FLOPS - Floating-point Operation and Integer Operation

Floating-point Operation and Integer Operation

FLOPS measures the computing ability of a computer. An example of a floating-point operation is the calculation of mathematical equations; as such, FLOPS is a useful measure of supercomputer performance. MIPS is used to measure the integer performance of a computer. Examples of integer operation include data movement (A to B) or value testing (If A = B, then C). MIPS as a performance benchmark is adequate for the computer when it is used in database query, word processing, spreadsheets, or to run multiple virtual operating systems. Frank H. McMahon, of the Lawrence Livermore National Laboratory, invented the terms FLOPS and MFLOPS (megaFLOPS) so that he could compare the so-called supercomputers of the day by the number of floating-point calculations they performed per second. This was much better than using the prevalent MIPS to compare computers as this statistic usually had little bearing on the arithmetic capability of the machine.

Fixed-point (integers). These designations refer to the format used to store and manipulate numeric representations of data without using a decimal point (it is 'fixed' at the end of the number). Fixed-point are designed to represent and manipulate integers – positive and negative whole numbers – for example 16 bits, yielding up to 65,536 possible bit patterns (216) that typically represent the whole numbers from -32768 to +32767.

Floating-point (real numbers). This is needed for very large or very small numbers, or numbers requiring the use of a decimal point (such as pi and other trigonometric values). The encoding scheme used by the processor for floating-point numbers is more complicated than for fixed-point. Floating-point representation is similar to scientific notation, except everything is carried out in base two, rather than base ten. The encoding scheme stores the sign, the exponent (in base two for Cray and IEEE floating point formats, or base 16 for IBM Floating Point Architecture) and the mantissa (number after the decimal point). While several similar formats are in use, the most common is ANSI/IEEE Std. 754-1985. This standard defines the format for 32-bit numbers called single precision, as well as 64-bit numbers called double precision and longer numbers called extended precision (used for intermediate results). Floating-point representations can support a much wider range of values than fixed-point, with the ability to represent very small numbers and very large numbers.

Dynamic range and precision. The exponentiation inherent in floating-point computation assures a much larger dynamic range – the largest and smallest numbers that can be represented - which is especially important when processing data sets which are extremely large or where the range may be unpredictable. As such, floating-point processors are ideally suited for computationally intensive applications.