Questions tagged [real-numbers]

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Real RAMs with “reasonable” operations

There is a large body of literature on RAMs with "reasonable" and "unreasonable" operations, where "unreasonable" operations would yield a machine with too much power to be practically feasible. For ...
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Is it a bad idea to require a correctness proof as part of a computable real number?

At 30:42 of Norman Wildberger's Difficulties with real numbers as infinite decimals (II) lecture, he raises the question whether "certificates of boundedness" (of the runtime of the algorithm to ...
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Semidecidable properties of computable reals

By computable real I mean $x\in\mathbb{R}$ such that there is some computable total function $p_x$ that takes a natural number $n$ and returns a dyadic rational $r$ such that $|x-r|<2^{-n}$. I ...
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Why mantissa and exponent are stored differently in a float?

As we know, in IEEE 754 standard, float number's exponent and mantissa are stored differently. While the exponent is stored as an unsigned number, taking advantage of the bias, the mantissa is in sign-...
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Computational complexity of logistic map

My question is pretty simple and to the point. Is there a known way to efficiently compute logistic maps to within a specified precision? In other words, the input is a value $x$ and integers $d,n$; ...
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Finding a path with a smallest product

Let $G$ be a graph whose edges have integer weights between 1 and 255. What is an efficient algorithm for finding a path between two vertices $s,t$, such that the product of weights on the path is ...
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When do you know whether an exponent represents a movement of the decimal point to the left?

I'm learning about floating point numbers and I don't quite understand when one should interpret an exponent as moving the decimal point to the left. By book shows an example of converting -10.5 ...