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Show HN: Rust library for numerical integration of real-valued functions

(github.com)
123 points mtantaoui | 3 comments | 19 Nov 24 12:41 UTC | HN request time: 0s | source

Integrate is a fast, small, lightweight Rust library for performing numerical integration of real-valued functions. It is designed to integrate functions, providing a simple and efficient way to approximate definite integrals using various numerical methods.

Integrate supports a variety of numerical integration techniques: - Newton-Cotes methods:

  - Rectangle Rule.
  - Trapezoidal Rule.
  - Simpson's Rule.
  - Newton's 3/8 Rule.
- Gauss quadrature methods:

  - Gauss-Legendre.
  - Gauss-Laguerre.
  - Gauss-Hermite.
  - Gauss-Chebyshev First Kind.
  - Gauss-Chebyshev Second Kind.
- Adaptive Methods:

  - Adaptive Simpson's method
- Romberg’s method.
1. wiz21c ◴[19 Nov 24 19:50 UTC] No.42187378[source]▶
In the rectangle method, there is "let x = a + i * h + (h / F1::from(2)...)"

I didn't check, but I wonder if it is not better to do x = a + (i+0.5)*h... My reasoning is that if "i" is very big, then i * h can be much bigger than h/2 and thus h/2 may be eaten by numerical precision when added to i*h... And then you have to convince the optimizer to do it the way you want. But well, it's late...

replies(1): >>42188835 #
2. zokier ◴[19 Nov 24 22:37 UTC] No.42188835[source]▶
herbie recommends `fma(h, (i + 0.5), a)`, but also doesn't report any accuracy problems with the original either
replies(1): >>42191905 #
3. wiz21c ◴[20 Nov 24 08:40 UTC] No.42191905[source]▶
yeah, fused mul-add is certainly better. Dunno how one epxresses that in rust though :-) Ahhh seems like there at least f64::mul_add() in stdlib :-)