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I'm have to write a C program, what it does is takes a integer as input. And gives output to the input(th) number of PI after decimal. Like if input is 100, output will be 9(100th digit of pi, after decimal is 9).
What will be the best algorithm for that?
p.s I don't want to save the value of pi into the string, and do it.
Your question is more a math question than a C programming one (so perhaps off-topic). Read first the wikipage on Pi and Approximations of π
If you need to compute only a few hundred (or even hundred thousands) digits, you just need to use some algorithm and code it using some bignum library (e.g. GMPlib, which has mpfr_const_pî ass commented by chtz).
Things become interesting for many billions of digits. I'm not expert on Pi, but look into Fabrice Bellard work on it (read the technical notes mentioning Chudnovsky's algorithm).
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I'm trying to think of some interesting, reusable way to implement big integers using passed amount of bytes or resizing themselves when needed. I have no idea how to make it optimal in any way tho. Are there any tricks I could use, or do I have to simply work on those numbers bit by bit while adding/multiplying/dividing?
edit: if it is important, I need it to safe text as number in base 10 so I can play with some ideas for encrypting it
Use The GNU Multiple Precision Arithmetic Library. If you try to reinvent the wheel you will end up with a square.
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I am creating a gp calculator in c++ ,But in gp the formulae has common ratio to the power of the term number. in order to get calculate that term i need to know how do i take the number as power for some other number, is there any operator for doing this.
If both arguments are floating point numbers, you have to use formula xᵐ = exp(m log x).
Supposedly std::pow does that for you. If your program requires to match some particular test patterns, further investigation may be required.
Know your <math>
As long as x != 0 to get any power:
exp(log(x)*power)
The interesting tidbit here is that if power is 1.0/y it will extract the y-root of the value.
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This is a simple code that counts two to the right degree. Starting from somewhere around 60 degrees the answer is incorrect.
I need to count 2^200. The answer shouldn't be in the form like "1.606938e+60", but by numbers. How to do this in C++?
#include <iostream>
using namespace std;
int main()
{
unsigned long long int n,z;
cin>>n;
z=pow(2,n);
cout<<z<<endl;
return 0;
}
You need to use std::set_precision(n) to get it to print in the format that you're expecting it, but if your numbers get high enough, you'll run into a second issue. pow returns a double, which loses precision in a big way with huge numbers. For more information on how to solve that, refer to this Stack Overflow answer.
Anyway you cant print such big number as a single integer or double value in c++ (not yet). Maybe there exist some 256 or 512 machine architectures and implementations which build in types are large enough, but its not possible in common. You probably need to use some data structure to store you number and operate on that.
This, this and this examples may be helpful.
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I have a decent grasp with c++, and I made a basic calculator that can add, subtract, multiply, and divide. but I am having a hard time trying to get it to calculate decimals. Help please???
Read http://floating-point-gui.de/ first.
You don't calculate decimals, you display a floating point number (often some double) with some decimals.
Use things like std::showpoint & std::fixed ...
If you want to show a lot of correct digits, you need to do arbitrary precision arithmetic or BigNums. Then use a library, such as GMPlib
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I accidentally saw on Internet that functional programming language SML allows to do arbitrary precision integer arithmetic. I had written big integer arithmetic on C++ before and I decided(for curiosity) to compare my implementation with SML's by computing factorial of big numbers. I found out that SML program works about 15 times faster than mine. My implementation uses elementary school multiplication algorithm. But as I know the fast algorithms (such as FFT or Karatsuba's algorithm) worked better than elementary school multiplication when multipliers aren't much different. In this case they are, because (n-1)! is much greater than n. My question is what are the other possible reasons that the SML program works so faster.
Three possible reasons:
It uses multiple CPU cores (easy to test)
It uses SIMD instructions
It uses GPU (rare, but not unheard of)