# floating-point

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## floating-point

(programming, mathematics)
A number representation consisting of a mantissa, M, an exponent, E, and a radix (or "base"). The number represented is M*R^E where R is the radix.

In science and engineering, exponential notation or scientific notation uses a radix of ten so, for example, the number 93,000,000 might be written 9.3 x 10^7 (where ^7 is superscript 7).

In computer hardware, floating point numbers are usually represented with a radix of two since the mantissa and exponent are stored in binary, though many different representations could be used. The IEEE specify a standard representation which is used by many hardware floating-point systems. Non-zero numbers are normalised so that the binary point is immediately before the most significant bit of the mantissa. Since the number is non-zero, this bit must be a one so it need not be stored. A fixed "bias" is added to the exponent so that positive and negative exponents can be represented without a sign bit. Finally, extreme values of exponent (all zeros and all ones) are used to represent special numbers like zero and positive and negative infinity.

Opposite: fixed-point.
References in periodicals archive ?
The Xtensa LX7 release also provides new tools, including a new hardware floating-point application binary interface (ABI) for increased floating-point C/C++ performance, as well as compiler and C library enhancements to add C99 complex float support.
Architectural Modification to Enhance the Floating-Point Performance of FPGAs.
floating-point MCUs Cutting-edge math engine comprised of 80 MHz floating-point C28x core, new Viterbi Complex Math Unit (VCU) and Control Law Accelerator (CLA) options Floating-point core greatly eases programming, improves compatibility with meta-language tools, and improves performance by up to 40% over fixed point New VCU complex math unit provides 75 tailored math instructions to accelerate processing of communications algorithms, such as those for PLC, by a factor of up to 7X
These complex systems in military applications such as radar and EW are first simulated or modeled using floating-point data processing, using C or MATLAB software.
A GFLOP is equal to a billion floating-point operations per second.
Furthermore, predictions based on the growth in the size of mathematical models solved as the memory and speed of computers increase suggest that floating-point arithmetic with unit roundoff [approximately equals] [10.
Microsoft says the software can test the processor to determine if the division flaw is present and can use software floating-point emulation in place of the faulty floating-point hardware if the customer has chosen this option.
Computer-aided design and manufacturing programs, for example, frequently pass data between disk and RAM, a process that relies on integer performance; visualization and analysis applications rely on floating-point performance and graphics processing; and concurrent-engineering functions require sufficient network resources.
To overcome that difficulty, computer scientists in the 1950s developed the floating-point system of arithmetic, expressing each number in two parts.

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