computer science

Long double

Long double 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 Long double rather than just read about it. In short: In C and related programming languages, long double refers to a floating-point data type that is often more precise than double precision though the language standard only requires it to be at least as precise as double. As with C's other floating-point types, it may not necessarily map to an IEEE format.

Key takeaways

Long double 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 Long double to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Long double from memory before moving on to harder problems.

Reference excerpt

In C and related programming languages, long double refers to a floating-point data type that is often more precise than double precision though the language standard only requires it to be at least as precise as double. As with C's other floating-point types, it may not necessarily map to an IEEE format.

History The long double type was present in the original 1989 C standard, but support was improved by the 1999 revision of the C standard, or C99, which extended the standard library to include functions operating on long double such as sinl() and strtold(). Long double constants are floating-point constants suffixed with "L" or "l" (lower-case L), e.g., 0.3333333333333333333333333333333333L or 3.1415926535897932384626433832795029L for quadruple precision. Without a suffix, the evaluation depends on FLT_EVAL_METHOD.

Implementations On the x86 architecture, most C compilers implement long double as the 80-bit extended precision type supported by x86 hardware (generally stored as 12 or 16 bytes to maintain data structure alignment), as specified in the C99 / C11 standards (IEC 60559 floating-point arithmetic (Annex F)). An exception is Microsoft Visual C++ for x86 (starting at 32-bit versions), which makes long double a synonym for double. The Intel C++ compiler on Microsoft Windows supports extended precision, but requires the /Qlong‑double switch for long double to correspond to the hardware's extended precision format. Compilers may also use long double for the IEEE 754 quadruple-precision binary floating-point format (binary128). This is the case on HP-UX, Solaris/SPARC, MIPS with the 64-bit or n32 ABI, 64-bit ARM (AArch64) (on operating systems using the standard AAPCS calling conventions, such as Linux), and z/OS with FLOAT(IEEE). Most implementations are in software, but some processors have hardware support. On some PowerPC systems, long double is implemented as a double-double arithmetic, where a long double value is regarded as the exact sum of two double-precision values, giving at least a 106-bit precision; with such a format, the long double type does not conform to the IEEE floating-point standard. Otherwise, long double is simply a synonym for double (double precision), e.g. on 32-bit ARM, 64-bit ARM (AArch64) (on Windows and macOS) and on 32-bit MIPS (old ABI, a.k.a. o32). With the GNU C Compiler, long double is 80-bit extended precision on x86 processors regardless of the physical storage used for the type (which can be either 96 or 128 bits), On some other architectures, long double can be double-double (e.g. on PowerPC) or 128-bit quadruple precision (e.g. on SPARC). As of gcc 4.3, a quadruple precision is also supported on x86, but as the nonstandard type __float128 rather than long double. Although the x86 architecture, and specifically the x87 floating-point instructions on x86, supports 80-bit extended-precision operations, it is possible to configure the processor to automatically round the output of the following operations to double (or even single) precision: addition, subtraction, multiplication, division and square root; register load operations, absolute value, remainder, scaling, exponentiation, logarithm, trigonometric operations, etc. always use the 80-bit extended precision. Conversely, in extended-precision mode, extended precision may be used for intermediate compiler-generated calculations even when the final results are stored at a lower precision (i.e. FLT_EVAL_METHOD == 2). With gcc on Linux, 80-bit extended precision is the default; on several BSD operating systems (FreeBSD and OpenBSD), double-precision mode is the default, and long double operations are effectively reduced to double precision. (NetBSD 7.0 and later, however, defaults to 80-bit extended precision ). However, it is possible to override this within an individual program via the FLDCW "floating-point load control-word" instruction. On x86_64, the BSDs default to 80-bit extended precision. Microsoft Windows with Visual C++ also sets the processor in double-precision mode by default, but this can again be overridden within an individual program (e.g. by the _controlfp_s function in Visual C++). The Intel C++ Compiler for x86, on the other hand, enables extended-precision mode by default. On IA-32 OS X, long double is 80-bit extended precision.

Other specifications In CORBA (from specification of 3.0, which uses "ANSI/IEEE Standard 754-1985" as its reference), "the long double data type represents an IEEE double-extended floating-point number, which has an exponent of at least 15 bits in length and a signed fraction of at least 64 bits", with GIOP/IIOP CDR, whose floating-point types "exactly follow the IEEE standard formats for floating point numbers", marshalling this as what seems to be IEEE 754-2008 binary128 a.k.a. quadruple precision without using that name.

See also Quadruple precision Extended precision

References

Worked examples

Example 1 — a first encounter with Long double

Start with the simplest possible case. Write down what Long double 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 Long double 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 Long double 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 Long double

In research: Long double 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 Long double 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: Long double is common in secondary-school and first-year university syllabi. It links to neighbouring topics C (programming language), Computer arithmetic, Data types, so understanding it makes those chapters shorter.
In everyday life: Look for Long double 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 Long double in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Long double 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 Long double out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Long double in simple terms?

Why does Long double 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 Long double?

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 Long double.