Questions tagged [fixed-point-arithmetics]

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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 ...
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40 views

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 ...
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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, ...
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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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Consider the function $ f: [-1,1] \rightarrow [-1,1] $ defined by $ \ f(x)=\frac{3}{2}x^2-1 $.

Consider the function $ f: [-1,1] \rightarrow [-1,1] $ defined by $ \ f(x)=\frac{3}{2}x^2-1 $. Find the fixed points and check their stablity. Answer: The fixed points are obtained by $ f(x)=x $...
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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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2k views

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 ...
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2answers
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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 ...
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77 views

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 ...