It employed ordinary base-10 fixed-point arithmetic.

These often process data using fixed-point arithmetic, though some more powerful versions use floating point arithmetic.

One notable feature is the pure fixed-point arithmetic to avoid rounding errors which would arise with floating-point arithmetic.

Tremor is an implementation of a Vorbis decoder using fixed-point arithmetic.

In systems without any floating-point hardware, the CPU emulates it using a series of simpler fixed-point arithmetic operations that run on the integer arithmetic logic unit.

Some structures are better for fixed-point arithmetic and others may be better for floating-point arithmetic.

The functionality of the library includes support for basic 2D graphics, image manipulation, text output, audio output, MIDI music, input and timers, as well as additional routines for fixed-point and floating-point matrix arithmetic, Unicode strings, file system access, file manipulation, data files, and ( limited, software-only ) 3D graphics.

See fixed-point arithmetic.

A " floating point " type is a compromise between the flexibility of a general rational type and the speed of fixed-point arithmetic.

# REDIRECT fixed-point arithmetic

On older, non-SIMD architectures, floating point arithmetic is much slower than using fixed-point arithmetic, so an alternative formulation is:

The TriMedia media processors support both fixed-point arithmetic as well as floating-point arithmetic, and have specific instructions to deal with complex filters and entropy coding.

Most DSP's use fixed-point arithmetic, because in real world signal processing the additional range provided by floating point is not needed, and there is a large speed benefit and cost benefit due to reduced hardware complexity.

Rounding is almost unavoidable in many computations — especially when dividing two numbers in integer or fixed-point arithmetic ; when computing mathematical functions such as square roots, logarithms, and sines ; or when using a floating point representation with a fixed number of significant digits.

Some programs ( especially those that use fixed-point arithmetic where no dedicated floating-point hardware is available ) will use behavior similar to the IEEE standard, using large positive and negative numbers to approximate infinities.

Its name comes from the words fractal and integer, since the first versions of it computed fractals by using only integer arithmetic ( also known as fixed-point arithmetic ), which led to much faster rendering on x86 computers without math coprocessors.

ISO / IEC TR 18037 specifies fixed-point data types for the C programming language ; vendors are expected to implement the language extensions for fixed point arithmetic in coming years.

A DAC converts an abstract finite-precision number ( usually a fixed-point binary number ) into a physical quantity ( e. g., a voltage or a pressure ).

Although BCD is not as widely used as in the past, decimal fixed-point and floating-point formats are still important and continue to be used in financial, commercial, and industrial computing, where subtle conversion and rounding errors that are inherent to floating point binary representations cannot be tolerated.

This divergence of culture is exhibited in the typical numerical representations used in data processing versus numerical ; data processing's measurements are typically represented by integers or by fixed-point or binary-coded decimal representations of numbers whereas the majority of data analysis's measurements are often represented by floating-point representation of rational numbers.

This is a fixed-point for f, because the set returned by f is the same as the set passed to f. Thus, a function g that applies f repeatedly and returns the set of original elements and all their descendants, is a fixed-point combinator.

A value of a fixed-point data type is essentially an integer that is scaled by a specific factor determined by the type.

The maximum value of a fixed-point type is simply the largest value that can be represented in the underlying integer type, multiplied by the scaling factor ; and similarly for the minimum value.

If both operands and the desired result are represented in the same fixed-point type, then the quotient of the two integers must be explicitly divided by the common scaling factor.

For example, one-tenth ( 0. 1 ) and one-hundredth ( 0. 01 ) can be represented only approximately by binary fixed-point or binary floating-point representations, while they can be represented exactly in decimal fixed-point or decimal floating-point representations.

* Fixed-Point Arithmetic-An Introduction Representing and implementing fixed-point arithmetic in digital signal processing, by Randy Yates

This divergence of culture is exhibited in the typical numerical representations used in data processing versus numerical ; data processing's measurements are typically represented by integers or by fixed-point or binary-coded decimal representations of numbers whereas the majority of data analysis's measurements are often represented by floating-point representation of rational numbers.

The equations are almost universally solved by means of an iterative, fixed-point type algorithm ( see the following section for more details ).

In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X.

Numbers can be stored in a fixed-point format, or in a floating-point format as a significand multiplied by an arbitrary exponent.

The first result in the field was the Schauder fixed-point theorem, proved in 1930 by Juliusz Schauder.

The family is characterized by their built-in, fixed-point digital signal processor ( DSP ) functionality supplied by 16-bit Multiply – accumulates ( MACs ), accompanied on-chip by a small and power-efficient microcontroller.

Moreover, even achieving this accuracy requires careful attention to scaling in order to minimize the loss of precision, and fixed-point FFT algorithms involve rescaling at each intermediate stage of decompositions like Cooley – Tukey.

Many fixed-point theorems yield algorithms for locating the least fixed point.

PL / I's principal domains are data processing, numerical computation, scientific computing, and systems programming ; it supports recursion, structured programming, linked data structure handling, fixed-point, floating-point, complex, character string handling, and bit string handling.

Because fixed-point combinators are higher-order functions, their history is intimately related to the development of lambda calculus.

The recursion theorem shows that no computable function is fixed point free, but there are many non-computable fixed-point free functions.

Fixed-point numbers are useful for representing fractional values, usually in base 2 or base 10, when the executing processor has no floating point unit ( FPU ) or if fixed-point provides improved performance or accuracy for the application at hand.

For example, consider a fixed-point type represented as a binary integer with b bits in two's complement format, with a scaling factor of 1 / 2 < sup > f </ sup > ( that is, the last f bits are fraction bits ): the minimum representable value is − 2 < sup > b-1 </ sup >/ 2 < sup > f </ sup > and the maximum value is ( 2 < sup > b-1 </ sup >- 1 )/ 2 < sup > f </ sup >.

The two most common classes of fixed-point types are decimal and binary.

Binary fixed-point types are most commonly used, because the rescaling operations can be implemented as fast bit shifts.

There are various notations used to represent word length and radix point in a binary fixed-point number.

Floating-point representations are easier to use than fixed-point representations, because they can handle a wider dynamic range and do not require programmers to specify the number of digits after the radix point.

However, if they are needed, fixed-point numbers can be implemented even in programming languages like C and C ++, which do not commonly include such support.

A common use of fixed-point BCD numbers is for storing monetary values, where the inexact values of binary floating-point numbers are often a liability.

These codecs use fixed-point arithmetic because many audio decoding hardware devices do not have an FPU ( partly to save money, but primarily to save power-integer units are much smaller in silicon area than an FPU ) and audio decoding requires enough performance that a software implementation of floating-point on low-speed devices would not produce output in real time.

Most commonly, these discrete values are represented as fixed-point words ( either proportional to the waveform values or companded ) or floating-point words.

Other significant differences are that the calling semantics for primitive rendering functions were changed in favor of vertex arrays, and fixed-point data types were introduced for vertex coordinates.