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Either my coworker or me did this in c++ before about 15 or more years:
double factor= exp(-21.0 * log(2.0));
where
a.) double exp (double x) returns the base-e exponential function of x.
b.) double log (double x) returns the natural logarithm of x.
Do you recognize what exp(-21.0 * log(2.0))?
Do you have an idea why one have the idea to calculate this in that way?
 
[Edit]
If I think again about it...: Maybe we were trying to invent "source code obfuscation" 
[Edit 1]
uuups, exp(-21.0, log(2.0)) should be of course exp(-21.0 * log(2.0));
It does not solve my Problem, but it answers my question
modified 19-Jan-21 21:04pm.
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You have just give the proof of why good comments are important.
M.D.V. 
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.
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I was thinking more proof why good naming is important.
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The value calculated is approximately 2^(-21). This contains 21 significant decimal digits, and it is (barely) possible that the compiler ignored digits after the first 16 (the accuracy of a 'double'). The calculated value may actually have been more accurate.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
-- 6079 Smith W.
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Quote: The calculated value may actually have been more accurate
That is also my idea. But no idea based on what knowledge that time we decided for this. And more, how I can prove that the above mentioned equation was/is perhaps more precise than pow(2.0, -21.0). Not really a big Thing, but if you have an idea it will be very welcome. This especally to Keep my old brain alive 
Thank you very much for your comment.
It does not solve my Problem, but it answers my question
modified 19-Jan-21 21:04pm.
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0x01AA wrote: Do you have an idea why one have the idea to calculate this in that way?
Two reasons:
1 - You didn't want to type in all the digits by hand and maybe get them wrong.
2 - Rather than creating some magic number, the code expresses how the magic number is calculated, which must have some now lost meaning.
Now, given #2, the only thing that's missing is a comment (or having a function that returns this calculation) that actually describes the intent of this magic number!
Latest Article - A Concise Overview of Threads
Learning to code with python is like learning to swim with those little arm floaties. It gives you undeserved confidence and will eventually drown you. - DangerBunny
Artificial intelligence is the only remedy for natural stupidity. - CDP1802
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Three possibilities:
1.
I really think you should be explicitly declaring 2.0d and -21.0d.
With your arguments, the compiler should use the overloaded pow(float, float) which returns a float which is then coerced to a double. This value may not have been as accurate as you desired.
2.
Maybe the library in use at the time did not allow negative numbers for the second parameter?
Googling "c++ pow function negative exponent" has a lot of hits and shows the work around you provided.
3.
Pentium CPU floating point bug?
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The math I learned in school didn't really cover what I usually work with: uint and int. Most math tools are all about the Real numbers or maybe Complex numbers, so they will happily tell me that x * 2 / 2 = x. I vaguely heard about SMT solvers but they seemed hard to use.
So I made my own thing, the first versions in 2013, but I think it's useful enough now that other people may occasionally find it useful: haroldbot.nl. Completely free of course, including ad free, I wouldn't spam the lounge with my commercial products. It also works offline if you save a complete copy of the page.
There are some fun features in addition to equality checking, such as some limited simplification (for example x * 2 / 2 can be simplified to what it really is, and it isn't x), and detecting invertibility, sometimes it even finds the inverse so for example you can put in x * 5 to find out how to "un-multiply" by 5.
By the way I wrote that entire thing in JavaScript and I still don't actually know JavaScript. It's a weird language.
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harold aptroot wrote: and I still don't actually know JavaScript
I am not sure anybody "knows" JavaScript. But every single one of them have written JavaScript apps. That's the magic.
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That's very cool. I tried a few things, like x * 4 / 2 and I really like how you show the simplified version and the proof. Nice work!
Latest Article - A Concise Overview of Threads
Learning to code with python is like learning to swim with those little arm floaties. It gives you undeserved confidence and will eventually drown you. - DangerBunny
Artificial intelligence is the only remedy for natural stupidity. - CDP1802
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What you talk about here is the usage of Abstract algebra. Fields, Integral domains, Euclid's factorization method (the same as continued fraction algorithm) etc. Gauss doctoral thesis was about this subject (Disquisitiones Arithmeticae).
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That all sounds pretty scary. By the way I use Hensel's lemma to find multiplicative inverses.
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Believe it or not but Algebra was actually created to make things easier for you
I didn't know about Hensel's lemma, but It kinda reminds me of Rouché's theorem - Wikipedia[^] which I find very cool.
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Post it in Free Tools Discussion Boards[^]
This way your post won't be relegated to the limbo after a few hours.
By the way, thanks. It looks pretty cool.
M.D.V.
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.
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Is the worst thing about Ancient History classes that the teacher tends to Babylon?
Sent from my Amstrad PC 1640
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
AntiTwitter: @DalekDave is now a follower!
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Math classes are much worse. They never let you eat pi.
... such stuff as dreams are made on
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sure history has it's downsides, but on the plus side: all those dates, keeps you regular!
This internet thing is amazing! Letting people use it: worst idea ever!
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The professor I had was a real Cretin
Everyone has a photographic memory; some just don't have film. Steven Wright
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The professor Ptolemy that Ur wrong and it's Ninevah business.
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Yes - he was Roman all over the place. Troy as he might he always made a real Mesopotamia of it. Egypt me out of a decent education and in the end it was all Greek to me.
Socialism is the Axe Body Spray of political ideologies: It never does what it claims to do, but people too young to know better keep buying it anyway. (Glenn Reynolds)
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True, but it Sparta general education.
... such stuff as dreams are made on
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"general education"
Well I took an accelerated course that was every day of the week. Every single day I would sit at the back and pyramid the desks at the board and wonder what I was doing there.
That's right - every week - seven wonders.
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That may have been your experience, but it's not Mayan.
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Aeneid time you realized your really Persian your luck with these?
At least that's his story.
| Ravings en masse^ |
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| "The difference between genius and stupidity is that genius has its limits." - Albert Einstein | | "If you are searching for perfection in others, then you seek disappointment. If you are seek perfection in yourself, then you will find failure." - Balboos HaGadol Mar 2010 |
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