[bit.permute] Create notation for the popcount of the first n bits.#9181
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This avoids having to put a complex expression into sub- and superscripts in the definitions of "expand" and "compress".
eisenwave
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Jul 15, 2026
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| \pnum | ||
| In the following descriptions, | ||
| let $N$ denote the value of \tcode{numeric_limits<T>::digits}, and | ||
| let $N$ denote the value of \tcode{numeric_limits<T>::digits}, | ||
| let $\alpha_n$ denote the value of the $n^\text{th}$ least significant bit | ||
| in the base-2 representation of an integer $\alpha$, | ||
| so that $\alpha$ equals $\sum_{n=0}^{N-1} \alpha_n 2^n$. | ||
| so that $\alpha$ equals $\sum_{n=0}^{N-1} \alpha_n 2^n$, | ||
| and let $\sigma(\alpha, n) = \sum_{k=0}^{n-1} \alpha_k$ | ||
| be the count of one-bits among the lowest $n$ bits of $\alpha$. |
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If this is going to be three relatively complex items, maybe it this should be using bullets.
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Done as a separate commit. I'm not sure that it makes a big difference. (Generally, what helps make complex expressions more scannable is to put them in a displayed equation, but I don't really see any good opportunities for this here.)
jwakely
approved these changes
Jul 16, 2026
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This avoids having to put a complex expression into sub- and superscripts in the definitions of "expand" and "compress".