26
votes
Accepted
Approximating constant π² to within error
You don't need to compare prev and new during each iteration.
The difference between the new and the previous sum is simply the ...
- 3,991
19
votes
Approximating constant π² to within error
So, you have a polynomial sequence and want to sum its terms while they are greater than a provided tolerance (i.e.: the tolerance is lower than the current computed term).
This is easily expressed ...
- 29.4k
19
votes
Accepted
IEEE 754 square root with Newton-Raphson
This answer uses pointer-casting for type-punning just to save space. In practice keep using your union (safe in ISO C99, and in C++ as a GNU and MSVC extension) or memcpy (safe in C and C++). This ...
- 3,110
17
votes
Accepted
Definite Integral Approximation using the Trapezoidal Method
If you are writing mathematical code in Python, then it is worth looking at NumPy, which is a library implementing (among other things) fast arithmetic operations on arrays of floating-point numbers.
...
- 50.1k
15
votes
Approximating constant π² to within error
Please fix the indentation (probably just a copy-pasting issue).
In Python, you don't need parenthesis around the expressions for block statements like if and ...
- 1,576
15
votes
Accepted
Numerical integration in C++: Newton-Cotes formulas
I wonder whether the #include "NewtonCotesFormulas.cpp" at the end of the NewtonCotesFormulas.h header file could be somehow avoided. I used it because without I'd get linking errors.
Yea, ...
- 11.7k
14
votes
Accepted
Mean π: Archimedes vs. Gauss - π computation through generalized means
Convergence testing
if pi == piold:
break
This is not usually done, because float equality has a lot of gotchas. In this case it's possible due to ...
- 71.1k
13
votes
Accepted
Python π = 1 + (1/2) + (1/3) + (1/4) - (1/5) + (1/6) + (1/7) + (1/8) + (1/9) - (1/10) ...1748 Euler
What you are approximating is
$$ \pi =\sum_{m=1}^{\infty}\frac{(-1)^{s(m)}}{m},$$
where \$s(m)\$ counts the number of appearances of primes of the form \$4k+1\$ in the prime decomposition of \$m\$, ...
- 24.2k
12
votes
Accepted
Simulating a two-body collision problem to find digits of Pi
First, this is an awesome video! Upvoted for that reason alone. :)
If n=2, the program finishes within milliseconds, whereas for n=3, it takes a whopping 115 seconds.
Do you know about big-O ...
- 19.7k
12
votes
Numerical integration in C++: Newton-Cotes formulas
Use an enum to give names to choices
Consider using an enum, or even better an enum class, ...
- 69.3k
11
votes
AVX assembly for fast atan2 approximation
So, just for fun, I've converted your code to intrinsics (and probably made a bunch of mistakes in the process):
...
- 741
11
votes
Implementing numerical integration
I see a few things that may help you improve your program.
Avoid pow for float
The use of ...
- 67.2k
11
votes
Accepted
Calculate Pi using Monte Carlo
One could consider at least the following points:
Instead of including <stdlib.h>, I'd include <cstdlib>.
In ...
- 3,649
11
votes
IEEE 754 square root with Newton-Raphson
FYI, in IEEE754 sqrt is a "basic" operation that's required to be correctly-rounded (rounding error <= 0.5ulp), same as + - * /. Hardware FPUs (I think) always ...
- 3,761
9
votes
AVX assembly for fast atan2 approximation
Functional problems.
Sign test
Rather than x < 0, use signbit(x).
Although I suspect this is faster, it is to allow code to ...
- 36.4k
9
votes
pure Python Bézier curve implementation
Unnecessary Generator
You've got an unnecessary generator expression here:
...
- 35.3k
9
votes
A probability distribution function, to be called repeatedly during numerical integration
This is a possible solution to harolds open point about exp in his answer.
Note that exp(x+y) = exp(x) * exp(y) holds for any ...
- 333
8
votes
Accepted
Finding the root of a function by Bisection Method
Headers and namespaces
The <cmath> header is referenced, but never used; it can be removed.
If we're to use std::vector, ...
- 88.3k
8
votes
Finding the root of a function by Bisection Method
A std::vector<T> vec is an arbitrary collection of Ts. vec might contain none, one or ...
- 19.7k
8
votes
Definite Integral Approximation using the Trapezoidal Method
You can use sum with a comprehension to create part_2.
You can move all the maths together if you think it looks nicer.
...
- 44.6k
8
votes
IEEE 754 square root with Newton-Raphson
I don't see why you define this constant yourself:
#define MANTISSA_SIZE 52
Given we already assume that FLT_RADIX is 2, we can ...
- 88.3k
8
votes
Accepted
C++ class to create and evaluate Chebyshev approximations of arbitrary functions
Naming things
You have a bounds checking evaluation function, operator(), and one that doesn't do bounds checking named ...
- 69.3k
8
votes
Accepted
Genetic algorithm to guess coefficient of a polynomial
This is not the best algorithm
If the goal is to get the best coefficients for a polynomial so it fits the given points, then a polynomial regression algorithm such as ...
- 69.3k
7
votes
Calculating Maclaurin series for sin(x)
I am not a Haskell expert. Few words from a numerical analyst point of view.
Your concern about recalculating factorial is very well founded. I recommend to take one more step and realize that ...
- 58.7k
7
votes
Implementing numerical integration
Improve robustness and readability
Don't using namespace with namespaces not designed for it.
Use const and ...
- 88.3k
7
votes
Accepted
A simple definite integrator class of a single variable in C++
You made multiple non-trivial edits while I wrote my answer, so there might be some divergence. (Personal annotation: Code should be (mostly) self explanatory. Don’t add a wall of text beforehand that ...
- 443
7
votes
Integrator 2.0: A Simple Integrator in C++17
#pragma once is non-standard.
size_t is never defined. If it's a misspelling of std::size_t...
- 88.3k
7
votes
A probability distribution function, to be called repeatedly during numerical integration
A typical way to reduce such cosines with an angle that is steadily counting up by the same increment, is to take a vector and rotate it step by step. That way, one cosine and one sine are calculated, ...
- 12.4k
7
votes
Accepted
Implementing a joint differential equation and eigenvalue solver
My primary goal here is to verify the correctness of my method and its implementation in code
You've done some things well - you have seemingly descriptive variable names and comments.
You need to ...
- 71.1k
6
votes
Accepted
Multithreaded Monte-Carlo Integration
Since C++17 (and its now 2018) You don;t need to do this ugly thing
namespace boost { namespace math { namespace quadrature {
}}}
You can simply do this:
...
- 97.7k
Only top scored, non community-wiki answers of a minimum length are eligible