xsum

xsum.ipynb

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      "source": "a = sum(inv, 1:10^7)\nb = sum(inv, 10^7:-1:1)\nA = sum(inv∘big, 1:10^7)\nB = sum(inv∘big, 10^7:-1:1)\n\nc = sum(inv(k) for k in 1:10^7)\nd = sum(inv(k) for k in 10^7:-1:1)\nC = sum(inv(big(k)) for k in 1:10^7)\nD = sum(inv(big(k)) for k in 10^7:-1:1)\n\n@show a b c d A B C D",
      "execution_count": 1,
      "outputs": [
        {
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          "text": "a = 16.69531136585985\nb = 16.69531136585985\nc = 16.695311365857272\nd = 16.695311365859965\nA = 16.6953113658598518153991189395404518842498697523730804627851359543562886921754\nB = 16.69531136585985181539911893954045188424986975237308046278513595435628869217375\nC = 16.69531136585985181539911893954045188424986975237308046278513595435628869215495\nD = 16.69531136585985181539911893954045188424986975237308046278513595435628869218591\n",
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          "data": {
            "text/plain": "16.69531136585985181539911893954045188424986975237308046278513595435628869218591"
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    {
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      "cell_type": "code",
      "source": "using Xsum\nxsum(inv, 1:10^7)",
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 2,
          "data": {
            "text/plain": "16.69531136585985"
          },
          "metadata": {}
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      "cell_type": "code",
      "source": "?xsum",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": "search: \u001b[0m\u001b[1mx\u001b[22m\u001b[0m\u001b[1ms\u001b[22m\u001b[0m\u001b[1mu\u001b[22m\u001b[0m\u001b[1mm\u001b[22m \u001b[0m\u001b[1mX\u001b[22m\u001b[0m\u001b[1ms\u001b[22m\u001b[0m\u001b[1mu\u001b[22m\u001b[0m\u001b[1mm\u001b[22m\n\n",
          "name": "stdout"
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          "execution_count": 3,
          "data": {
            "text/plain": "\u001b[36m  xsum([f,] itr)\u001b[39m\n\n  Compute the exactly rounded double-precision sum of calling \u001b[36mf\u001b[39m (which\n  defaults to \u001b[36midentity\u001b[39m) on the elements of the iterable collection \u001b[36mitr\u001b[39m. That\n  is, return the sum as if (1) the elements of \u001b[36mf.(itr)\u001b[39m were converted to\n  double (\u001b[36mFloat64\u001b[39m) precision, (2) summed in \u001b[4minfinite\u001b[24m precision, and (3)\n  rounded to the closest double-precision value in the final result. Both real\n  and complex sums are supported.",
            "text/markdown": "```\nxsum([f,] itr)\n```\n\nCompute the exactly rounded double-precision sum of calling `f` (which defaults to `identity`) on the elements of the iterable collection `itr`. That is, return the sum as if (1) the elements of `f.(itr)` were converted to double (`Float64`) precision, (2) summed in *infinite* precision, and (3) rounded to the closest double-precision value in the final result.    Both real and complex sums are supported.\n",
            "text/latex": "\\begin{verbatim}\nxsum([f,] itr)\n\\end{verbatim}\nCompute the exactly rounded double-precision sum of calling \\texttt{f} (which defaults to \\texttt{identity}) on the elements of the iterable collection \\texttt{itr}. That is, return the sum as if (1) the elements of \\texttt{f.(itr)} were converted to double (\\texttt{Float64}) precision, (2) summed in \\emph{infinite} precision, and (3) rounded to the closest double-precision value in the final result.    Both real and complex sums are supported.\n\n"
          },
          "metadata": {}
        }
      ]
    },
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      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
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