In computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. For example, 12.345 is a floating-point number in base ten with five digits of precision:
IEEE 754-1985 is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. During its 23 years, it was the most widely used format for floating-point computation. It was implemented in software, in the form of floating-point libraries, and in hardware, in the instructions of many CPUs and FPUs. The first integrated circuit to implement the draft of what was to become IEEE 754-1985 was the Intel 8087.
Precision Architecture RISC (PA-RISC) or Hewlett Packard Precision Architecture, is a general purpose computer instruction set architecture (ISA) developed by Hewlett-Packard from the 1980s until the 2000s.
Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands. The notation does not need any parentheses for as long as each operator has a fixed number of operands.
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.
The IEEE Standard for Floating-Point Arithmetic is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard.
A scientific calculator is an electronic calculator, either desktop or handheld, designed to perform calculations using basic and complex mathematical operations and functions. They have completely replaced slide rules and are used in both educational and professional settings.
The HP-35 was Hewlett-Packard's first pocket calculator and the world's first scientific pocket calculator: a calculator with trigonometric and exponential functions. It was introduced in 1972.
C99 is an informal name for ISO/IEC 9899:1999, a past version of the C programming language standard. It extends the previous version (C90) with new features for the language and the standard library, and helps implementations make better use of available computer hardware, such as IEEE 754-1985 floating-point arithmetic, and compiler technology. The C11 version of the C programming language standard, published in 2011, updates C99.
The HP-42S RPN Scientific is a programmable RPN Scientific hand held calculator introduced by Hewlett-Packard in 1988. It has advanced functions suitable for applications in mathematics, linear algebra, statistical analysis, computer science and others.
CORDIC, also known as Volder's algorithm, or: Digit-by-digit methodCircular CORDIC, Linear CORDIC, Hyperbolic CORDIC, and Generalized Hyperbolic CORDIC, is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, and exponentials and logarithms with arbitrary base, typically converging with one digit per iteration. CORDIC is therefore also an example of digit-by-digit algorithms. CORDIC and closely related methods known as pseudo-multiplication and pseudo-division or factor combining are commonly used when no hardware multiplier is available, as the only operations it requires are additions, subtractions, bitshift and lookup tables. As such, they all belong to the class of shift-and-add algorithms. In computer science, CORDIC is often used to implement floating-point arithmetic when the target platform lacks hardware multiply for cost or space reasons.
The HP-12C is a financial calculator made by Hewlett-Packard (HP) and its successor HP Inc. as part of the HP Voyager series, introduced in 1981. It is HP's longest and best-selling product and is considered the de facto standard among financial professionals. There have been multiple revisions over the years, with newer revisions moving to an ARM processor running a software emulator of the original Nut processor. Critics claim that its 1980s technology is antiquated, but proponents point out that it is still the de facto and de jure in high finance.
HP calculators are various calculators manufactured by the Hewlett-Packard company over the years.
Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are equivalent. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 and +0, regarded as equal by the numerical comparison operations but with possible different behaviors in particular operations. This occurs in the sign-magnitude and ones' complement signed number representations for integers, and in most floating-point number representations. The number 0 is usually encoded as +0, but can still be represented by +0, −0, or 0.
The Hewlett-Packard Voyager series of calculators were introduced by Hewlett-Packard in 1981. All members of this series are programmable, use Reverse Polish Notation, and feature continuous memory. Nearly identical in appearance, each model provided different capabilities and was aimed at different user markets.
Extended precision refers to floating-point number formats that provide greater precision than the basic floating-point formats. Extended precision formats support a basic format by minimizing roundoff and overflow errors in intermediate values of expressions on the base format. In contrast to extended precision, arbitrary-precision arithmetic refers to implementations of much larger numeric types using special software.
France Rode was a Slovenian engineer and inventor best known for his work on the HP-35 pocket calculator. He was one of the four lead engineers at Hewlett-Packard assigned to this project.
The HP-21 was a scientific calculator produced by Hewlett-Packard between 1975 and 1978. It was designed as a replacement for the HP-35, and was one of a set of three calculators, the others being the HP-22 and HP-25, which were similarly built but aimed at different markets.
Unums are a family of number formats and arithmetic for implementing real numbers on a computer, proposed by John L. Gustafson in 2015. They are designed as an alternative to the ubiquitous IEEE 754 floating-point standard. The latest version is known as posits.
Floating-point error mitigation is the minimization of errors caused by the fact that real numbers cannot, in general, be accurately represented in a fixed space. By definition, floating-point error cannot be eliminated, and, at best, can only be managed.
