Questions tagged [floating-point]
Mathematical questions concerning floating point numbers, a finite approximation of the real numbers used in computing.
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What is the result of 3-digit chopping for 0.000234?
I am trying to understand if the 0."000" part counted as digit or not.
If 0."000" is not "digit", then the result should 0.000234.
If yes, then the result should be 0.00
Which one is correct?
Here'...
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pow and its relative error
Investigating the floating-point implementation of the $\operatorname{pow}(x,b)=x^b$ with $x,b\in\Bbb R$ in some library implementations, I found that some pow ...
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How to calculate the inverse of sum of a Kronecker product and a diagonal matrix
I want to calculate the inverse of a matrix of the form $S = (A\otimes B+C)$, where $A$ and $B$ are symetric and invertible, $C$ is a diagonal matrix with positive elements. Basically if the ...
CommunityBot
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How do 24 significant bits give from 6 to 9 significant decimal digits?
was reading IEEE 754 single-precision binary floating-point format: binary32 when I ran into
The IEEE 754 standard specifies a binary32 as having:
Sign bit: 1 bit
Exponent width: 8 bits
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The upper and lower limits of IEEE-754 standard
So there's something I just can't understand about ieee-754.
The specific questions are:
Which range of numbers can be represented by IEEE-754 standard using base 2 in single (double) precision?
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How to convert 601.0 to IEEE-754 Single Precision
I am trying to understand how to convert from decimal to IEEE-754 Single Precision binary representation.
I make up a random number which happen to be 601.00
I tried my best to figure it out and ...
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Floating point arithmetic ( IEEE-754 standard ) commutative law (*,+)
How can I prove that: $ fl(a \ op \ b) = fl(b \ op \ a), \: op = +,*.$.
I have been reading and searching the big majority say that its true.
like here. However, I can not find a mathematical proof ...
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Find point in 3D plane
I have four points in a 3D space, example:
$$(0,0,1),\
(1,0,1),\
(1,0,2)\ \mbox{and}\ (0,0,2).$$
Then I have a 2D position on that square plane:
$$x = 0.5,\ y = 0.5.$$
I need to find out the 3D ...
CommunityBot
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Solving a quadratic equation with precision when using floating point variables
I know how to solve a basic quadratic equation with the formula
$$t_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$
but I learned that if $b \approx \sqrt{b^2-4ac}$ floating point precision may give ...
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How to transform this expression to a numerically stable form?
I have this function
$$f(x, t)=\frac{\left(1+x\right)^{1-t}-1}{1-t}$$
Where $x \ge 0$ and $t \ge 0$.
I want to use it in neural network, and thus need it to be differentiable.
While it has a ...
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Algebraic Structures involving 𝙽𝚊𝙽 (absorbing element).
IEEE 754 floating point numbers contain the concept of 𝙽𝚊𝙽 (not a number), which "dominates" arithmetical operations ($+,-,⋅,÷$ will return ...
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Floating point number,Mantissa,Exponent
In this computer, numbers are stored in $12$-bits. We will also assume
that for a floating point (real) number, $6$ bits of these bits are reserved for
the mantissa (or significand) with $2^{k-1}-1$ ...
CommunityBot
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Solve $10^{10^z} = 10^{10^x}+10^{10^y}$ for $z$ with floating point accuracy
In the following equation
$$10^{10^z} = 10^{10^x}+10^{10^y}$$
I want to find an algorithm that computes $z$ in a floating point accurate manner given any values of $x$ and $y$ (e.g. $x=y=2000$). The ...
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Proof that $\epsilon_{mach} \leq \frac{1}{2} b^{1-n}$
I have a question about the proof of the following statement:
For each set of machine numbers $F(b, n, E_{min}, E_{max})$ with $E_{min} < E_{max}$ the following inequality holds: $\epsilon_{mach} \...
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Find original inputs $x$ and $^y$ for a given product, possible or not? [closed]
$387,381,625,547,900,583,936$ is the product of this calculation $21\cdot2^{64}$.
If I only have the product and the multiplier $2$ (without the exponent) would it be possible to find the other inputs ...
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