongly-typed numerics in C++.
We're thrilled to announce a major expansion of mp-units learning resources: comprehensive
tutorials and hands-on workshops that make learning type-safe physical quantities and units
both accessible and engaging. Whether you're taking your first steps with the library or
ready to master advanced patterns, we've got you covered.
We're excited to announce a major enhancement to the mp-units documentation: an
automated systems reference generator that extracts and documents all quantities, units,
dimensions, and their relationships directly from the library's C++ source code.
, but there was really not much
to share.