{
  "$type": "site.standard.document",
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  "path": "/t/infinite-precision-intermediate-arithmetic-how-much-would-break/24383#post_20",
  "publishedAt": "2026-06-09T18:18:38.000Z",
  "site": "https://internals.rust-lang.org",
  "tags": [
    "1 + 2 + 3 + 4 + ... = -1/2"
  ],
  "textContent": "One reason that twos-complement ends up working well is that in the same sense as 1 + 2 + 3 + 4 + ... = -1/2, you can easily see that 1 + 2 + 4 + 8 + ... = -1:\n\n\n     S = 1 + 2 + 4 + 8 + ...\n\n    2S = 2 + 4 + 8 + 16 + ...\n\n    2S - S =       (2 + 4 + 8 + 16 + ...)\n             - (1 + 2 + 4 + 8 + ...)\n\n         S = -1\n\n\nand thus `0b111...111` being -1 is, in a sense, more mathematically correct than treating it as a sign-magnitude representation.\n\nSo infinite precision bitops are thus really not a problem at all.",
  "title": "Infinite precision intermediate arithmetic: how much would break?"
}