#need help understanding pi & output of variables

30 messages · Page 1 of 1 (latest)

ocean patrolBOT
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gilded olive
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original:
3.141592653589793|2384626433832795028841971693993
output:
3.141592653589793|115997963468544185161590576171875
                 ^ Precision loss after 15 points
gilded olive
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the first one

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long double has i think 15 points of precision

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you may be allowed to set more than 15 decimal points but they will become random after 15 points

barren dew
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;cpp << std::numeric_limits<long double>::digits10

sullen pewterBOT
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Program Output
18
jr-#6677 | 51ms | c++ | x86-64 gcc 10.1 | godbolt.org
barren dew
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;cpp << std::numeric_limits<double>::digits10

sullen pewterBOT
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Program Output
15
jr-#6677 | 84ms | c++ | x86-64 gcc 10.1 | godbolt.org
barren dew
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technically platform dependent of course (@white verge @gilded olive)

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For the questions
1: You can specify an arbitrary number of digits in a double literal in the source file, the compiler will convert it to the closest double and then it's converted to the closest long double

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;compile -std=c++20

#include <iostream>
#include <cmath>
#include <iomanip>
#include <numbers>

int main() {
    double pi_d = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214;
    long double pi_ld1 = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214;
    long double pi_ld2 = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214L; // <--------------- note the L to make it a long double literal
    std::cout << std::setprecision(18);
    std::cout << pi_d << std::endl;
    std::cout << pi_ld1 << std::endl;
    std::cout << pi_ld2 << std::endl;
    std::cout << std::numbers::pi_v<long double> << std::endl;
}
sullen pewterBOT
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Program Output
3.14159265358979312
3.14159265358979312
3.14159265358979324
3.14159265358979324
jr-#6677 | 50ms | c++ | x86-64 gcc 12.2 | godbolt.org
barren dew
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I think 2 should be answered

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3: pi_v doesn't support 60 decimal places

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numbers::pi_v<long double> can give you the closest long double representation of pi and setprecision(60) will tell cout to print 60 decimal digits of representation of that number

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4 how do people / computers calculate pi to X digit... what formula or programing language do they use? (this is kinda dumb also i didnt google this maybe i can find it but incase you know)

There are a lot of cool algorithms 🙂

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First you'll need some way of actually storing a number that has billions of digits (or whatnot)

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There are plenty of arbitrary-precision arithmetic libraries out there

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gmp is a good one

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for computing, you can do anything from simulating darts being thrown at a board to highly advanced algorithms that I can't claim to understand

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this arctan formula is cool

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(there is a better way to approximate the arctan itself too)

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But, all contemporary records have been set with the chudnovsky formula (or variants of it)

image.png
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it gives you about 14 digits of pi per term

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hope that helps @white verge

ocean patrolBOT
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