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Round to nearest, ties to even – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value with an even least significant digit. Round to nearest, ties away from zero (or ties to away ) – rounds to the nearest value; if the number falls midway, it is rounded to the nearest value above (for positive numbers ...
This variant of the round-to-nearest method is also called convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, odd–even rounding, [6] or bankers' rounding. [ 7 ] This is the default rounding mode used in IEEE 754 operations for results in binary floating-point formats.
The 10-bit format has a 5-bit mantissa, and the 11-bit format has a 6-bit mantissa. [8] [9] IEEE SA Working Group P3109 is currently working on a standard for 8-bit minifloats optimized for machine learning. The current draft defines not one format, but a family of 7 different formats, named "binary8pP", where "P" is a number from 1 to 7.
The "decimal" data type of the C# and Python programming languages, and the decimal formats of the IEEE 754-2008 standard, are designed to avoid the problems of binary floating-point representations when applied to human-entered exact decimal values, and make the arithmetic always behave as expected when numbers are printed in decimal.
The IEEE 754 specification—followed by all modern floating-point hardware—requires that the result of an elementary arithmetic operation (addition, subtraction, multiplication, division, and square root since 1985, and FMA since 2008) be correctly rounded, which implies that in rounding to nearest, the rounded result is within 0.5 ulp of ...
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
RRDtool has a graph function, which presents data from an RRD in a customizable graphical format. RRDtool (round-robin database tool) aims to handle time series data such as network bandwidth, temperatures or CPU load. The data is stored in a circular buffer based database, thus the system storage footprint remains constant over time.
The Siemens 7.700 and 7.500 series mainframes and their successors support the same floating-point formats and instructions as the IBM System/360 and System/370. The VAX processor implemented non-IEEE quadruple-precision floating point as its "H Floating-point" format. It had one sign bit, a 15-bit exponent and 112-fraction bits, however the ...