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Questions tagged [fixed-point-arithmetics]

A fixed-point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point. Fixed-point number representation can be compared to the more complicated floating-point number representation.

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Calculating the fixed-point representation of (1 - √0.5) to arbitrary levels of precision

I have a constant 0.29289321881345247559915563789515..., which can be calculated using the equation (1 - √0.5) and then ...
Kittoes0124's user avatar
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Composite functions and fixed point free property

Given 2 functions: $f: X \to X$ and $g: X \to X$, $f$ and $g$ are one-to-one $f$ and $g$ are fixed point free composite functions $f \circ g$, $\; g \circ f$, $\; f^2 \equiv f \circ f\;$ and $\;g^2 \...
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Proving that $\sin(\lambda x)$ only has one fixed point, if $\lambda$ is smaller than one.

I've been trying to prove that $\sin(\lambda x)$ only has a single fixed point (over all the real number) for $0< \lambda < 1$. I've thought of using the fixed point theorem, since it's obvious ...
Rodrigo's user avatar
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Find the equilibrium point for a single neural network layer

Given a matrix $\mathbf{W}\in\mathbb{R}^{n\times n}$ and a vector $\mathbf{b}\in\mathbb{R}^{n}$, find the equilibirum for the following single-layer neural network: $$ f(\mathbf{x})=\text{ReLU}(\...
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Can one do Conjugate Gradient for non-floating point arithmetics?

So the last few years I have used Krylov subspace methods (mostly Conjugate Gradient) for solving various kinds of problems in science and engineering, but in all of these applications I have only ...
mathreadler's user avatar
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Elchanan Mossel’s Dice Paradox using fixed point updating

The problem: You throw a dice until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws gave even numbers. The following is the ...
Roland's user avatar
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Understanding error propagation in fixed-point multiplication

I'm writing a test suite that checks the correctness of a fixed-point arithmetic library that I wrote. Specifically, it deals with Q4.4 numbers, i.e. 4 integer bits and 4 fractional, so its precision ...
Giulio Muscarello's user avatar
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Solution to rational Diophantine equations in fixed point

I'm trying to solve the following system of equations for $p$ and $q$, given fixed integers $x$, $y$ and $c$: $$r = {{c x + p} \over {c y + q}} \ , \, \, \, r \in \mathbb{Z}$$ where $$\{x, y, p, q, ...
Luke Hutchison's user avatar
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Banach and Caristi fixed point theorems

We all know that caristi fixed point theorem is a generalisation of banach fixed point theorem . We are able to derivate banach fixed point theorem from caristi fixed point theorem by taking a ...
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Fixed to float in archived (font2openvg) code

i found this link from some forum, so i thought the source code must have been useful to some: font2openvg.cpp.txt The question is, why divide 4096 to convert a fixed to float? ...
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Converting Decimal to Fixed Point Number

I am having trouble to get the intuition behind the following approach: We take the fraction point (say: .642) and continuously multiply by 2, taking whatever ends up right of the point as our next ...
Kevin Wu's user avatar
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How many bits do I need to store a given fraction?

Unlike integers, decimal fractions cannot be directly represented in binary. Therefore, what is the procedure to find how many bits to use to express a given binary fraction are sufficient? Basically ...
quantum231's user avatar
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Formalizing a self referential sentence

In The logic of provability, by G. Boolos, we are asked to ponder about this statement: If this statement is consistent, then you will have an exam tomorrow, but you cannot deduce from this ...
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Matrices over integer fields to solve complex polynomials.

Inspired by the fruitful answer to this question regarding numerically solving polynomial equations in terms of simpler fields (in that case representing real numbers as fractions of integers), I ...
mathreadler's user avatar