computer science

ISO/IEC 10967

ISO/IEC 10967 is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand ISO/IEC 10967 rather than just read about it. In short: ISO/IEC 10967, Language independent arithmetic (LIA), is a series of standards on computer arithmetic. It is compatible with IEEE 754 (also published as IEC 60559), and much of the specifications are for IEEE 754 special values (though such values are not required by LIA itself, unless the parameter iec559 is true).

Key takeaways

ISO/IEC 10967 belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect ISO/IEC 10967 to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of ISO/IEC 10967 from memory before moving on to harder problems.

Reference excerpt

ISO/IEC 10967, Language independent arithmetic (LIA), is a series of standards on computer arithmetic. It is compatible with IEEE 754 (also published as IEC 60559), and much of the specifications are for IEEE 754 special values (though such values are not required by LIA itself, unless the parameter iec559 is true). It was developed by the working group ISO/IEC JTC1/SC22/WG11, which was disbanded in 2011. LIA consists of three parts:

Part 1: Integer and floating point arithmetic, second edition published 2012. Part 2: Elementary numerical functions, first edition published 2001. Part 3: Complex integer and floating point arithmetic and complex elementary numerical functions, first edition published 2006.

Parts

Part 1 Part 1 deals with the basic integer and floating point datatypes (for multiple radices, including 2 and 10), but unlike IEEE 754-2008 not the representation of the values. Part 1 also deals with basic arithmetic, including comparisons, on values of such datatypes. The parameter iec559 is expected to be true for most implementations of LIA-1. Part 1 was revised, to the second edition, to become more in line with the specifications in parts 2 and 3.

Part 2 Part 2 deals with some additional "basic" operations on integer and floating point datatype values, but focuses primarily on specifying requirements on numerical versions of elementary functions. Much of the specifications in LIA-2 are inspired by the specifications in Ada for elementary functions.

Part 3 Part 3 generalizes parts 1 and 2 to deal with imaginary and complex datatypes and arithmetic and elementary functions on such values. Much of the specifications in LIA-3 are inspired by the specifications for imaginary and complex datatypes and operations in C, Ada and Common Lisp.

Bindings Each of the parts provide suggested bindings for a number of programming languages. These are not part of the LIA standards, just suggestions, and are not complete. Authors of a programming language standard may wish to alter the suggestions before any incorporation in the programming language standard. The C99, C11 and C17 standards for C, and in 2013, the standards for C++ and Modula-2, have partial bindings to LIA-1.

See also ISO/IEC 11404, General purpose datatypes

References

External links ISO/IEC 10967-1:2012, complete text of Part 1: Integer and floating point arithmetic. ISO/IEC 10967-2:2001, complete text of Part 2: Elementary numerical functions. ISO/IEC 10967-3:2006, complete text of Part 3: Complex integer and floating point arithmetic and complex elementary numerical functions.

Worked examples

Example 1 — a first encounter with ISO/IEC 10967

Start with the simplest possible case. Write down what ISO/IEC 10967 claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to ISO/IEC 10967 before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about ISO/IEC 10967 ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of ISO/IEC 10967

In research: ISO/IEC 10967 appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses ISO/IEC 10967 in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: ISO/IEC 10967 is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer arithmetic, ISO/IEC standards, so understanding it makes those chapters shorter.
In everyday life: Look for ISO/IEC 10967 outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study ISO/IEC 10967 in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what ISO/IEC 10967 means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain ISO/IEC 10967 out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is ISO/IEC 10967 in simple terms?

Why does ISO/IEC 10967 matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study ISO/IEC 10967?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on ISO/IEC 10967.