{"id":6254,"date":"2026-09-23T17:59:26","date_gmt":"2026-09-23T08:59:26","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=6254"},"modified":"2026-09-23T17:59:26","modified_gmt":"2026-09-23T08:59:26","slug":"13-1_rand","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/num\/13-1_rand\/","title":{"rendered":"13.1 \u4e00\u69d8\u4e71\u6570"},"content":{"rendered":"\n\u672c\u7bc0\u3067\u306f, \u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u4e71\u6570 (\u4e00\u69d8\u4e71\u6570) \u306e\u751f\u6210\u6cd5\u3092\u8aac\u660e\u3059\u308b.<\/p>\n<p>\u4e00\u69d8\u4e71\u6570\u3092\u751f\u6210\u3059\u308b\u969b\u306b\u306f, \u307e\u305a\u975e\u8ca0\u6574\u6570\u306e\u533a\u9593 [0, m) \u4e0a\u3067\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u6574\u6570\u4e71\u6570\u751f\u6210\u3059\u308b. \u6b21\u306b, \u5b9f\u6570\u4e71\u6570\u304c\u5fc5\u8981\u3067\u3042\u308c\u3070\u9069\u5f53\u306a\u533a\u9593\u306e\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306b\u5909\u63db\u3059\u308b\u306e\u304c\u4e00\u822c\u7684\u3067\u3042\u308b.<\/p>\n<h3>13.1.1 \u7dda\u5f62\u5408\u540c\u6cd5<\/h3>\n<p>\u53e4\u304f\u304b\u3089\u4f7f\u308f\u308c\u3066\u3044\u308b\u4e71\u6570\u751f\u6210\u6cd5\u306f\u7dda\u5f62\u5408\u540c\u6cd5\u3067\u3042\u308b.<\/p>\n<p>3 \u500b\u306e\u975e\u8ca0\u6574\u6570\u30d1\u30e9\u30e1\u30fc\u30bf\u3092 a, c \u304a\u3088\u3073 m \u3068\u3057, \\(0 \\le a < m, 0 \\le c < m\\) \u3068\u3059\u308b. a \u3092\u4e57\u6570, c \u3092\u5897\u5206, m \u3092\u6cd5\u3068\u3088\u3076. \u9069\u5f53\u306a\u521d\u671f\u5024 \\(X_0 (0 \\le X_0 < m)\\) \u3092\u9078\u3073, \u6b21\u306e\u6f38\u5316\u5f0f\u306b\u3088\u308a\u533a\u9593 [0, m) \u306e\u6574\u6570\u5217\u3092\u751f\u6210\u3059\u308b. \\(X_0\\) \u3092\u30b7\u30fc\u30c9\u3068\u3088\u3076.\n\\[\nX_{i+1} = (a X_i + c) \\space mod \\space m\n\\]\n\u30d1\u30e9\u30e1\u30fc\u30bf a, c \u304a\u3088\u3073 m \u3092\u9069\u5207\u306b\u9078\u3076\u3068\u4e71\u6570\u5217\u304c\u5f97\u3089\u308c\u308b. \u3053\u306e\u65b9\u6cd5\u3067\u306f\u540c\u3058\u30b7\u30fc\u30c9 \\(X_0\\) \u304b\u3089\u306f\u540c\u3058\u4e71\u6570\u5217\u304c\u5f97\u3089\u308c\u308b. \u3059\u306a\u308f\u3061, \u6700\u9577\u3067 m \u306e\u5468\u671f\u3067\u540c\u3058\u6570\u5217\u3092\u7e70\u308a\u8fd4\u3059\u3053\u3068\u306b\u306a\u308b.\n\n\n\n<h4>13.1.1.1 \u6cd5 m \u306e\u9078\u3073\u65b9<\/h4>\n<p>\u4e71\u6570\u751f\u6210\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u3057\u3066\u306f\u5468\u671f\u306f\u3067\u304d\u308b\u3060\u3051\u9577\u3044\u65b9\u304c\u3088\u3044. \u3068\u3053\u308d\u304c\u5468\u671f\u306f m \u3088\u308a\u5927\u304d\u304f\u306f\u306a\u3089\u306a\u3044\u304b\u3089, \u307e\u305a\u306f\u3067\u304d\u308b\u3060\u3051\u5927\u304d\u306a m \u3092\u9078\u3073\u305f\u3044.<\/p>\n<p>\u4e71\u6570\u306e\u751f\u6210\u901f\u5ea6\u3092\u8003\u3048\u308b\u3068, \u4f8b\u3048\u3070 32 \u30d3\u30c3\u30c8\u7b26\u53f7\u306a\u3057\u6574\u6570\u3067\u3042\u308c\u3070 m = \\(2^{32}\\) (\\(2^{\u30ef\u30fc\u30c9\u9577}\\)) \u3068\u3059\u308b\u306e\u304c\u3088\u3055\u305d\u3046\u3067\u3042\u308b. \u305d\u3046\u3059\u308b\u3068, \u6642\u9593\u304c\u304b\u304b\u308b\u6f14\u7b97\u3067\u3042\u308b mod m \u306e\u305f\u3081\u306e\u9664\u7b97\u3092\u7701\u304f\u3053\u3068\u304c\u3067\u304d\u308b. \u4f8b\u3068\u3057\u3066, C \u8a00\u8a9e\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4ee5\u4e0b\u306b\u793a\u3059 (unsigned int \u578b\u306f 32 \u30d3\u30c3\u30c8\u306e\u30c7\u30fc\u30bf\u3068\u3059\u308b).<\/p>\n<div class=\"hcb_wrap\">\n<pre class=\"prism line-numbers lang-c\" data-lang=\"C\"><code>#define A\t69069\r\n#define C\t4243209856\r\n\r\nunsigned int ex_rand(unsigned int *x) {\r\n    *x = *x * A + C;\r\n    return *x;\r\n}<\/code><\/pre>\n<\/div>\n<p>x \u306b\u30b7\u30fc\u30c9 (\u521d\u671f\u5024) \u3092\u5165\u308c\u3066\u547c\u3073\u51fa\u305b\u3070\u4e71\u6570\u5217\u3092\u751f\u6210\u3059\u308b.<\/p>\n<p>\u30b3\u30fc\u30c9\u4e0a\u3067\u306f\u7279\u306b mod m \u306e\u8a08\u7b97\u3092\u884c\u3063\u3066\u3044\u306a\u3044\u304c, *x * A + C \u306e\u8a08\u7b97\u3092\u884c\u3063\u305f\u3068\u304d\u306b \\(2^{32}\\) \u3092\u8d85\u3048\u3066\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u3057\u3066\u3082\u7121\u8996\u3057\u3066\u8a08\u7b97\u3092\u7d9a\u884c\u3059\u308b\u305f\u3081, \u4e8b\u5b9f\u4e0a mod \\(2^{32}\\) \u306e\u8a08\u7b97\u3092\u884c\u3063\u3066\u3044\u308b\u306e\u3068\u540c\u3058\u306b\u306a\u308b.<\/p>\n<p>\u7dda\u5f62\u5408\u540c\u6cd5\u3067\u6ce8\u610f\u3059\u3079\u304d\u70b9\u3068\u3057\u3066\u4e0b\u4f4d\u30d3\u30c3\u30c8\u306e\u975e\u30e9\u30f3\u30c0\u30e0\u6027\u304c\u3042\u308b. \u3053\u3053\u3067, d \u304c m \u306e\u56e0\u5b50\u3067\u3042\u308b\u3082\u306e\u3068\u3057\u3066, \u6b21\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3068\u3059\u308b.<br \/>\n\\[<br \/>\nY_n = X_n \\space mod \\space d<br \/>\n\\]\n\u305d\u3046\u3059\u308b\u3068, \u6b21\u5f0f\u3082\u6210\u308a\u7acb\u3064.<br \/>\n\\[<br \/>\nY_{n+1} = (a Y_n + c) \\space mod \\space d<br \/>\n\\]\n\u3059\u306a\u308f\u3061, \u5c0f\u3055\u306a\u56e0\u5b50 d \u3092\u6301\u3064 m \u306e\u5834\u5408, \u4e71\u6570\u5217\u306e\u4e0b\u4f4d d \u30d3\u30c3\u30c8\u306f\u77ed\u3044\u5468\u671f\u3067\u540c\u3058\u5024\u3092\u7e70\u308a\u8fd4\u3059\u305f\u3081\u30e9\u30f3\u30c0\u30e0\u6027\u304c\u4f4e\u3044.<\/p>\n<p>m = \\(2^{32}\\) \u306e\u5834\u5408\u306b\u306f d = 2, 4, 8, &#8230; \u3068\u306a\u308a\u3046\u308b\u304b\u3089\u4e0b\u4f4d\u6570\u30d3\u30c3\u30c8\u306f\u304b\u306a\u308a\u898f\u5247\u7684\u306b\u306a\u308b. \u7279\u306b\u6700\u7d42\u30d3\u30c3\u30c8\u306f 0, 1 \u3092\u7e70\u308a\u8fd4\u3059\u304b 0 \u307e\u305f\u306f 1 \u306e\u5b9a\u6570\u306b\u306a\u308b.<\/p>\n<p>\u4e0a\u306e C \u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u30b7\u30fc\u30c9\u3092 13 \u3068\u3057\u3066\u4e71\u6570\u3092\u751f\u6210\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f. \u5de6\u304b\u3089, \u751f\u6210\u3055\u308c\u305f\u4e71\u6570, mod 2 \u3068\u3057\u305f\u5834\u5408, mod 8 \u3068\u3057\u305f\u5834\u5408\u3092\u793a\u3059.<\/p>\n<pre>\r\n4244107753  1  1\r\n 413715221  1  5\r\n 427421521  1  1\r\n2215051101  1  5\r\n 282686713  1  1\r\n4210462437  1  5\r\n 142691553  1  1\r\n2856139693  1  5\r\n2812793097  1  1\r\n2498959285  1  5\r\n<\/pre>\n<p>&nbsp;<br \/>\n\u6700\u7d42\u30d3\u30c3\u30c8\u306f\u5e38\u306b 1 \u3068\u306a\u3063\u3066\u3044\u308b. mod 8 \u3067\u3082\u5468\u671f\u306f 2 \u3067\u3042\u308b.<\/p>\n<p>\u4e00\u65b9, m \u3068\u3057\u3066\u5927\u304d\u306a\u7d20\u6570\u3092\u9078\u3079\u3070, \u4e0b\u4f4d\u5074\u3082\u542b\u3081\u3066\u30e9\u30f3\u30c0\u30e0\u306a\u6570\u5217\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u305d\u3046\u3067\u3042\u308b\u304c\u3053\u308c\u306f\u5f8c\u3067\u8ff0\u3079\u308b\u5225\u306e\u554f\u984c\u304c\u3042\u308b.<\/p>\n<p>\u3057\u304b\u3057\u306a\u304c\u3089, \u5b9f\u6570\u4e71\u6570 (\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570 ) \u306b\u5909\u63db\u3057\u3066\u4f7f\u3046\u5834\u5408\u306a\u3069, \u591a\u304f\u306e\u5fdc\u7528\u3067\u306f\u4e0b\u4f4d\u5074\u306e\u898f\u5247\u6027\u306f\u554f\u984c\u306b\u306a\u3089\u306a\u3044\u305f\u3081, \u5b9f\u88c5\u4e0a\u306f m = \\(2^{\u30ef\u30fc\u30c9\u9577}\\) \u304c\u3088\u304f\u4f7f\u308f\u308c\u308b. \u305f\u3060\u3057, \u4f7f\u7528\u3059\u308b\u5074\u304c\u4ee5\u4e0a\u306e\u3053\u3068\u3092\u7406\u89e3\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308b.<\/p>\n<h4>13.1.1.2 \u4e57\u6570 a \u304a\u3088\u3073\u5897\u5206 c \u306e\u9078\u3073\u65b9<\/h4>\n<p>\u5927\u304d\u306a m \u3092\u4f7f\u7528\u3057\u305f\u3068\u3057\u3066, \u5468\u671f\u304c\u6700\u9577\u306e\u5024 m \u3068\u306a\u308b\u305f\u3081\u306e a \u3068 c \u306e\u9078\u3073\u65b9\u306e\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n<ul>\n<li>c \u3068 m \u306f\u4e92\u3044\u306b\u7d20\u3067\u3042\u308b<\/li>\n<li>m \u306e\u7d20\u56e0\u6570 p \u306b\u5bfe\u3057 a = 1 (mod p) \u3067\u3042\u308b<\/li>\n<li>m \u304c 4 \u306e\u500d\u6570\u306e\u3068\u304d\u306f a = 1 (mod 4) \u3067\u3042\u308b<\/li>\n<\/ul>\n<p>\u3053\u308c\u304b\u3089, m \u3092\u7d20\u6570\u3068\u3057\u305f\u3068\u304d\u306b\u306f, \u6700\u9577\u5468\u671f m \u3068\u3059\u308b a \u306f 1 \u306e\u307f\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b. \u3053\u308c\u306f \\(X_{i+1} = (X_i + c) \\space mod \\space m\\) \u3068\u306a\u308a\u30e9\u30f3\u30c0\u30e0\u306a\u6570\u5217\u306b\u306f\u306a\u3089\u306a\u3044.<\/p>\n<p>\u7dda\u5f62\u5408\u540c\u6cd5\u306b\u304a\u3044\u3066 c = 0 \u3068\u3057\u305f\u3082\u306e\u3092\u4e57\u6cd5\u5408\u540c\u6cd5\u3068\u3088\u3076.<br \/>\n\\[<br \/>\nX_{i+1} = a X_i \\space mod \\space m<br \/>\n\\]\n\u4e0a\u306e\u6761\u4ef6\u3088\u308a, \u4e57\u6cd5\u5408\u540c\u6cd5\u3067\u306f\u6700\u9577\u5468\u671f m \u306f\u9054\u6210\u3067\u304d\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308b.<\/p>\n<p>m = \\(2^e\\) (e &ge; 4) \u306e\u5834\u5408\u306e\u4e57\u6cd5\u5408\u540c\u6cd5\u306e\u6700\u9577\u5468\u671f\u306f\u6b21\u306e\u6761\u4ef6\u306e\u3082\u3068\u3067 \\(2^{e-2}\\) \u306b\u306a\u308b.<\/p>\n<ul>\n<li>\\(X_0\\) \u3068 m \u304c\u4e92\u3044\u306b\u7d20\u3067\u3042\u308b<\/li>\n<li>a mod 8 \u304c 3 \u307e\u305f\u306f 5 \u3067\u3042\u308b<\/li>\n<\/ul>\n<h4>13.1.1.3 \u7dda\u5f62\u5408\u540c\u6cd5\u306e\u30b7\u30fc\u30c9<\/h4>\n<p>\u6700\u9577\u5468\u671f\u3092\u9054\u6210\u3057\u3066\u3044\u306a\u3044\u5834\u5408\u306b\u306f\u30b7\u30fc\u30c9\u306e\u5024\u306b\u5236\u9650\u304c\u4ed8\u304f. \u3053\u308c\u306f, \u9054\u6210\u3055\u308c\u308b\u5468\u671f (< m) \u306e\u6570\u5217\u306b\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u5024\u3092\u30b7\u30fc\u30c9\u306b\u3057\u3066\u306f\u3044\u3051\u306a\u3044\u305f\u3081\u3067\u3042\u308b.\n\n\u4f8b\u3048\u3070, m \u304c 2 \u306e\u7d2f\u4e57\u306e\u4e57\u6cd5\u5408\u540c\u6cd5\u3067\u306f\u6700\u826f\u306e\u5468\u671f\u3067\u3082 m\/4 \u3067\u3042\u308b\u304b\u3089\u30b7\u30fc\u30c9\u306b\u306f\u5236\u9650\u304c\u3042\u308b. \u7279\u306b\u30b7\u30fc\u30c9\u3092 0 \u306b\u3067\u304d\u306a\u3044\u3053\u3068\u306f\u660e\u3089\u304b\u3067\u3042\u308b\u304b\u3089, \u4e57\u6cd5\u5408\u540c\u6cd5\u3067\u5f97\u3089\u308c\u308b\u4e71\u6570\u5217\u306b\u306f 0 \u306f\u542b\u307e\u308c\u306a\u3044\u3053\u3068\u306b\u306a\u308b. \u3053\u306e\u5834\u5408, \u30b7\u30fc\u30c9\u306f\u5947\u6570\u306b\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u304f\u3066, \u751f\u6210\u3055\u308c\u308b\u4e71\u6570\u3082\u5947\u6570\u3067\u3042\u308b.\n\n\n\n<h4>13.1.1.4 \u7dda\u5f62\u5408\u540c\u6cd5\u306e\u5b9f\u88c5\u4f8b<\/h4>\n<p>\u3053\u3053\u307e\u3067, \u6700\u9577\u5468\u671f\u306b\u306a\u308b a, c \u304a\u3088\u3073 m \u306e\u9078\u3073\u65b9\u3092\u898b\u3066\u304d\u305f\u304c, \u3053\u308c\u3060\u3051\u3067\u306f\u30e9\u30f3\u30c0\u30e0\u306b\u3059\u308b\u305f\u3081\u306e\u5341\u5206\u6761\u4ef6\u306b\u306f\u306a\u3089\u306a\u3044. \u5b9f\u969b\u306b\u3069\u3046\u3084\u308b\u3068\u826f\u3044\u3082\u306e\u3092\u9078\u3079\u308b\u304b\u306f\u96e3\u3057\u3044\u554f\u984c\u3067\u3042\u308b\u304c, \u53c2\u8003\u307e\u3067\u306b\u65e2\u5b58\u306e\u4e71\u6570\u751f\u6210\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u8abf\u3079\u3066\u307f\u308b.<\/p>\n<p>\u4e0b\u8868\u306b\u7dda\u5f62\u5408\u540c\u6cd5\u306b\u3088\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u4f8b\u3092\u793a\u3059.<br \/>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tr>\n<td>\u30d7\u30ed\u30b0\u30e9\u30e0<\/td>\n<td>\u6a5f\u7a2e<\/td>\n<td>m<\/td>\n<td>a<\/td>\n<td>c<\/td>\n<td>\u5468\u671f<\/td>\n<\/tr>\n<tr>\n<td>RANDU<\/td>\n<td>IBM 360\/370<\/td>\n<td>2<sup>31<\/sup><\/td>\n<td>65539 (= 2<sup>16<\/sup> + 3)<\/td>\n<td>0<\/td>\n<td>2<sup>29<\/sup><\/td>\n<\/tr>\n<tr>\n<td>Unix rand<\/td>\n<td>Unix (V7 \u306a\u3069)<\/td>\n<td>2<sup>31<\/sup><\/td>\n<td>1103515245<\/td>\n<td>12345<\/td>\n<td>2<sup>31<\/sup><\/td>\n<\/tr>\n<tr>\n<td>rand (\u6a19\u6e96 C)<\/td>\n<td>Windows (Visual C\/C++ \u306a\u3069)<\/td>\n<td>2<sup>31<\/sup><\/td>\n<td>214013<\/td>\n<td>2531011<\/td>\n<td>2<sup>31<\/sup> (\u305f\u3060\u3057, RAND_MAX = 2<sup>15<\/sup> &#8211; 1)<\/td>\n<\/tr>\n<tr>\n<td>rand48<\/td>\n<td>Unix (System V \u306a\u3069)<\/td>\n<td>2<sup>48<\/sup><\/td>\n<td>25214903917<\/td>\n<td>11<\/td>\n<td>2<sup>48<\/sup><\/td>\n<\/tr>\n<tr>\n<td>Rnd<\/td>\n<td>Excel VBA<\/td>\n<td>2<sup>24<\/sup><\/td>\n<td>16598013<\/td>\n<td>12820163<\/td>\n<td>2<sup>24<\/sup><\/td>\n<\/tr>\n<\/table>\n<\/div>\n<h4>RANDU<\/h4>\n<p>IBM 360\/370 \u30e1\u30a4\u30f3\u30d5\u30ec\u30fc\u30e0\u3067\u5e83\u304f\u4f7f\u308f\u308c\u305f RANDU (FORTRAN \u95a2\u6570) \u306f c = 0 \u3092\u4f7f\u7528\u3059\u308b\u4e57\u6cd5\u5408\u540c\u6cd5\u3067\u3042\u308b. a mod 8 = 3 \u3068\u306a\u3063\u3066\u304a\u308a, \u4e57\u6cd5\u5408\u540c\u6cd5\u306e\u6700\u5927\u5468\u671f 2<sup>31-2<\/sup> \u3092\u9054\u6210\u3057\u3066\u3044\u308b. \u3057\u304b\u3057, \u3053\u306e a \u306e\u5024\u3067\u306f \\(X_{k+2} = 6X_{k+1} &#8211; 9X_k (modulo \\space 2^{31})\\) \u304c\u6210\u308a\u7acb\u3061, \u751f\u6210\u3055\u308c\u308b\u4e71\u6570\u5217\u306e\u5f15\u304d\u7d9a\u304f 3 \u500b\u306e\u9593\u306b\u9ad8\u3044\u76f8\u95a2\u304c\u751f\u3058\u308b\u3068\u3044\u3046\u554f\u984c\u304c\u898b\u3064\u304b\u3063\u3066\u3044\u308b. \u307e\u305f, a \u304c\u5947\u6570, c = 0 \u3067\u3042\u308b\u304b\u3089, \u5947\u6570\u306e\u521d\u671f\u5024\u3067\u306f\u5947\u6570\u3060\u3051\u304c\u751f\u6210\u3055\u308c, \u5076\u6570\u306e\u521d\u671f\u5024\u3067\u306f\u5076\u6570\u3060\u3051\u304c\u751f\u6210\u3055\u308c\u308b.<\/p>\n<h4>Unix rand<\/h4>\n<p>rand \u95a2\u6570\u306f \u53e4\u3044 Unix (V7 \u306a\u3069) \u304b\u3089\u4f7f\u308f\u308c\u3066\u3044\u308b\u95a2\u6570\u3067\u3042\u308b. 32 \u30d3\u30c3\u30c8\u6f14\u7b97\u3092\u884c\u3046\u304c, \u4e0b\u4f4d\u30d3\u30c3\u30c8\u306e\u898f\u5247\u6027\u306e\u554f\u984c\u3092\u907f\u3051\u308b\u305f\u3081\u306b, \u7b26\u53f7\u3092\u9664\u3044\u3066\u4e0a\u4f4d 15 \u30d3\u30c3\u30c8\u304c\u8fd4\u3055\u308c\u308b. a = 1103515245 (= 3<sup>5<\/sup> x 5 x 7 x 129749) \u3068 c = 12345 (= 3 x 5 823) \u306f\u6700\u9577\u5468\u671f\u3068\u306a\u308b\u6761\u4ef6\u3092\u6e80\u305f\u3059.<\/p>\n<h4>\u6a19\u6e96 C\/C++ rand<\/h4>\n<p>Unix rand \u3068\u540c\u540d\u306e\u95a2\u6570\u304c\u6a19\u6e96 C\/C++ \u306b\u3082\u898f\u5b9a\u3055\u308c\u3066\u304a\u308a\u73fe\u4ee3\u306e C\/C++ \u30b3\u30f3\u30d1\u30a4\u30e9\u30fc\u306b\u3082\u3042\u308b. \u6a19\u6e96 C\/C++ \u3067\u306f\u5b9f\u88c5\u306f\u30b3\u30f3\u30d1\u30a4\u30e9\u30fc\u4f9d\u5b58\u3067, \u6574\u6570\u4e71\u6570\u306e\u6700\u5927\u5024\u304c RAND_MAX \u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3053\u3068\u306b\u306a\u3063\u3066\u3044\u308b.<\/p>\n<p>Windows \u3067\u306f RAND_MAX = 2<sup>15<\/sup> &#8211; 1 (Visual C\/C++ \u306a\u3069) \u3067, Unix rand \u3068\u4f3c\u3066\u3044\u308b\u304c a \u3068 c \u306e\u5024\u306f\u7570\u306a\u308a, a = 214013 (= 17 x 12589) \u3068 c = 2531011 (= 7 x 17 x 21269) \u3067, \u6700\u9577\u5468\u671f\u3068\u306a\u308b\u6761\u4ef6\u3092\u6e80\u305f\u3059.<\/p>\n<p>\u73fe\u4ee3\u306e Linux (glibc) \u3067\u306f RAND_MAX = 2<sup>31<\/sup> &#8211; 1 \u3068\u5b9a\u7fa9\u3055\u308c, \u5b9f\u969b\u306b\u306f\u5f8c\u8ff0\u306e random \u304c\u547c\u3073\u51fa\u3055\u308c\u308b.<\/p>\n<h4>rand48<\/h4>\n<p>Unix (System V \u306a\u3069) \u306b\u304a\u3044\u3066 rand \u306e\u5f8c\u7d99\u3068\u3057\u3066\u4f7f\u308f\u308c\u3066\u304d\u305f rand48 \u306f, m = 2<sup>48<\/sup> \u3068\u3057\u3066\u5468\u671f\u3092\u9577\u304f\u3068\u3063\u305f\u3082\u306e\u3067\u3042\u308b\u304c, \u9577\u3044\u30d3\u30c3\u30c8\u9577\u306e\u4e57\u7b97\u304c\u5fc5\u8981\u306a\u305f\u3081\u8a08\u7b97\u901f\u5ea6\u306f\u3084\u3084\u9045\u304f\u306a\u308b. a = 25214903917 (= 7 x 443 x 739 x 11003) \u3068 c = 11 \u306f\u6700\u9577\u5468\u671f\u3068\u306a\u308b\u6761\u4ef6\u3092\u6e80\u305f\u3059.<\/p>\n<h4>Rnd<\/h4>\n<p>VBA (Excel) \u306e Rnd \u3067\u306f m = 2<sup>24<\/sup> \u3067\u3042\u308b. a = 16598013 (= 3 x 227 x 24373) \u3068 c = 12820163 (= 2293 x 5591) \u306f\u6700\u9577\u5468\u671f\u3068\u306a\u308b\u6761\u4ef6\u3092\u6e80\u305f\u3059.<\/p>\n<h3>13.1.2 \u30e9\u30b0\u4ed8\u304d\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6cd5<\/h3>\n<p>\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306f\u6b21\u306e\u6f38\u5316\u5f0f\u3067\u751f\u6210\u3055\u308c\u308b.<br \/>\n\\[<br \/>\nX_i = (X_{i-1} + X_{i-2}) \\space \u305f\u3060\u3057, X_1 = X_2 = 1<br \/>\n\\]\n\u3053\u308c\u306b\u300c\u30e9\u30b0\u300d\u3092\u6301\u305f\u305b\u305f\u6b21\u306e\u6f38\u5316\u5f0f\u3067\u751f\u6210\u3055\u308c\u308b\u6570\u5217\u3092\u30e9\u30b0\u4ed8\u304d\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u3068\u3088\u3076.<br \/>\n\\[<br \/>\nX_i = (X_{i-k} + X_{i-l}) mod m, \\space i \\ge k (k > l)<br \/>\n\\]\nk \u3068 l \u3092\u30e9\u30b0 (\u9045\u308c) \u3068\u3088\u3076. \u3053\u306e\u6570\u5217\u3067\u306f, m = 2<sup>e<\/sup> \u306e\u5834\u5408\u306e\u5468\u671f\u304c 2<sup>(e-1)<\/sup>(2<sup>k<\/sup> &#8211; 1) \u3068\u5927\u304d\u306a\u5024\u306b\u306a\u308b (l, k) \u5bfe\u304c\u77e5\u3089\u308c\u3066\u304a\u308a, \u6b21\u306e\u3088\u3046\u306a\u3082\u306e\u304c\u3042\u308b.<br \/>\n\\[<br \/>\n(24, 55), (38, 89),(37, 100), (30, 127), (83, 258), (107, 378), (273, 607), \\dots<br \/>\n\\]\n\u3053\u306e\u6570\u5217\u306e\u7279\u9577\u306f, \u5468\u671f\u304c\u9577\u304f, \u7dda\u5f62\u5408\u540c\u6cd5\u3068\u9055\u3044\u639b\u3051\u7b97\u3092\u542b\u307e\u306a\u3044\u306e\u3067\u8a08\u7b97\u901f\u5ea6\u7684\u306b\u6709\u5229\u306a\u3053\u3068\u3067\u3042\u308b. \u305f\u3060\u3057, \u751f\u6210\u3055\u308c\u308b\u6570\u5217\u306e\u30e9\u30f3\u30c0\u30e0\u6027\u306e\u7406\u8ad6\u306f\u3088\u304f\u308f\u304b\u3063\u3066\u3044\u306a\u3044.<\/p>\n<h4>Knuth \u306e ran_array<\/h4>\n<p>Knuth \u306e ran_array \u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 (\u6587\u732e [1]) \u3067\u306f, l = 37, k = 100, m = 2<sup>30<\/sup> \u3092\u63a1\u7528\u3057\u3066\u304a\u308a, \u5468\u671f\u306f\u304a\u304a\u3088\u305d 2<sup>129<\/sup> \u3067\u3042\u308b. \u305f\u3060\u3057, \u6b21\u306e\u3088\u3046\u306b\u8db3\u3057\u7b97\u3067\u306f\u306a\u304f\u5f15\u304d\u7b97\u3092\u4f7f\u3046.<br \/>\n\\[<br \/>\nX_i = (X_{i-k} &#8211; X_{i-l}) \\space mod \\space m<br \/>\n\\]\n\u3053\u308c\u3092\u4f7f\u3046\u969b\u306b\u306f, 1009 \u500b\u306e\u4e71\u6570\u3092\u751f\u6210\u3057, \u305d\u306e\u3046\u3061\u6700\u521d\u306e 100 \u500b\u3060\u3051\u3092\u63a1\u7528\u3059\u308b\u3053\u3068\u304c\u63a8\u5968\u3055\u308c\u3066\u3044\u308b.<\/p>\n<h4>Unix \u306e random<\/h4>\n<p>Unix (BSD \u306a\u3069) \u306b\u306f rand \u3068 rand48 \u306e\u4ed6\u306b random \u3068\u3044\u3046\u95a2\u6570\u304c\u3042\u308b\u304c, \u305d\u306e\u5b9f\u88c5\u306b\u306f\u3053\u306e\u65b9\u6cd5\u304c\u4f7f\u308f\u308c\u3066\u3044\u308b.<\/p>\n<p>\\(X_i\\) \u306e\u904e\u53bb\u5024\u3092\u4fdd\u6301\u3059\u308b\u30d0\u30c3\u30d5\u30a1\u306e\u30b5\u30a4\u30ba\u3092 8, 32, 64, 128 \u307e\u305f\u306f 256 \u30d0\u30a4\u30c8\u306b\u8a2d\u5b9a\u3067\u304d\u308b (5 \u7a2e\u985e\u306e\u52d5\u4f5c\u30e2\u30fc\u30c9\u3092\u9078\u629e\u3067\u304d\u308b). \u30c7\u30d5\u30a9\u30eb\u30c8\u5024\u306f 128 \u30d0\u30a4\u30c8\u3067, \u305d\u306e\u3068\u304d\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306f l = 3, k = 31, m = 2<sup>31<\/sup> \u3067, \u5468\u671f\u306f 16 x (2<sup>31<\/sup> &#8211; 1) \u3068\u306a\u308b.<\/p>\n<p>\u30d0\u30c3\u30d5\u30a1 (\u904e\u53bb\u5024) \u306e\u521d\u671f\u5316\u306b\u306f\u53e4\u3044 rand \u304c\u4f7f\u308f\u308c\u3066\u3044\u308b. \u306a\u304a, \u30d0\u30c3\u30d5\u30a1\u30b5\u30a4\u30ba\u304c 8 \u30d0\u30a4\u30c8\u306e\u5834\u5408\u306b\u306f\u7dda\u5f62\u5408\u540c\u6cd5\u304c\u4f7f\u7528\u3055\u308c, \u53e4\u3044 rand \u3068\u540c\u3058\u52d5\u4f5c\u3092\u3059\u308b (\u305f\u3060\u3057, RAND_MAX = 2<sup>31<\/sup> &#8211; 1 \u3067\u3042\u308b).<\/p>\n<h3>13.1.3 \u30e1\u30eb\u30bb\u30f3\u30cc\u30fb\u30c4\u30a4\u30b9\u30bf\u30fc (MT)<\/h3>\n<p>\u8d85\u9577\u5468\u671f\u3067\u7d71\u8a08\u7684\u6027\u8cea\u304c\u3088\u3044\u7591\u4f3c\u4e71\u6570\u751f\u6210\u5668\u3067\u3042\u308b. \u5177\u4f53\u4f8b\u3068\u3057\u3066\u63d0\u793a\u3055\u308c\u305f MT19937  (\u5468\u671f 2<sup>19937<\/sup> &#8211; 1) \u306f\u975e\u5e38\u306b\u9ad8\u901f\u3067\u3042\u308b. \u3053\u308c\u306f, Python \u3084 C++11 \u306a\u3069\u3067\u6a19\u6e96\u4e71\u6570\u751f\u6210\u5668\u3068\u3057\u3066\u63a1\u7528\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3067\u3082\u77e5\u3089\u308c\u3066\u3044\u308b.<\/p>\n<p>\u4ee5\u4e0b, \u305d\u306e\u539f\u7406\u306e\u5927\u96d1\u628a\u306a\u8aac\u660e\u3092\u8a66\u307f\u308b\u304c, LFSR, GFSR, TGFSR \u305d\u3057\u3066 MT \u3068\u6bb5\u968e\u7684\u306b\u9032\u3081\u308b.<\/p>\n<h4>13.1.3.1 LFSR (\u7dda\u5f62\u5e30\u9084\u30b7\u30d5\u30c8\u30ec\u30b8\u30b9\u30bf)<\/h4>\n<p>\\(a_i\\) \u306f\u5024\u304c 0 \u307e\u305f\u306f 1 \u306e p \u500b\u306e\u30d3\u30c3\u30c8\u5217\u3068\u3059\u308b.<br \/>\n\\[<br \/>\na_0, a_1, a_2, \\dots, a_{p-1}<br \/>\n\\]\n\u3053\u308c\u3089\u3092\u3059\u3079\u3066\u304c 0 \u3067\u306f\u306a\u3044\u3088\u3046\u306b\u4efb\u610f\u306b 0 \u307e\u305f\u306f 1 \u306b\u521d\u671f\u5316\u3057\u3066\u304a\u304d, i &ge; p \u3068\u3057\u3066\u6b21\u306e\u6f38\u5316\u5f0f\u306b\u3088\u308a\u30d3\u30c3\u30c8\u5217\u3092\u751f\u6210\u3059\u308b.<br \/>\n\\[<br \/>\na_i = c_1 a_{i-1} + c_2 a_{i-2} + \\dots + c_p a_{i-p} \\space (modulo \\space 2)<br \/>\n\\]\n\u305f\u3060\u3057, \\(c_1, c_2, \\dots\\) \u306f 0 \u307e\u305f\u306f 1 \u306e\u4fc2\u6570\u3067\u3042\u308b.<\/p>\n<p>\u3053\u3053\u3067, \u6b21\u306e\u3088\u3046\u306a p \u6b21\u306e\u591a\u9805\u5f0f\u3092\u8003\u3048\u308b.<br \/>\n\\[<br \/>\n1 + c_1 x + c_2 x^2 + c_3 x^3 + \\dots + c_p x^p \\space (modulo \\space 2), \\space \u305f\u3060\u3057, c_p = 1<br \/>\n\\]\n\u3053\u308c\u304c p \u6b21\u306e\u539f\u59cb\u591a\u9805\u5f0f\u306b\u306a\u308b\u3088\u3046\u306b p \u304a\u3088\u3073\u4fc2\u6570\u3092\u9078\u3076\u3053\u3068\u304c\u3067\u304d\u3066, \u305d\u306e\u3068\u304d, \u30d3\u30c3\u30c8\u5217 \\(\\{ a_i \\}\\) \u306e\u5468\u671f\u306f 2<sup>p<\/sup> &#8211; 1 \u306b\u306a\u308b. \u3053\u306e\u3088\u3046\u306a\u30d3\u30c3\u30c8\u5217\u3092\u7dda\u5f62\u6700\u9577\u5468\u671f\u5217 (M \u7cfb\u5217) \u3068\u3088\u3076.<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u5f97\u3089\u308c\u308b\u30d3\u30c3\u30c8\u5217 \\(\\{ a_i \\}\\) \u304b\u3089\u30ef\u30fc\u30c9\u9577\u3076\u3093\u3092\u5207\u308a\u51fa\u3057\u3066\u4e71\u6570\u5217\u3068\u3059\u308b\u3082\u306e\u3092 LFSR (\u7dda\u5f62\u5e30\u9084\u30b7\u30d5\u30c8\u30ec\u30b8\u30b9\u30bf) \u751f\u6210\u5668\u3068\u3088\u3076.<\/p>\n<h4>3.1.3.2 GFSR (\u4e00\u822c\u5316\u5e30\u9084\u30b7\u30d5\u30c8\u30ec\u30b8\u30b9\u30bf)<\/h4>\n<p>\u3053\u3053\u3067 \\(\\{ a_i \\}\\) \u304b\u3089 w \u30d3\u30c3\u30c8\u3092\u53d6\u308a\u51fa\u3057\u305f\u6570\u5217 \\(\\{ x_i \\}\\) \u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3059\u308b.<br \/>\n\\[<br \/>\nx_i = ( a_{i+s_1} a_{i+s_2} \\dots a_{i+s_w} )<br \/>\n\\]\n\u305f\u3060\u3057, \\(x_i\\) \u306f 0 \u307e\u305f\u306f 1 \u306e\u8981\u7d20 w \u500b\u304b\u3089\u306a\u308b\u30d9\u30af\u30c8\u30eb\u3067, w \u30d3\u30c3\u30c8\u306e\u30ef\u30fc\u30c9\u3068\u6349\u3048\u3066\u3088\u3044.<\/p>\n<p>\\(s_1, s_2, \\dots, s_l\\) \u306f\u4e92\u3044\u306b\u72ec\u7acb\u3067 n \u3068\u306f\u7121\u95a2\u4fc2\u306a\u5b9a\u6570\u3067\u3042\u308b. \u305f\u3060\u3057, w = 32 (32 \u30d3\u30c3\u30c8\/\u30ef\u30fc\u30c9) \u306e\u5834\u5408\u306b\u306f \\(s_1 = 0, s_2 = 1, \\dots, s_32 = 31\\) \u3068\u3057\u3066\u3088\u3044\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b.<\/p>\n<p>\u3053\u306e\u3088\u3046\u306a\u6570\u5217 \\(\\{ x_i \\}\\) \u306f \\(\\{ a_i \\}\\) \u3068\u540c\u69d8\u306b\u6b21\u306e\u6f38\u5316\u5f0f\u3092\u6e80\u305f\u3059.<br \/>\n\\[<br \/>\nx_i = c_1 x_{i-1} + c_2 x_{i-2} + \\dots + c_p x_{i-p} \\space (modulo \\space 2), \\space \u305f\u3060\u3057, c_p = 1<br \/>\n\\]\n\u3053\u3053\u3067, \u4fc2\u6570 \\(c_i\\) \u3092 \\(c_q\\) \u3068 \\(c_p\\) (q &lt; p) \u4ee5\u5916\u306f\u3059\u3079\u3066 0 \u306b\u306a\u308b\u3088\u3046\u306b\u9078\u3076\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u6b21\u5f0f\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\nx_i = x_{i-q} + x_{i-p} \\space (modulo \\space 2)<br \/>\n\\]\n\u3053\u306e\u3088\u3046\u306a q \u3068 p \u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b.<\/p>\n<p>\u306a\u304a, modulo 2 \u3067\u306e + \u6f14\u7b97\u306f\u30d3\u30c3\u30c8\u3054\u3068\u306e XOR \u3067\u884c\u3046\u3053\u3068\u304c\u3067\u304d, \u6b21\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b. \u5b9f\u969b\u306b\u8a08\u7b97\u3092\u884c\u3046\u3068\u304d\u306b\u306f XOR \u6f14\u7b97\u306f\u304d\u308f\u3081\u3066\u9ad8\u901f\u3067\u3042\u308b.<br \/>\n\\[<br \/>\nx_i = x_{i-q} \\oplus x_{i-p} \\space (i = p, p+1, \\dots)<br \/>\n\\]\n\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u5f97\u3089\u308c\u308b\u6570\u5217\u3092\u4e71\u6570\u5217\u3068\u3057\u3066\u4f7f\u3046\u65b9\u6cd5\u306f GFSR (\u4e00\u822c\u5316\u5e30\u9084\u30b7\u30d5\u30c8\u30ec\u30b8\u30b9\u30bf) \u751f\u6210\u5668\u3068\u3088\u3070\u308c\u308b.<\/p>\n<p>\u306a\u304a, \u8ad6\u6587\u7b49\u3067\u306f (\u540c\u7b49\u306e) \u6b21\u5f0f\u3067\u8868\u3055\u308c\u308b\u3053\u3068\u304c\u591a\u3044\u3088\u3046\u3067\u3042\u308b.<br \/>\n\\[<br \/>\nx_{k+n} = x_{k+m} \\oplus x_k \\space (k = 0, 1, \\dots)<br \/>\n\\]\n\u305f\u3060\u3057, m \u304a\u3088\u3073 n \u306f\u6b63\u306e\u6574\u6570\u3067 n &gt; m \u3067\u3042\u308b.<\/p>\n<h4>3.1.3.3 TGFSR (\u306d\u3058\u308c (Twisted) \u4e00\u822c\u5316\u5e30\u9084\u30b7\u30d5\u30c8\u30ec\u30b8\u30b9\u30bf)<\/h4>\n<p>TGFSR \u306f, GFSR \u306e\u6f38\u5316\u5f0f\u3092\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u305f\u3082\u306e\u3067\u3042\u308b.<br \/>\n\\[<br \/>\nx_{k+n} = x_{k+m} \\oplus x_k A \\space (k = 0, 1, \\dots)<br \/>\n\\]\n\u305f\u3060\u3057, \\(A\\) \u306f\u8981\u7d20\u304c 0 \u307e\u305f\u306f 1 \u306e\u6b21\u306e\u3088\u3046\u306a w x w \u884c\u5217\u3067\u3042\u308b. w \u306f\u30ef\u30fc\u30c9\u9577\u3067\u3042\u308b.<br \/>\n\\[<br \/>\nA =<br \/>\n\\begin{pmatrix}<br \/>\n0 &#038; 1 \\\\<br \/>\n  &#038;  &#038; 1 \\\\<br \/>\n  &#038;  &#038;   &#038; \\ddots \\\\<br \/>\n  &#038;  &#038;   &#038;  &#038; 1 \\\\<br \/>\na_0 &#038; a_1 &#038; a_2 &#038; \\dots &#038; a_{w-2} &#038; a_{w-1} \\\\<br \/>\n\\end{pmatrix}<br \/>\n\\]\n\u3053\u306e\u884c\u5217\u306b\u5bfe\u3057\u3066\u306f, \u30b7\u30d5\u30c8\u6f14\u7b97\u3068 XOR \u306a\u3069\u306e\u30d3\u30c3\u30c8\u6f14\u7b97\u3092\u7528\u3044\u3066 \\(x_k A\\) \u3092\u9ad8\u901f\u306b\u8a08\u7b97\u3067\u304d\u308b. \u307e\u305f, \\(A\\) \u306e\u7279\u6027\u591a\u9805\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\n\\phi_A(t) = a_0 + a_1 t + a_2 t^2 + \\dots + a_{w-1}t^{w-1} + t^w<br \/>\n\\]\n\u3053\u3053\u3067, n, m \u304a\u3088\u3073 \\(\\phi_A(t)\\) \u3092, \\(\\phi_A\\) \u306e\u6b21\u6570\u304c w \u3067, \\(\\phi_A(t^n + t^m)\\) \u304c\u539f\u59cb\u591a\u9805\u5f0f\u306b\u306a\u308b\u3088\u3046\u306b\u9078\u3076\u3068, \u3053\u306e\u6f38\u5316\u5f0f\u306b\u3088\u308a\u751f\u6210\u3055\u308c\u308b\u6570\u5217\u306e\u5468\u671f\u306f \\(2^{nw} &#8211; 1\\) \u306b\u9054\u3059\u308b.<\/p>\n<p>TGFSR \u306b\u306f\u7d71\u8a08\u7684\u6027\u8cea\u4e0a\u306e\u554f\u984c\u304c\u898b\u3064\u304b\u3063\u3066\u304a\u308a, \u305d\u308c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u6570\u5217 \\(\\{x_i\\}\\) \u306b\u6b21\u306e\u5909\u63db\u3092\u65bd\u3057\u305f\u6570\u5217 \\(\\{z_i\\}\\) \u3092\u7528\u3044\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y = x \\oplus ((x << s) \\space AND \\space b) \\\\\n&#038; z = y \\oplus ((y << t) \\space AND \\space c) \\\\\n\\end{align}\n\\]\ns \u304a\u3088\u3073 t \u306f\u6574\u6570\u3067, 0 &ge; s, t &ge; w - 1 \u3067\u3042\u308b. b \u304a\u3088\u3073 c \u306f 1 \u30ef\u30fc\u30c9\u9577\u306e\u30d3\u30c3\u30c8\u30de\u30b9\u30af\u3067\u3042\u308b.\n\n\u3053\u308c\u3092\u30c6\u30f3\u30d1\u30ea\u30f3\u30b0\u3068\u3088\u3076.\n\n\n\n<h4>3.1.3.4 \u30e1\u30eb\u30bb\u30f3\u30cc\u30fb\u30c4\u30a4\u30b9\u30bf\u30fc (MT)<\/h4>\n<p>TGFSR \u306e\u6f38\u5316\u5f0f\u3092\u3055\u3089\u306b\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3059\u308b.<br \/>\n\\[<br \/>\nx_{k+n} = x_{k+m} \\oplus (x_k^u | x_{k+1}^l)A \\space (k = 0, 1, \\dots)<br \/>\n\\]\n\\((x_k^u | x_{k+1}^l)\\) \u306f \\(x_k\\) \u306e\u4e0a\u4f4d w \u2212 r \u30d3\u30c3\u30c8\u3068 \\(x_{k+1}\\) \u306e\u4e0b\u4f4d r \u30d3\u30c3\u30c8\u3092\u9023\u7d50\u3057\u305f\u884c\u30d9\u30af\u30c8\u30eb\u3092\u8868\u3059. \u305f\u3060\u3057, 0 &le; r &le; w &#8211; 1 \u3067\u3042\u308b. \u3053\u306e\u6f38\u5316\u5f0f\u306b\u3088\u308a\u751f\u6210\u3055\u308c\u308b\u6570\u5217\u306e\u6700\u5927\u5468\u671f\u306f \\(2^{nw-r} &#8211; 1\\) \u306b\u306a\u308b.<\/p>\n<p>\u307e\u305f, \u30c6\u30f3\u30d1\u30ea\u30f3\u30b0\u3092\u6b21\u306e\u3088\u3046\u306b\u5909\u66f4\u3059\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y = x \\oplus (x >> u) \\\\<br \/>\n&#038; y = y \\oplus ((y << s) \\space AND \\space b) \\\\\n&#038; y = y \\oplus ((y << t) \\space AND \\space c) \\\\\n&#038; z = y \\oplus (y >> l) \\\\<br \/>\n\\end{align}<br \/>\n\\]\nu \u304a\u3088\u3073 l \u306f\u6574\u6570\u3067\u3042\u308b.<\/p>\n<p>\u4ee5\u4e0a\u304b\u3089, \u5468\u671f\u306b\u95a2\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u306f w, n, m, r \u304a\u3088\u3073 a, \u30c6\u30f3\u30d1\u30ea\u30f3\u30b0\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306f l, u, s, t, b \u304a\u3088\u3073 c \u3067\u3042\u308b.<\/p>\n<p>\u3053\u308c\u3089\u3092\u3046\u307e\u304f\u5b9a\u3081\u305f\u5b9f\u88c5\u4f8b\u3068\u3057\u3066\u8ad6\u6587\u3067\u63d0\u793a\u3055\u308c\u305f MT19937 \u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u5024\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n<p>(w, n, m, r) = (32, 624, 397, 31)<br \/>\na = 9908B0DF<br \/>\nu = 11<br \/>\ns = 7, b = 9D2C5680<br \/>\nt = 15, c = EFC60000<br \/>\nl = 18<\/p>\n<p>\u5468\u671f\u306f 2<sup>nw-r<\/sup> &#8211; 1 = 2<sup>19937<\/sup> &#8211; 1 \u3067, \u3053\u308c\u306f\u30e1\u30eb\u30bb\u30f3\u30cc\u7d20\u6570\u3067\u3042\u308b.<\/p>\n<p>\u30db\u30fc\u30e0\u30da\u30fc\u30b8 (\u6587\u732e [4]) \u306b\u8a73\u3057\u3044\u8aac\u660e\u3068\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u63b2\u8f09\u3055\u308c\u3066\u3044\u308b. \u306a\u304a, \u8ad6\u6587\u767a\u8868\u5f8c\u3082\u958b\u767a\u304c\u7d99\u7d9a\u3055\u308c\u3066\u304a\u308a, \u305d\u306e\u5f8c\u306e\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u306b\u5bfe\u5fdc\u3057\u305f\u6539\u826f\u7248\u306e SFMT (SIMD-oriented Fast Mersenne Twister) \u304c 2007 \u5e74\u306b\u767a\u8868\u3055\u308c\u3066\u3044\u308b. \u307e\u305f, MT19937 \u306e 64 \u30d3\u30c3\u30c8\u7248\u3082\u767a\u8868\u3055\u308c\u3066\u3044\u308b.<\/p>\n<h3>13.1.4 \u4e71\u6570\u306e\u691c\u5b9a<\/h3>\n<p>\u751f\u6210\u3055\u308c\u305f\u4e71\u6570\u5217\u304c\u826f\u3044\u4e71\u6570\u5217\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\u3059\u308b\u305f\u3081\u306e\u691c\u5b9a\u6cd5\u306f\u591a\u6570\u63d0\u6848\u3055\u308c\u3066\u3044\u308b. Knuth \u306e\u672c (\u6587\u732e [1]) \u306b\u306f\u7a2e\u3005\u306e\u691c\u5b9a\u6cd5\u304c\u8a73\u3057\u304f\u89e3\u8aac\u3055\u308c\u3066\u3044\u308b. \u307e\u305f, \u3044\u304f\u3064\u304b\u306e\u691c\u5b9a\u30c4\u30fc\u30eb\u304c\u516c\u958b\u3055\u308c\u3066\u3044\u308b.<\/p>\n<h4>NIST (\u7c73\u56fd\u6a19\u6e96\u6280\u8853\u5c40) \u306e\u691c\u5b9a\u30c4\u30fc\u30eb SP800-22<\/h4>\n<p>NIST \u306e\u691c\u5b9a\u30c4\u30fc\u30eb\u304c\u30db\u30fc\u30e0\u30da\u30fc\u30b8 http:\/\/csrc.nist.gov\/groups\/ST\/toolkit\/rng\/documentation_software.html \u304b\u3089\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u4f7f\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b (\u6700\u65b0\u7248\u306f 2014 \u5e74 7 \u6708\u7248).<\/p>\n<p>\u3053\u308c\u3092\u4f7f\u7528\u3057\u3066\u4e0a\u306b\u3042\u3052\u305f\u3044\u304f\u3064\u304b\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u691c\u5b9a\u3059\u308b. \u3053\u306e\u30c4\u30fc\u30eb\u306e\u691c\u5b9a\u9805\u76ee\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<br \/>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tr>\n<td>No.<\/td>\n<td>\u691c\u5b9a\u9805\u76ee<\/td>\n<td>\u30c6\u30b9\u30c8\u6570<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1\u6b21\u5143\u5ea6\u6570\u691c\u5b9a (Frequency (Monobit) test)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>\u30d6\u30ed\u30c3\u30af\u5358\u4f4d\u306e\u5ea6\u6570\u691c\u5b9a (Frequency test within a block)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>\u9023\u306e\u691c\u5b9a (Runs test)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>\u30d6\u30ed\u30c3\u30af\u5358\u4f4d\u306e\u6700\u9577\u9023\u691c\u5b9a (Test for the longest run)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>2\u5024\u884c\u5217\u30e9\u30f3\u30af\u691c\u5b9a (Binary matrix rank test)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>DFT\u691c\u5b9a (DFT spectral test)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>\u91cd\u306a\u308a\u306e\u306a\u3044\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u9069\u5408\u691c\u5b9a (Non-overlapping template matching test)<\/td>\n<td>148<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>\u91cd\u306a\u308a\u306e\u3042\u308b\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u9069\u5408\u691c\u5b9a (Overlapping template matching test)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>Maurer \u306e\u30e6\u30cb\u30d0\u30fc\u30b5\u30eb\u7d71\u8a08\u691c\u5b9a (Maurer&#8217;s universal statistical test)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>\u7dda\u5f62\u8907\u96d1\u5ea6\u691c\u5b9a (Linear complexity test)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>\u7cfb\u5217\u691c\u5b9a (Serial test)<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>\u8fd1\u4f3c\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u691c\u5b9a (Approximate entropy test)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>13<\/td>\n<td>\u7d2f\u7a4d\u548c\u691c\u5b9a (Cumulative sums test)<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>14<\/td>\n<td>\u30e9\u30f3\u30c0\u30e0\u504f\u5dee\u691c\u5b9a (Random excursions test)<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td>15<\/td>\n<td>\u5909\u5f62\u30e9\u30f3\u30c0\u30e0\u504f\u5dee\u691c\u5b9a (Random excursions variant test)<\/td>\n<td>18<\/td>\n<\/tr>\n<\/table>\n<\/div>\n<p>\u3053\u306e\u30c4\u30fc\u30eb\u306f\u30d3\u30c3\u30c8\u5217\u3092\u5165\u529b\u3068\u3059\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b. \u305d\u3053\u3067, \u5404\u4e71\u6570\u751f\u6210\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u6574\u6570\u5024 (\u6d6e\u52d5\u5c0f\u6570\u306b\u5909\u63db\u3059\u308b\u524d\u306e\u5024) \u3092\u305d\u306e\u6709\u52b9\u306a\u30d3\u30c3\u30c8\u5e45\u3060\u3051\u53d6\u308a\u51fa\u3057\u3066, \u6841\u306e\u5927\u304d\u3044\u65b9\u304b\u3089\u306e\u30d3\u30c3\u30c8\u5217\u3092\u5165\u529b\u3068\u3057\u305f. \u30d3\u30c3\u30c8\u9577 100 \u4e07\u30d3\u30c3\u30c8\u306e\u6a19\u672c 1000 \u672c\u3092\u4e71\u6570\u751f\u6210\u30d7\u30ed\u30b0\u30e9\u30e0\u3054\u3068\u306b\u7528\u610f\u3057\u305f.<\/p>\n<p>\u691c\u5b9a\u7d50\u679c\u3092\u4e0b\u8868\u306b\u793a\u3059. \u25cb \u306f\u9805\u76ee\u3092\u30d1\u30b9\u3057, \u00d7 \u306f\u30d1\u30b9\u3057\u306a\u304b\u3063\u305f\u3053\u3068\u3092\u793a\u3059. \u30c6\u30b9\u30c8\u6570\u304c\u8907\u6570\u3042\u308b\u3082\u306e\u306b\u3064\u3044\u3066\u306f, \u30d1\u30b9\u3057\u306a\u304b\u3063\u305f\u30c6\u30b9\u30c8\u306e\u6570\u3092\u793a\u3057\u305f.<\/p>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tr>\n<td rowspan=\"2\">No.<\/td>\n<td>\u4e57\u6cd5\u5408\u540c\u6cd5<\/td>\n<td colspan=\"4\">\u7dda\u5f62\u5408\u540c\u6cd5<\/td>\n<td colspan=\"2\">\u30e9\u30b0\u4ed8\u304d\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6cd5<\/td>\n<td>\u30e1\u30eb\u30bb\u30f3\u30cc\u30c4\u30a4\u30b9\u30bf\u30fc<\/td>\n<\/tr>\n<tr>\n<td>RANDU<\/td>\n<td>Unix rand<\/td>\n<td>rand (\u6a19\u6e96 C)<\/td>\n<td>rand48<\/td>\n<td>VBA Rnd<\/td>\n<td>random<\/td>\n<td>ran_array<\/td>\n<td>mt19937<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>\u00d7<\/td>\n<td>\u00d7<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>\u00d7137\/148<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u00d71\/148<\/td>\n<td>\u00d7147\/148<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>13<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>14<\/td>\n<td>\u00d78\/8<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<tr>\n<td>15<\/td>\n<td>\u00d718\/18<\/td>\n<td>\u00d71\/18<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u00d7<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<td>\u25cb<\/td>\n<\/tr>\n<\/table>\n<\/div>\n\u30fbRANDU \u304a\u3088\u3073 Unix rand \u306b\u3064\u3044\u3066\u306f\u5b9f\u6a5f\u306e\u3082\u306e\u3067\u306f\u306a\u304f, \u540c\u4e00\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u3057\u3066 Windows \u4e0a\u3067\u5b9f\u9a13\u3092\u884c\u3063\u305f.<br \/>\n\u30fbrand (\u6a19\u6e96 C) \u306f Windows \u306e Visual C \u3092\u4f7f\u7528\u3057\u305f.<br \/>\n\u30fbrand48, ranarray \u304a\u3088\u3073 mt19937 \u306f XLPack (Windows) \u3092\u4f7f\u7528\u3057\u305f. rand48 \u3067\u306f mrand48 (32 \u30d3\u30c3\u30c8\u6574\u6570), mt19937 \u3067\u306f genrand_int32 (32 \u30d3\u30c3\u30c8\u6574\u6570) \u3092\u4f7f\u7528\u3057\u305f.<br \/>\n\u30fbVBA Rnd \u306f Windows \u306e Office 365 \u3092\u4f7f\u7528\u3057\u305f.<br \/>\n\u30fbrandom \u306f Linux (ubuntu 26.04) \u3092\u4f7f\u7528\u3057\u305f.<\/p>\n<p>RANDU \u3068 VBA Rnd \u306f\u304b\u306a\u308a\u6210\u7e3e\u304c\u60aa\u304b\u3063\u305f. RANDU \u306f\u3059\u3067\u306b\u4f7f\u308f\u308c\u3066\u3044\u306a\u3044\u304c, VBA \u306e Rnd \u306f\u5468\u671f\u3082\u77ed\u304f, \u7d71\u8a08\u7684\u6027\u8cea\u304c\u554f\u984c\u306b\u306a\u308b\u3088\u3046\u306a\u7528\u9014\u3078\u306e\u9069\u7528\u306f\u63a7\u3048\u305f\u65b9\u304c\u3088\u3044.<\/p>\n<p>\u53e4\u3044 Unix rand \u3068 Windows (Visual C) \u306e rand \u306f\u3053\u306e\u691c\u5b9a\u3067\u306f\u601d\u3063\u3066\u3044\u305f\u3088\u308a\u826f\u3044\u7d50\u679c\u3067\u3042\u3063\u305f. \u3053\u308c\u306f, \u4e0b\u4f4d 16 \u30d3\u30c3\u30c8\u3092\u6368\u3066, \u4e0a\u4f4d 15 \u30d3\u30c3\u30c8\u3057\u304b\u4f7f\u3063\u3066\u3044\u306a\u3044\u305f\u3081\u304b\u3082\u3057\u308c\u306a\u3044. \u3057\u304b\u3057, Windows \u306e Visual C \u306e rand \u3092\u4f7f\u7528\u3059\u308b\u969b\u306b\u306f 15 \u30d3\u30c3\u30c8\u306e\u7cbe\u5ea6\u3057\u304b\u306a\u3044\u3053\u3068\u3092\u610f\u8b58\u3057\u3066\u304a\u3044\u305f\u65b9\u304c\u3088\u3044.<\/p>\n<p>rand48, Random, ranarray \u306a\u3069\u306f\u554f\u984c\u70b9\u306e\u6307\u6458\u3082\u3042\u308b\u3088\u3046\u3060\u304c, \u3053\u306e\u691c\u5b9a\u306e\u7bc4\u56f2\u3067\u306f\u826f\u3044\u6210\u7e3e\u3067\u3042\u3063\u305f.<\/p>\n<h4>3 \u6b21\u5143\u7a7a\u9593\u3067\u306e\u5206\u5e03\u306e\u30d7\u30ed\u30c3\u30c8<\/h4>\n<p>\u751f\u6210\u3055\u308c\u305f\u4e71\u6570\u5217\u306e 3 \u6b21\u5143\u7a7a\u9593\u3067\u306e\u5206\u5e03\u3092\u6b21\u306e\u624b\u9806\u306b\u3088\u308a\u30d7\u30ed\u30c3\u30c8\u3059\u308b.<\/p>\n<ul>\n<li>\u4e71\u6570 (\u5024\u3092 0.0 \uff5e 1.0 \u306e\u5b9f\u6570\u306b\u5909\u63db) \u3092 3 \u3064\u751f\u6210\u3057, \u305d\u308c\u3089\u3092 xyz \u5ea7\u6a19\u3068\u3059\u308b\u70b9\u3092\u5358\u4f4d\u7acb\u65b9\u4f53\u306b\u30d7\u30ed\u30c3\u30c8\u3059\u308b.<\/li>\n<li>\u3053\u308c\u3092 2<sup>31<\/sup> \u56de\u7e70\u308a\u8fd4\u3059. \u305f\u3060\u3057, VBA Rnd \u3067\u306f 2<sup>24<\/sup> \u56de\u3068\u3057\u305f.<\/li>\n<li>\u5358\u4f4d\u7acb\u65b9\u4f53\u306e\u539f\u70b9\u4ed8\u8fd1\u306e\u4e00\u8fba 0.02 (\u305f\u3060\u3057, VBA Rnd \u3067\u306f 0.1) \u306e\u7acb\u65b9\u4f53\u306b\u30d7\u30ed\u30c3\u30c8\u3055\u308c\u305f\u70b9\u3092\u8868\u793a\u3059\u308b.<\/li>\n<\/ul>\n<p>\u7d50\u679c\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/13-1_1_Rnd_rand_1.png\" alt=\"\" width=\"800\" height=\"320\" class=\"aligncenter size-full wp-image-6276\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/13-1_1_Rnd_rand_1.png 800w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/13-1_1_Rnd_rand_1-300x120.png 300w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/13-1_1_Rnd_rand_1-768x307.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/13-1_2_mt32_ranarray_1.png\" alt=\"\" width=\"800\" height=\"320\" class=\"aligncenter size-full wp-image-6277\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/13-1_3_rand48_random_1.png\" alt=\"\" width=\"800\" height=\"320\" class=\"aligncenter size-full wp-image-6278\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/13-1_3_rand48_random_1.png 800w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/13-1_3_rand48_random_1-300x120.png 300w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/13-1_3_rand48_random_1-768x307.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>VBA Rnd \u3067\u306f\u306f\u3063\u304d\u308a\u3068\u69cb\u9020\u304c\u898b\u3048\u3066, \u5e73\u884c\u306a\u5e73\u9762\u306e\u4e0a\u306b\u306e\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b. rand (Windows Visual C) \u306f VBA Rnd \u3068\u540c\u3058\u6761\u4ef6\u3067\u306f\u30e9\u30f3\u30c0\u30e0\u306a\u30d7\u30ed\u30c3\u30c8\u306b\u898b\u3048\u305f\u304c, \u30b5\u30f3\u30d7\u30eb\u6570 (\u56de\u6570) \u3092 2<sup>31<\/sup> \u306b\u5897\u3084\u3057, \u30d7\u30ed\u30c3\u30c8\u3059\u308b\u9818\u57df\u3092\u4e00\u8fba 0.1 \u304b\u3089 0.02 \u306b\u5c0f\u3055\u304f\u3059\u308b\u3068\u56f3\u306e\u3088\u3046\u306b\u69cb\u9020\u304c\u898b\u3048\u305f. \u660e\u3089\u304b\u306b\u30e9\u30f3\u30c0\u30e0\u6027\u306b\u554f\u984c\u304c\u3042\u308b\u3068\u8a00\u3048\u308b.<\/p>\n<p>\u4ed6\u306e\u751f\u6210\u5668 (\u30e1\u30eb\u30bb\u30f3\u30cc\u30c4\u30a4\u30b9\u30bf\u30fc, ranarray, rand48, random) \u3067\u306f\u500b\u306e\u30d7\u30ed\u30c3\u30c8\u3067\u306f\u30e9\u30f3\u30c0\u30e0\u306b\u898b\u3048\u308b. NIST \u306e\u30b9\u30da\u30af\u30c8\u30eb\u691c\u5b9a\u3067\u3082\u5408\u683c\u3057\u3066\u3044\u308b\u306e\u3067\u3088\u3055\u305d\u3046\u3060\u304c, \u305d\u308c\u305e\u308c\u306e\u5468\u671f\u306b\u8fd1\u3044\u3082\u3063\u3068\u5927\u304d\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u3067\u3084\u3063\u3066\u307f\u305f\u3044\u3068\u3053\u308d\u3067\u306f\u3042\u308b.<\/p>\n<p>Excel VBA \u3067\u4f7f\u7528\u3059\u308b Rnd \u3084 XLPack \u3067\u306f, \u4e71\u6570\u306e\u751f\u6210\u901f\u5ea6\u3082\u9045\u304f, \u7d71\u8a08\u7684\u6027\u8cea\u304c\u554f\u984c\u306b\u306a\u308b\u3088\u3046\u306a\u5927\u898f\u6a21\u306a\u4f7f\u3044\u65b9\u306f\u3055\u308c\u306a\u3044\u3068\u601d\u3046\u304c, \u3053\u3053\u3067\u8aac\u660e\u3057\u305f\u5185\u5bb9\u306f\u7406\u89e3\u3057\u3066\u304a\u3044\u305f\u65b9\u304c\u3088\u3044.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u7bc0\u3067\u306f, \u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u4e71\u6570 (\u4e00\u69d8\u4e71\u6570) \u306e\u751f\u6210\u6cd5\u3092\u8aac\u660e\u3059\u308b. \u4e00\u69d8\u4e71\u6570\u3092\u751f\u6210\u3059\u308b\u969b\u306b\u306f, \u307e\u305a\u975e\u8ca0\u6574\u6570\u306e\u533a\u9593 [0, m) \u4e0a\u3067\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u6574\u6570\u4e71\u6570\u751f\u6210\u3059\u308b. \u6b21\u306b, \u5b9f\u6570\u4e71\u6570\u304c\u5fc5\u8981\u3067\u3042\u308c\u3070\u9069\u5f53\u306a\u533a\u9593\u306e\u6d6e\u52d5\u5c0f\u6570\u70b9 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[13],"tags":[],"class_list":["post-6254","post","type-post","status-publish","format-standard","hentry","category-num"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u672c\u7bc0\u3067\u306f, \u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u4e71\u6570 (\u4e00\u69d8\u4e71\u6570) \u306e\u751f\u6210\u6cd5\u3092\u8aac\u660e\u3059\u308b. \u4e00\u69d8\u4e71\u6570\u3092\u751f\u6210\u3059\u308b\u969b\u306b\u306f, \u307e\u305a\u975e\u8ca0\u6574\u6570\u306e\" \/>\n\t<meta name=\"robots\" content=\"max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n\t<meta name=\"author\" content=\"Administrator\"\/>\n\t<meta name=\"google-site-verification\" content=\"5PEQMQVhF0wv5i-xMYW9a3HzuBwixzVduoR2arr5UDM\" \/>\n\t<meta name=\"msvalidate.01\" content=\"EEB9704E04960338720AEA89E77E749F\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/www.ktech.biz\/jp\/num\/13-1_rand\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.1.1\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/13-1_rand\\\/#article\",\"name\":\"13.1 \\u4e00\\u69d8\\u4e71\\u6570 | K \\u30c6\\u30af\\u30ce\\u30ed\\u30b8\\u30fc\",\"headline\":\"13.1 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