update efficiency of calculating binomial coefficients
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説明
I can make a formal PR/Issue, but just sitting on my phone talking with chatGPT trying to figure out how to efficiently calculate binomial coefficients,I was looking at how you solve binomial coefficients in this package; @stdlib/math-base-special-binomcoef, and was wondering if a solution such as this would be better?
```ts
function binomialCoefficientLog(n, k) {
if (k > n) return 0;
if (k === 0 || k === n) return 1;
let logSum = 0;
for (let i = 0; i < k; i++) {
logSum += Math.log(n - i) - Math.log(i + 1);
}
return Math.exp(logSum);
}
```
This basically breaks it down to it's most simplest form (with log for maintaining precision) by stopping the loop once we reach k, so only calculating necessary values. Basically O(k) time complexity and O(1) space complexity.
Obviously error handling would need to be added but in a nutshell this is what I was thinking.
コントリビューションガイド
調査の方向性
Start with @stdlib/math-base-special-binomcoef and inspect how it currently calculates binomial coefficients. Compare the proposed O(k) time and O(1) space approach, including precision and error handling, then determine whether a change is warranted. Done means the implementation is improved without losing correctness, with relevant validation for the supported inputs.
索引モデルが issue の本文から書いたものです。
評価
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- javascript
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- performance
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