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Computation of Euler gamma by the method of Karatsuba (2000)
{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "# Euler定数のKaratsubaの方法による計算\n\n黒木玄\n\n2018-07-06"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "https://math.stackexchange.com/questions/129777/what-is-the-fastest-most-efficient-algorithm-for-estimating-eulers-constant-g\n \nで, Euler定数の計算に関するKaratsubaさんによる論文(2000)\n\nhttps://link.springer.com/article/10.1023%2FA%3A1019137125281\n\nが紹介されていた. その結論は次のセルの通り."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "showimg(mime, fn) = open(fn) do f\n base64 = base64encode(f)\n display(\"text/html\", \"\"\"<img src=\"data:$mime;base64,$base64\">\"\"\")\nend\nshowimg(\"text/png\", \"Karatsuba2000.png\")",
"execution_count": 1,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": "<img 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\">"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "この方法を最も素朴に書いたJulia言語のコードは次のセルの通り. 簡単に計算効率を上げることができるが, ここではあえて最も素朴なコードで済ませた場合にどうなるかを確認してみたい."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "function Karatsuba(K)\n k = big(K)\n g = 1 - log(k)*sum(r->(-1)^(r-1)*k^(r+1)/(factorial(r-1)*(r+1)), 1:12k+1)\n g = g + sum(r->(-1)^(r-1)*k^(r+1)/(factorial(r-1)*(r+1)^2), 1:12k+1)\nend\n\nfunction KaratsubaError(K)\n k = big(K)\n 2/factorial(big(2k))+2*k^2*e^(-k)\nend",
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 2,
"data": {
"text/plain": "KaratsubaError (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "setprecision(round(Int, 10/3*10))\nKaratsubaError(3000)",
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 3,
"data": {
"text/plain": "2.3541102338e-1296"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "setprecision(round(Int, 10/3*5000))\n@time g = Karatsuba(3000)\n@show g - eulergamma\ng",
"execution_count": 4,
"outputs": [
{
"output_type": "stream",
"text": " 92.248542 seconds (7.30 M allocations: 10.888 GiB, 0.88% gc time)\ng - eulergamma = 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"source": "round(g, 1298)-round(big(eulergamma), 1298)",
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"cell_type": "markdown",
"source": "1298桁まで正確に求めることができたようだ."
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"data": {
"description": "Computation of Euler gamma by the method of Karatsuba (2000)",
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