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These four methods are called directed rounding to an integer, as the displacements from the original number x to the rounded value y are all directed toward or away from the same limiting value (0, +∞, or −∞). Directed rounding is used in interval arithmetic and is often required in financial calculations.
Reliable Computing, An open electronic journal devoted to numerical computations with guaranteed accuracy, bounding of ranges, mathematical proofs based on floating-point arithmetic, and other theory and applications of interval arithmetic and directed rounding.
A round number is an integer that ends with one or more "0"s (zero-digit) in a given base. [1] So, 590 is rounder than 592, but 590 is less round than 600. In both technical and informal language, a round number is often interpreted to stand for a value or values near to the nominal value expressed.
The IEEE standard has four different rounding modes; the first is the default; the others are called directed roundings. Round to Nearest – rounds to the nearest value; if the number falls midway it is rounded to the nearest value with an even (zero) least significant bit, which means it is rounded up 50% of the time (in IEEE 754-2008 this ...
Round toward 0 – directed rounding towards zero (also known as truncation). Round toward +∞ – directed rounding towards positive infinity (also known as rounding up or ceiling ). Round toward −∞ – directed rounding towards negative infinity (also known as rounding down or floor ).
This corresponds to the sticky rounding mode (term used by J. S. Moore, T. Lynch, and M. Kaufmann, A Mechanically Checked Proof of the Correctness of the Kernel of the AMD5K86™ Floating-Point Division Algorithm, 1996), a.k.a. rounding to odd (term used by S. Boldo and G. Melquiond, Emulation of a FMA and correctly-rounded sums: proved ...
Rounding, reducing the number of significant figures in a number; Round number, ending with one or more zeroes; Round (cryptography) Roundness (geology)
Rounds (parameter 1) by (parameter 2) decimal places, and formats. Scientific notation is used for numbers greater than 1×10^9, or less than 1×10^−4. Template parameters [Edit template data] Parameter Description Type Status number 1 The number to be rounded Number required decimal places 2 The number of decimal places, if negative the number is rounded so the last (parameter 2) digits are ...