computer science

GNU Multiple Precision Arithmetic Library

GNU Multiple Precision Arithmetic Library 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 GNU Multiple Precision Arithmetic Library rather than just read about it. In short: GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There are no practical limits to the precision except the ones implied by the available memory (operands may be of up to 232−1 bits on 32-bit machines and 237 bits on 64-bit machines).

Key takeaways

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

Reference excerpt

GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There are no practical limits to the precision except the ones implied by the available memory (operands may be of up to 232−1 bits on 32-bit machines and 237 bits on 64-bit machines). GMP has a rich set of functions, and the functions have a regular interface. The basic interface is for C, but wrappers exist for other languages, including Ada, C++, C#, Julia, .NET, OCaml, Perl, PHP, Python, R, Ruby, and Rust. Before 2008, Kaffe, a Java virtual machine, used GMP to support Java built-in arbitrary precision arithmetic. Shortly after, GMP support was added to GNU Classpath, as the backends to java.math.BigInteger and java.math.BigDecimal. The main target applications of GMP are cryptography applications and research, Internet security applications, and computer algebra systems. GMP aims to be faster than any other arbitrary-precision arithmetic (big number) library for all operand sizes. Some important factors in doing this are:

Full words are the basic type for all arithmetic. Different algorithms are used for different operand sizes; algorithms which are more efficient with large numbers are not used when dealing with small numbers. Assembly language (specialized for different processors) is used in the most common inner loops to optimize them as much as possible. The first GMP release was made in 1991. It is constantly developed and maintained. GMP is part of the GNU project (although its website being off gnu.org may cause confusion), and is distributed under the GNU Lesser General Public License (LGPL). GMP is used for integer arithmetic in many computer algebra systems such as Mathematica and Maple. It is also used in the Computational Geometry Algorithms Library (CGAL). GMP is needed to build the GNU Compiler Collection (GCC).

C library interface The C library interface defines:

mpz_t (multiprecision integer) mpq_t (multiprecision rational) mpf_t (multiprecision floating-point number) gmp_randstate_t (random state, used for producing random numbers) Functions are prefixed with the type name (for example, operations on multiprecision integers are prefixed with mpz, etc.) The library also provides additional utilities (all prefixed with gmp), such as gmp_scanf, gmp_printf, etc.

Example Here is an example of C code showing the use of the GMP library to multiply and print large numbers:

This code calculates the value of 7612058254738945 × 9263591128439081 {\displaystyle 7612058254738945\times 9263591128439081} . Compiling and running this program gives this result. (The -lgmp flag is used if compiling on Unix-type systems.)

C++ library interface The C++ library interface defines the classes:

mpz_class (corresponds to mpz_t) mpq_class (corresponds to mpq_t) mpf_class (corresponds to mpf_t) gmp_randclass (offers random number utilities) The free-standing functions in the C library are integrated as methods in the C++ classes. The C++ library places all symbols globally, and does not use a library namespace. It is recommended to avoid auto in declarations. For returning to the C type, each class offers a corresponding get_mp_t() method (for example mpz_class::get_mpz_t()).

Example For comparison, one can write instead the following equivalent C++ program. (The -lgmpxx -lgmp flags are used if compiling on Unix-type systems.)

Language bindings

Illustrations

Worked examples

Example 1 — a first encounter with GNU Multiple Precision Arithmetic Library

Start with the simplest possible case. Write down what GNU Multiple Precision Arithmetic Library 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 GNU Multiple Precision Arithmetic Library 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 GNU Multiple Precision Arithmetic Library 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 GNU Multiple Precision Arithmetic Library

In research: GNU Multiple Precision Arithmetic Library 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 GNU Multiple Precision Arithmetic Library 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: GNU Multiple Precision Arithmetic Library is common in secondary-school and first-year university syllabi. It links to neighbouring topics C (programming language) libraries, Computer arithmetic, Free software programmed in C, so understanding it makes those chapters shorter.
In everyday life: Look for GNU Multiple Precision Arithmetic Library 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 GNU Multiple Precision Arithmetic Library in 20 minutes

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

Frequently asked questions

What is GNU Multiple Precision Arithmetic Library in simple terms?

Why does GNU Multiple Precision Arithmetic Library 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 GNU Multiple Precision Arithmetic Library?

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 GNU Multiple Precision Arithmetic Library.