{"id":2197,"date":"2025-03-24T08:48:02","date_gmt":"2025-03-23T23:48:02","guid":{"rendered":"https:\/\/dexall.co.jp\/articles\/?p=2197"},"modified":"2025-03-26T13:45:10","modified_gmt":"2025-03-26T04:45:10","slug":"c%e3%81%ae%e6%ad%a3%e3%81%97%e3%81%84%e4%b9%97%e8%a8%88%e7%ae%97%e5%ae%8c%e5%85%a8%e3%82%ac%e3%82%a4%e3%83%89%ef%bc%9a5%e3%81%a4%e3%81%ae%e5%ae%9f%e8%a3%85%e6%96%b9%e6%b3%95%e3%81%a8%e6%80%a7","status":"publish","type":"post","link":"https:\/\/dexall.co.jp\/articles\/?p=2197","title":{"rendered":"C++ \u3067\u9069\u5207\u306a\u4e57\u3092\u8a08\u7b97\u3059\u308b 7 \u3064\u306e\u52b9\u7387\u7684\u306a\u65b9\u6cd5 \u2014 \u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u6bd4\u8f03\u3068\u5b9f\u88c5\u30c6\u30af\u30cb\u30c3\u30af"},"content":{"rendered":"\n<p>C++\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306b\u304a\u3044\u3066\u3001\u3079\u304d\u4e57\uff08\u7d2f\u4e57\uff09\u8a08\u7b97\u306f\u79d1\u5b66\u8a08\u7b97\u3001\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u51e6\u7406\u3001\u6697\u53f7\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3001\u91d1\u878d\u30e2\u30c7\u30ea\u30f3\u30b0\u306a\u3069\u591a\u304f\u306e\u5206\u91ce\u3067\u983b\u7e41\u306b\u4f7f\u7528\u3055\u308c\u308b\u57fa\u672c\u7684\u306a\u6570\u5b66\u6f14\u7b97\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u5358\u7d14\u306b\u898b\u3048\u308b\u3053\u306e\u64cd\u4f5c\u3082\u3001\u5b9f\u88c5\u65b9\u6cd5\u306b\u3088\u3063\u3066\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3084\u7cbe\u5ea6\u306b\u5927\u304d\u306a\u5dee\u304c\u751f\u3058\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u7279\u306b\u9ad8\u6027\u80fd\u304c\u6c42\u3081\u3089\u308c\u308b\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3084\u3001\u5927\u91cf\u306e\u8a08\u7b97\u3092\u884c\u3046\u30b7\u30b9\u30c6\u30e0\u3067\u306f\u3001\u6700\u9069\u306a\u3079\u304d\u4e57\u8a08\u7b97\u306e\u5b9f\u88c5\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u3002C++\u306b\u306f\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e<code>std::pow<\/code>\u95a2\u6570\u304b\u3089\u3001\u30d3\u30c3\u30c8\u6f14\u7b97\u3092\u6d3b\u7528\u3057\u305f\u9ad8\u901f\u5b9f\u88c5\u307e\u3067\u3001\u69d8\u3005\u306a\u3079\u304d\u4e57\u8a08\u7b97\u306e\u624b\u6cd5\u304c\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001C++\u3067\u306e\u3079\u304d\u4e57\u8a08\u7b97\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001\u4ee5\u4e0b\u306e7\u3064\u306e\u52b9\u7387\u7684\u306a\u5b9f\u88c5\u65b9\u6cd5\u3092\u8a73\u3057\u304f\u89e3\u8aac\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u95a2\u6570<code>std::pow<\/code>\u306e\u6d3b\u7528<\/li>\n\n\n\n<li>\u6574\u6570\u3079\u304d\u4e57\u306e\u305f\u3081\u306e\u30ab\u30b9\u30bf\u30e0\u518d\u5e30\u95a2\u6570<\/li>\n\n\n\n<li>\u30eb\u30fc\u30d7\u3092\u4f7f\u3063\u305f\u7c21\u6613\u5b9f\u88c5<\/li>\n\n\n\n<li>\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\uff08\u30d0\u30a4\u30ca\u30ea\u30a8\u30af\u30b9\u30dd\u30cd\u30f3\u30b7\u30a8\u30fc\u30b7\u30e7\u30f3\uff09<\/li>\n\n\n\n<li>\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u30e1\u30bf\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3092\u7528\u3044\u305f\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u9593\u8a08\u7b97<\/li>\n\n\n\n<li>\u30d3\u30c3\u30c8\u6f14\u7b97\u3092\u6d3b\u7528\u3057\u305f\u9ad8\u901f\u3079\u304d\u4e57\u8a08\u7b97<\/li>\n\n\n\n<li>\u6574\u6570\u578b\u7279\u5316\u306e\u30ab\u30b9\u30bf\u30e0\u5b9f\u88c5<\/li>\n<\/ol>\n\n\n\n<p>\u305d\u308c\u305e\u308c\u306e\u65b9\u6cd5\u306b\u3064\u3044\u3066\u3001\u5b9f\u88c5\u65b9\u6cd5\u3001\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u7279\u6027\u3001\u9069\u7528\u30b7\u30fc\u30f3\u3092\u89e3\u8aac\u3057\u3001\u5b9f\u969b\u306e\u30b3\u30fc\u30c9\u4f8b\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u3053\u308c\u3089\u306e\u5b9f\u88c5\u65b9\u6cd5\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u6bd4\u8f03\u3084\u3001\u6ce8\u610f\u70b9\u3001\u6700\u9069\u5316\u30c6\u30af\u30cb\u30c3\u30af\u306b\u3064\u3044\u3066\u3082\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u8a18\u4e8b\u306f\u3001C++\u3067\u306e\u6570\u5024\u8a08\u7b97\u306e\u6700\u9069\u5316\u306b\u8208\u5473\u304c\u3042\u308b\u958b\u767a\u8005\u3001\u79d1\u5b66\u6280\u8853\u8a08\u7b97\u3084\u30b2\u30fc\u30e0\u958b\u767a\u306b\u643a\u308f\u308b\u30d7\u30ed\u30b0\u30e9\u30de\u30fc\u3001\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u30af\u30ea\u30c6\u30a3\u30ab\u30eb\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3092\u958b\u767a\u3057\u3066\u3044\u308b\u65b9\u3005\u306b\u7279\u306b\u5f79\u7acb\u3064\u5185\u5bb9\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u305d\u308c\u3067\u306f\u3001C++\u306b\u304a\u3051\u308b\u3079\u304d\u4e57\u8a08\u7b97\u306e\u57fa\u790e\u304b\u3089\u3001\u9ad8\u5ea6\u306a\u6700\u9069\u5316\u30c6\u30af\u30cb\u30c3\u30af\u307e\u3067\u3001\u6bb5\u968e\u7684\u306b\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"toc\"><br \/>\n<b>Warning<\/b>:  Undefined array key \"is_admin\" in <b>\/home\/xs392991\/dexall.co.jp\/public_html\/articles\/wp-content\/themes\/sango-theme\/library\/gutenberg\/dist\/classes\/Toc.php<\/b> on line <b>116<\/b><br \/>\n<br \/>\n<b>Warning<\/b>:  Undefined array key \"is_category_top\" in <b>\/home\/xs392991\/dexall.co.jp\/public_html\/articles\/wp-content\/themes\/sango-theme\/library\/gutenberg\/dist\/classes\/Toc.php<\/b> on line <b>121<\/b><br \/>\n<br \/>\n<b>Warning<\/b>:  Undefined array key \"is_top\" in <b>\/home\/xs392991\/dexall.co.jp\/public_html\/articles\/wp-content\/themes\/sango-theme\/library\/gutenberg\/dist\/classes\/Toc.php<\/b> on line <b>128<\/b><br \/>\n    <div id=\"toc_container\" class=\"sgb-toc--bullets js-smooth-scroll\" data-dialog-title=\"\u76ee\u6b21\">\n      <p class=\"toc_title\">\u76ee\u6b21 <\/p>\n      <ul class=\"toc_list\">  <li class=\"first\">    <a href=\"#i-0\">C++ \u306b\u304a\u3051\u308b\u9069\u5207\u306a\u4e57\u8a08\u7b97\u306e\u57fa\u790e\u77e5\u8b58<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-1\">\u3075\u3055\u308f\u3057\u3044\u4e57\u3068\u306f\u4f55\u304b \u2014 \u6570\u5b66\u7684\u306a\u6982\u5ff5\u304b\u3089\u5b9f\u88c5\u307e\u3067<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-2\">C++ \u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306b\u304a\u3051\u308b\u6b63\u3057\u3044\u4e57\u306e\u91cd\u8981\u6027<\/a>      <\/li>    <\/ul>  <\/li>  <li>    <a href=\"#i-3\">\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306b\u3088\u308b\u9069\u5207\u306a\u4e57\u8a08\u7b97<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-4\">std::pow\u95a2\u6570\u306e\u4f7f\u3044\u65b9\u3068\u6ce8\u610f\u70b9<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-5\">cmath \u30d8\u30c3\u30c0\u30fc\u304c\u63d0\u4f9b\u3059\u308b\u4ed6\u306e\u6307\u6570\u95a2\u6570<\/a>      <\/li>    <\/ul>  <\/li>  <li>    <a href=\"#i-6\">C++ \u3067\u9069\u5207\u306a\u4e57\u3092\u5b9f\u88c5\u3059\u308b 7 \u3064\u306e\u65b9\u6cd5<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-7\">\u65b9\u6cd51:\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u95a2\u6570std::pow\u306e\u6d3b\u7528<\/a>      <\/li>      <li>        <a href=\"#i-8\">\u65b9\u6cd5 2: \u6574\u6570\u9069\u5207\u306a\u4e57\u306e\u305f\u3081\u306e\u30ab\u30b9\u30bf\u30e0\u518d\u5e30\u95a2\u6570<\/a>      <\/li>      <li>        <a href=\"#i-9\">\u65b9\u6cd5 3: \u30eb\u30fc\u30d7\u3092\u4f7f\u3063\u305f\u7c21\u6613\u5b9f\u88c5<\/a>      <\/li>      <li>        <a href=\"#i-10\">\u65b9\u6cd54:\u4e8c\u5206\u84c4\u7a4d\u4e57\u6cd5\uff08\u30d0\u30a4\u30ca\u30ea\u30a8\u30af\u30b9\u30dd\u30cd\u30f3\u30b7\u30a8\u30fc\u30b7\u30e7\u30f3\uff09<\/a>      <\/li>      <li>        <a href=\"#i-11\">\u65b9\u6cd5 5: \u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u30e1\u30bf\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3092\u7528\u3044\u305f\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u9593\u8a08\u7b97<\/a>      <\/li>      <li>        <a href=\"#i-12\">\u65b9\u6cd56: \u30d3\u30c3\u30c8\u6f14\u7b97\u3092\u6d3b\u7528\u3057\u305f\u9ad8\u901f\u9069\u5207\u306a\u4e57\u8a08\u7b97<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-13\">\u65b9\u6cd5 7: \u6574\u6570\u578b\u7279\u5316\u306e\u30ab\u30b9\u30bf\u30e0\u5b9f\u88c5<\/a>      <\/li>    <\/ul>  <\/li>  <li>    <a href=\"#i-14\">\u9069\u5207\u306a\u4e57\u8a08\u7b97\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u6bd4\u8f03<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-15\">\u7570\u306a\u308b\u5b9f\u88c5\u65b9\u6cd5\u306e\u5b9f\u884c\u901f\u5ea6\u6bd4\u8f03<\/a>      <\/li>      <li>        <a href=\"#i-16\">\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\u3068\u52b9\u7387\u6027\u306e\u5206\u6790<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-17\">\u6d6e\u52d5\u5c0f\u6570\u70b9\u8aa4\u5dee\u3068\u305d\u306e\u5bfe\u51e6\u6cd5<\/a>      <\/li>    <\/ul>  <\/li>  <li>    <a href=\"#i-18\">\u9069\u5207\u306a\u4e57\u8a08\u7b97\u306b\u304a\u3051\u308b\u6ce8\u610f\u70b9\u3068\u6700\u9069\u5316\u30c6\u30af\u30cb\u30c3\u30af<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-19\">\u5927\u304d\u306a\u6307\u6570\u5024\u306e\u6271\u3044\u65b9\u3068\u6841\u3042\u3075\u308c\u306e\u9632\u6b62\u7b56<\/a>      <\/li>      <li>        <a href=\"#i-20\">\u8ca0\u3051\u306e\u6307\u6570\u5bfe\u5fdc\u306e\u5b9f\u88c5\u65b9\u6cd5<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-21\">\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\uff080\u4e57\u30011\u4e57\u30012\u4e57\uff09\u306e\u6700\u9069\u5316<\/a>      <\/li>    <\/ul>  <\/li>  <li>    <a href=\"#i-22\">\u5b9f\u7528\u7684\u306a\u4e57\u8a08\u7b97\u306e\u5fdc\u7528\u4f8b<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-23\">\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u51e6\u7406\u306b\u304a\u3051\u308b\u9069\u5207\u306a\u4e57\u8a08\u7b97<\/a>      <\/li>      <li>        <a href=\"#i-24\">\u6697\u53f7\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u306e\u6b63\u3057\u3044\u4e57\u306e\u6d3b\u7528\u6cd5<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-25\">\u79d1\u5b66\u6280\u8853\u8a08\u7b97\u3067\u306e\u9ad8\u7cbe\u5ea6\u3079\u304d\u4e57\u8a08\u7b97<\/a>      <\/li>    <\/ul>  <\/li>  <li>    <a href=\"#i-26\">C++20\u4ee5\u964d\u306e\u6b63\u3057\u3044\u4e57\u8a08\u7b97\u306e\u65b0\u6a5f\u80fd\u3068\u5c06\u6765\u5c55\u671b<\/a>    <ul class=\"menu_level_1\">      <li class=\"first last\">        <a href=\"#i-27\">C++20\u3067\u8ffd\u52a0\u3055\u308c\u305f\u6570\u5b66\u95a2\u9023\u306e\u65b0\u6a5f\u80fd<\/a>      <\/li>    <\/ul>  <\/li>  <li class=\"last\">    <a href=\"#i-28\">\u307e\u3068\u3081\u3068\u5b9f\u8df5\u7684\u306a\u30b3\u30fc\u30c9\u30b5\u30f3\u30d7\u30eb<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-29\">\u30e6\u30fc\u30b9\u30b1\u30fc\u30b9\u5225\u306e\u9069\u5207\u306a\u4e57\u8a08\u7b97\u5b9f\u88c5\u306e\u9078\u629e<\/a>      <\/li>      <li>        <a href=\"#i-30\">\u3059\u3050\u306b\u4f7f\u3048\u308b\u4e57\u8a08\u7b97\u306e\u30b3\u30fc\u30c9\u30b9\u30cb\u30da\u30c3\u30c8\u96c6<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-31\">\u307e\u3068\u3081<\/a>      <\/li>    <\/ul>  <\/li><\/ul>\n      <a href=\"#\" class=\"sgb-toc-button js-toc-button\" rel=\"nofollow\" data-open-dialog=\"true\"><i class=\"fa fa-list\"><\/i><span class=\"sgb-toc-button__text\">\u76ee\u6b21\u3078<\/span><\/a>\n    <\/div><\/div><h2 class=\"wp-block-heading\" id=\"i-0\">C++ \u306b\u304a\u3051\u308b\u9069\u5207\u306a\u4e57\u8a08\u7b97\u306e\u57fa\u790e\u77e5\u8b58<\/h2>\n\n\n\n<p>C++\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306b\u304a\u3044\u3066\u3001\u52b9\u7387\u7684\u306a\u3079\u304d\u4e57\u8a08\u7b97\u306f\u69d8\u3005\u306a\u5fdc\u7528\u5206\u91ce\u3067\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u3053\u306e\u57fa\u790e\u77e5\u8b58\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3079\u304d\u4e57\u306e\u6570\u5b66\u7684\u6982\u5ff5\u304b\u3089\u5b9f\u88c5\u307e\u3067\u3001\u305d\u3057\u3066C++\u3067\u306e\u91cd\u8981\u6027\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-1\">\u3075\u3055\u308f\u3057\u3044\u4e57\u3068\u306f\u4f55\u304b \u2014 \u6570\u5b66\u7684\u306a\u6982\u5ff5\u304b\u3089\u5b9f\u88c5\u307e\u3067<\/h3>\n\n\n\n<p>\u3079\u304d\u4e57\uff08\u7d2f\u4e57\uff09\u306f\u3001\u540c\u3058\u6570\u3092\u7279\u5b9a\u306e\u56de\u6570\u3060\u3051\u639b\u3051\u5408\u308f\u305b\u308b\u6570\u5b66\u7684\u6f14\u7b97\u3067\u3059\u3002\u4e00\u822c\u7684\u306b\u3001a^n\uff08a\u306en\u4e57\uff09\u3068\u8868\u8a18\u3055\u308c\u3001\u3053\u308c\u306fa\u3092n\u56de\u639b\u3051\u5408\u308f\u305b\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">a^n = a \u00d7 a \u00d7 ... \u00d7 a\uff08n\u500b\u306ea\u306e\u7a4d\uff09\n<\/pre>\n\n\n\n<p>\u4f8b\u3048\u3070\u30012^3 = 2 \u00d7 2 \u00d7 2 = 8 \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3079\u304d\u4e57\u8a08\u7b97\u306b\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>0\u4e57<\/strong>: \u4efb\u610f\u306e\u6570\u306e0\u4e57\u306f1\u3067\u3059\uff080^0\u306f\u6570\u5b66\u7684\u306b\u8b70\u8ad6\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u591a\u304f\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u306f1\u3068\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\uff09<\/li>\n\n\n\n<li><strong>\u8ca0\u306e\u6307\u6570<\/strong>: a^(-n) = 1\/(a^n)\u3002\u4f8b\u3048\u3070\u30012^(-2) = 1\/(2^2) = 1\/4 = 0.25<\/li>\n\n\n\n<li><strong>\u5c0f\u6570\u6307\u6570<\/strong>: a^(1\/n)\u306fa\u306en\u4e57\u6839\u3092\u8868\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u30019^(1\/2) = \u221a9 = 3<\/li>\n<\/ul>\n\n\n\n<p>C++\u306b\u304a\u3051\u308b\u3079\u304d\u4e57\u8a08\u7b97\u306e\u5b9f\u88c5\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u6570\u5b66\u7684\u6027\u8cea\u3092\u8003\u616e\u3057\u306a\u304c\u3089\u3001\u4f7f\u7528\u3059\u308b\u30c7\u30fc\u30bf\u578b\u3068\u64cd\u4f5c\u306e\u7279\u6027\u306b\u5408\u308f\u305b\u305f\u5b9f\u88c5\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>\u6574\u6570\u578b\u3079\u304d\u4e57\u3068\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u3079\u304d\u4e57\u306e\u9055\u3044<\/strong>:<\/p>\n\n\n<div id=\"id-59cece91-0435-44cb-bd92-a846dda05076\">\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u7279\u6027<\/th><th>\u6574\u6570\u578b\u3079\u304d\u4e57<\/th><th>\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u3079\u304d\u4e57<\/th><\/tr><\/thead><tbody><tr><td>\u7d50\u679c\u306e\u7cbe\u5ea6<\/td><td>\u53b3\u5bc6\uff08\u8aa4\u5dee\u306a\u3057\uff09<\/td><td>\u8fd1\u4f3c\uff08\u4e38\u3081\u8aa4\u5dee\u3042\u308a\uff09<\/td><\/tr><tr><td>\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u306e\u30ea\u30b9\u30af<\/td><td>\u9ad8\u3044\uff08\u7279\u306b\u5927\u304d\u306a\u6307\u6570\u5024\uff09<\/td><td>\u6bd4\u8f03\u7684\u4f4e\u3044\uff08\u6307\u6570\u8868\u73fe\u3092\u4f7f\u7528\uff09<\/td><\/tr><tr><td>\u6307\u6570\u306e\u5236\u9650<\/td><td>\u901a\u5e38\u306f\u6574\u6570\u306e\u307f<\/td><td>\u4efb\u610f\u306e\u5b9f\u6570<\/td><\/tr><tr><td>\u5b9f\u88c5\u306e\u8907\u96d1\u3055<\/td><td>\u7279\u6b8a\u30b1\u30fc\u30b9\u3067\u6700\u9069\u5316\u53ef\u80fd<\/td><td>\u4e00\u822c\u7684\u306b\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u4f7f\u7528<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<p>C++\u3067\u306e\u5b9f\u88c5\u306b\u304a\u3044\u3066\u306f\u3001\u3053\u308c\u3089\u306e\u7279\u6027\u3092\u7406\u89e3\u3057\u3001\u8a08\u7b97\u306e\u76ee\u7684\u3084\u8981\u4ef6\u306b\u5fdc\u3058\u305f\u9069\u5207\u306a\u65b9\u6cd5\u3092\u9078\u3076\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-2\">C++ \u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306b\u304a\u3051\u308b\u6b63\u3057\u3044\u4e57\u306e\u91cd\u8981\u6027<\/h3>\n\n\n\n<p>C++\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u304a\u3044\u3066\u3001\u3079\u304d\u4e57\u8a08\u7b97\u306e\u6b63\u78ba\u6027\u3068\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u306f\u4ee5\u4e0b\u306e\u7406\u7531\u304b\u3089\u975e\u5e38\u306b\u91cd\u8981\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3078\u306e\u5f71\u97ff<\/strong>:\n<ul class=\"wp-block-list\">\n<li>\u3079\u304d\u4e57\u8a08\u7b97\u306f\u79d1\u5b66\u8a08\u7b97\u3084\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u983b\u7e41\u306b\u4f7f\u7528\u3055\u308c\u3001\u5185\u90e8\u30eb\u30fc\u30d7\u3067\u4f55\u767e\u4e07\u56de\u3082\u5b9f\u884c\u3055\u308c\u308b\u3053\u3068\u304c\u3042\u308b<\/li>\n\n\n\n<li>\u975e\u52b9\u7387\u306a\u5b9f\u88c5\u306f\u5168\u4f53\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u6642\u9593\u306b\u5927\u304d\u304f\u5f71\u97ff\u3059\u308b<\/li>\n\n\n\n<li>\u7279\u306b\u7d44\u307f\u8fbc\u307f\u30b7\u30b9\u30c6\u30e0\u3084\u9ad8\u6027\u80fd\u8a08\u7b97\u3067\u306f\u3001\u6700\u9069\u5316\u304c\u4e0d\u53ef\u6b20<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u6570\u5024\u7cbe\u5ea6\u306e\u554f\u984c<\/strong>:\n<ul class=\"wp-block-list\">\n<li>\u6d6e\u52d5\u5c0f\u6570\u70b9\u8a08\u7b97\u3067\u306f\u3001\u4e38\u3081\u8aa4\u5dee\u304c\u84c4\u7a4d\u3057\u3001\u7d50\u679c\u306e\u7cbe\u5ea6\u306b\u5f71\u97ff\u3059\u308b<\/li>\n\n\n\n<li>\u53cd\u5fa9\u8a08\u7b97\u3084\u518d\u5e30\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u306f\u3001\u5c0f\u3055\u306a\u8aa4\u5dee\u304c\u5927\u304d\u306a\u554f\u984c\u306b\u767a\u5c55\u3059\u308b\u3053\u3068\u304c\u3042\u308b<\/li>\n\n\n\n<li>\u91d1\u878d\u8a08\u7b97\u3084\u79d1\u5b66\u7684\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u9ad8\u3044\u7cbe\u5ea6\u304c\u6c42\u3081\u3089\u308c\u308b<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u30e1\u30e2\u30ea\u52b9\u7387\u3068\u6700\u9069\u5316<\/strong>:\n<ul class=\"wp-block-list\">\n<li>\u9069\u5207\u306a\u3079\u304d\u4e57\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\u3092\u524a\u6e1b\u3057\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b<\/li>\n\n\n\n<li>\u30b3\u30f3\u30d1\u30a4\u30e9\u304c\u6700\u9069\u5316\u3057\u3084\u3059\u3044\u30b3\u30fc\u30c9\u3092\u66f8\u304f\u3053\u3068\u3067\u3001\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u304c\u5927\u5e45\u306b\u5411\u4e0a\u3059\u308b<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>C++\u306e\u7279\u6027\u3092\u6d3b\u304b\u3057\u305f\u3079\u304d\u4e57\u8a08\u7b97\u306e\u5b9f\u88c5\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u8003\u616e\u70b9\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u306e\u6d3b\u7528<\/strong>: \u69d8\u3005\u306a\u6570\u5024\u578b\u306b\u5bfe\u5fdc\u3057\u305f\u30b8\u30a7\u30cd\u30ea\u30c3\u30af\u306a\u5b9f\u88c5<\/li>\n\n\n\n<li><strong>\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97<\/strong>: \u5b9a\u6570\u3079\u304d\u4e57\u306e\u5834\u5408\u3001\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u8a08\u7b97\u3092\u5b8c\u4e86<\/li>\n\n\n\n<li><strong>\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u5bfe\u7b56<\/strong>: \u5927\u304d\u306a\u6570\u5024\u3092\u6271\u3046\u5834\u5408\u306e\u6841\u3042\u3075\u308c\u9632\u6b62\u7b56<\/li>\n\n\n\n<li><strong>\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u56fa\u6709\u306e\u6700\u9069\u5316<\/strong>: SSE\/AVX\u547d\u4ee4\u306a\u3069\u3092\u6d3b\u7528\u3057\u305f\u9ad8\u901f\u5316<\/li>\n<\/ul>\n\n\n\n<p>\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001C++\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u63d0\u4f9b\u3059\u308b\u3079\u304d\u4e57\u8a08\u7b97\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"i-3\">\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306b\u3088\u308b\u9069\u5207\u306a\u4e57\u8a08\u7b97<\/h2>\n\n\n\n<p>C++\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306f\u3001\u3079\u304d\u4e57\u8a08\u7b97\u3092\u884c\u3046\u305f\u3081\u306e\u69d8\u3005\u306a\u95a2\u6570\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u591a\u304f\u306e\u30e6\u30fc\u30b9\u30b1\u30fc\u30b9\u3067\u5341\u5206\u306a\u7cbe\u5ea6\u3068\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u767a\u63ee\u3057\u307e\u3059\u3002\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306b\u3088\u308b\u3079\u304d\u4e57\u8a08\u7b97\u306e\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-4\">std::pow\u95a2\u6570\u306e\u4f7f\u3044\u65b9\u3068\u6ce8\u610f\u70b9<\/h3>\n\n\n\n<p><code>std::pow<\/code> \u95a2\u6570\u306f\u3001C++\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e <code>&lt;cmath&gt;<\/code> \u30d8\u30c3\u30c0\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3001\u6700\u3082\u4e00\u822c\u7684\u306a\u3079\u304d\u4e57\u8a08\u7b97\u95a2\u6570\u3067\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u3001\u6307\u5b9a\u3055\u308c\u305f\u57fa\u6570\uff08\u5e95\uff09\u3092\u6307\u5b9a\u3055\u308c\u305f\u6307\u6570\u3067\u7d2f\u4e57\u3057\u305f\u7d50\u679c\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>\u57fa\u672c\u7684\u306a\u69cb\u6587\u3068\u5b9a\u7fa9\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\/\/ \u57fa\u672c\u7684\u306a\u30aa\u30fc\u30d0\u30fc\u30ed\u30fc\u30c9\ndouble pow(double base, double exponent);\nfloat pow(float base, float exponent);\nlong double pow(long double base, long double exponent);\n\n\/\/ C++11\u4ee5\u964d\u306e\u6df7\u5408\u578b\u30aa\u30fc\u30d0\u30fc\u30ed\u30fc\u30c9\ntemplate&lt;class T1, class T2&gt;\nauto pow(T1 base, T2 exponent) -&gt; decltype(\/* \u5b9f\u88c5\u4f9d\u5b58\u306e\u623b\u308a\u5024\u578b *\/);\n<\/pre>\n\n\n\n<p><strong>\u57fa\u672c\u7684\u306a\u4f7f\u7528\u4f8b\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;cmath&gt;\n#include &lt;iostream&gt;\n\nint main() {\n    \/\/ \u57fa\u672c\u7684\u306a\u4f7f\u7528\u6cd5\n    double result1 = std::pow(2.0, 3.0);  \/\/ 2\u00b3 = 8.0\n    double result2 = std::pow(5.0, 2.0);  \/\/ 5\u00b2 = 25.0\n    double result3 = std::pow(2.0, -1.0); \/\/ 2\u207b\u00b9 = 0.5\n    double result4 = std::pow(9.0, 0.5);  \/\/ 9^(1\/2) = 3.0\uff08\u5e73\u65b9\u6839\uff09\n    \n    std::cout &lt;&lt; \"2^3 = \" &lt;&lt; result1 &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"5^2 = \" &lt;&lt; result2 &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"2^(-1) = \" &lt;&lt; result3 &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"9^(0.5) = \" &lt;&lt; result4 &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p><strong><code>std::pow<\/code>\u95a2\u6570\u4f7f\u7528\u6642\u306e\u6ce8\u610f\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u578b\u5909\u63db\u3068\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9<\/strong>:\n<ul class=\"wp-block-list\">\n<li>\u6574\u6570\u306e\u3079\u304d\u4e57\u8a08\u7b97\u3067\u3082\u5185\u90e8\u7684\u306b\u306f\u6d6e\u52d5\u5c0f\u6570\u70b9\u6f14\u7b97\u304c\u884c\u308f\u308c\u308b\u305f\u3081\u3001\u5c0f\u3055\u306a\u4e38\u3081\u8aa4\u5dee\u304c\u751f\u3058\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059<\/li>\n\n\n\n<li>\u6574\u6570\u304b\u3089\u6d6e\u52d5\u5c0f\u6570\u70b9\u3078\u306e\u5909\u63db\u3068\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u304b\u3089\u6574\u6570\u3078\u306e\u5909\u63db\u306b\u3088\u308b\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u304c\u3042\u308a\u307e\u3059<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\/\/ \u6574\u6570\u3079\u304d\u4e57\u306e\u4f8b\nint base = 2;\nint exp = 10;\n\/\/ \u6574\u6570\u3092\u6e21\u3057\u3066\u3082\u5185\u90e8\u7684\u306b\u306f\u6d6e\u52d5\u5c0f\u6570\u70b9\u6f14\u7b97\u306b\u306a\u308b\nint result = static_cast&lt;int&gt;(std::pow(base, exp)); \/\/ 1024\n\/\/ \u5c0f\u3055\u306a\u4e38\u3081\u8aa4\u5dee\u304c\u751f\u3058\u308b\u3053\u3068\u304c\u3042\u308b\uff08\u7279\u306b\u5927\u304d\u306a\u6570\u5024\u3084\u7cbe\u5ea6\u304c\u91cd\u8981\u306a\u5834\u5408\uff09\n<\/pre>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\u306e\u51e6\u7406<\/strong>:\n<ul class=\"wp-block-list\">\n<li><code>std::pow(0, 0)<\/code> \u306f\u901a\u5e381\u3092\u8fd4\u3057\u307e\u3059\u304c\u3001\u6570\u5b66\u7684\u306b\u306f\u672a\u5b9a\u7fa9\u3067\u3059<\/li>\n\n\n\n<li>\u8ca0\u306e\u57fa\u6570\u306e\u975e\u6574\u6570\u6307\u6570\uff08\u4f8b: <code>std::pow(-2, 0.5)<\/code>\uff09\u306f\u8907\u7d20\u6570\u9818\u57df\u306e\u8a08\u7b97\u3068\u306a\u308a\u3001NaN\u3092\u8fd4\u3057\u307e\u3059<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u8003\u616e\u70b9<\/strong>:\n<ul class=\"wp-block-list\">\n<li>\u6574\u6570\u306e\u5c0f\u3055\u3044\u3079\u304d\u4e57\uff080,1,2\u306a\u3069\uff09\u306e\u5834\u5408\u3001\u76f4\u63a5\u8a08\u7b97\u3057\u305f\u65b9\u304c\u9ad8\u901f\u3067\u3059<\/li>\n\n\n\n<li>\u5185\u90e8\u30eb\u30fc\u30d7\u3067\u983b\u7e41\u306b\u547c\u3073\u51fa\u3059\u5834\u5408\u3001\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u304c\u30dc\u30c8\u30eb\u30cd\u30c3\u30af\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\/\/ \u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u6700\u9069\u5316\u306e\u4f8b\ndouble optimizedPow(double base, int exponent) {\n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u3092\u9ad8\u901f\u306b\u51e6\u7406\n    if (exponent == 0) return 1.0;\n    if (exponent == 1) return base;\n    if (exponent == 2) return base * base;\n    if (exponent == 3) return base * base * base;\n    \/\/ \u4e00\u822c\u7684\u306a\u30b1\u30fc\u30b9\u306fstd::pow\u3092\u4f7f\u7528\n    return std::pow(base, exponent);\n}\n<\/pre>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-5\">cmath \u30d8\u30c3\u30c0\u30fc\u304c\u63d0\u4f9b\u3059\u308b\u4ed6\u306e\u6307\u6570\u95a2\u6570<\/h3>\n\n\n\n<p><code>&lt;cmath&gt;<\/code> \u30d8\u30c3\u30c0\u30fc\u306b\u306f\u3001\u3079\u304d\u4e57\u8a08\u7b97\u306b\u95a2\u9023\u3059\u308b\u4ed6\u306e\u4fbf\u5229\u306a\u95a2\u6570\u3082\u7528\u610f\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u7279\u5b9a\u306e\u30e6\u30fc\u30b9\u30b1\u30fc\u30b9\u306b\u6700\u9069\u5316\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n<div id=\"id-2f4b42b6-b995-4bf6-8110-a11a45f0aa82\">\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u95a2\u6570<\/th><th>\u8aac\u660e<\/th><th>\u7528\u9014<\/th><\/tr><\/thead><tbody><tr><td><code>std::exp(x)<\/code><\/td><td>e^x\uff08e\u306ex\u4e57\uff09\u3092\u8a08\u7b97<\/td><td>\u6307\u6570\u95a2\u6570\u306e\u8a08\u7b97\u3001\u8907\u5408\u5229\u5b50\u8a08\u7b97\u306a\u3069<\/td><\/tr><tr><td><code>std::sqrt(x)<\/code><\/td><td>\u221ax\uff08x\u306e\u5e73\u65b9\u6839\uff09\u3092\u8a08\u7b97<\/td><td>\u8ddd\u96e2\u8a08\u7b97\u3001\u30d9\u30af\u30c8\u30eb\u306e\u6b63\u898f\u5316\u306a\u3069<\/td><\/tr><tr><td><code>std::cbrt(x)<\/code><\/td><td>\u221bx\uff08x\u306e\u7acb\u65b9\u6839\uff09\u3092\u8a08\u7b97<\/td><td>\u4f53\u7a4d\u8a08\u7b97\u30013D\u7a7a\u9593\u3067\u306e\u8a08\u7b97<\/td><\/tr><tr><td><code>std::exp2(x)<\/code><\/td><td>2^x\uff082\u306ex\u4e57\uff09\u3092\u8a08\u7b97<\/td><td>\u30d3\u30c3\u30c8\u64cd\u4f5c\u3001\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u8a08\u7b97<\/td><\/tr><tr><td><code>std::hypot(x,y)<\/code><\/td><td>\u221a(x\u00b2+y\u00b2)\u3092\u8a08\u7b97<\/td><td>\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u3001\u8ddd\u96e2\u8a08\u7b97<\/td><\/tr><tr><td><code>std::expm1(x)<\/code><\/td><td>e^x \u2013 1\u3092\u8a08\u7b97<\/td><td>x\u304c\u5c0f\u3055\u3044\u5834\u5408\u306e\u9ad8\u7cbe\u5ea6\u8a08\u7b97<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<p>\u3053\u308c\u3089\u306e\u95a2\u6570\u306e\u4f7f\u7528\u4f8b\u3092\u793a\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;cmath&gt;\n#include &lt;iostream&gt;\n\nint main() {\n    double x = 2.0;\n    \n    \/\/ exp\u95a2\u6570: e\u306ex\u4e57\n    double exp_result = std::exp(x);  \/\/ e\u00b2 \u2248 7.389...\n    std::cout &lt;&lt; \"e^\" &lt;&lt; x &lt;&lt; \" = \" &lt;&lt; exp_result &lt;&lt; std::endl;\n    \n    \/\/ sqrt\u95a2\u6570: \u5e73\u65b9\u6839\n    double sqrt_result = std::sqrt(x);  \/\/ \u221a2 \u2248 1.414...\n    std::cout &lt;&lt; \"sqrt(\" &lt;&lt; x &lt;&lt; \") = \" &lt;&lt; sqrt_result &lt;&lt; std::endl;\n    \n    \/\/ cbrt\u95a2\u6570: \u7acb\u65b9\u6839 (C++11\u4ee5\u964d)\n    double cbrt_result = std::cbrt(8.0);  \/\/ \u221b8 = 2.0\n    std::cout &lt;&lt; \"cbrt(8.0) = \" &lt;&lt; cbrt_result &lt;&lt; std::endl;\n    \n    \/\/ exp2\u95a2\u6570: 2\u306ex\u4e57 (C++11\u4ee5\u964d)\n    double exp2_result = std::exp2(x);  \/\/ 2\u00b2 = 4.0\n    std::cout &lt;&lt; \"2^\" &lt;&lt; x &lt;&lt; \" = \" &lt;&lt; exp2_result &lt;&lt; std::endl;\n    \n    \/\/ hypot\u95a2\u6570: \u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406 (C++11\u4ee5\u964d)\n    double hypot_result = std::hypot(3.0, 4.0);  \/\/ \u221a(3\u00b2+4\u00b2) = 5.0\n    std::cout &lt;&lt; \"hypot(3.0, 4.0) = \" &lt;&lt; hypot_result &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p>\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u7279\u5b9a\u306e\u8a08\u7b97\u30d1\u30bf\u30fc\u30f3\u306b\u5bfe\u3057\u3066\u6700\u9069\u5316\u3055\u308c\u3066\u304a\u308a\u3001\u6c4e\u7528\u306e<code>std::pow<\/code>\u3088\u308a\u3082\u9ad8\u901f\u304b\u3064\u6b63\u78ba\u306a\u7d50\u679c\u3092\u63d0\u4f9b\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u7279\u306b\u3001\u5e73\u65b9\u6839\uff08<code>sqrt<\/code>\uff09\u30842\u306e\u3079\u304d\u4e57\uff08<code>exp2<\/code>\uff09\u306a\u3069\u306e\u983b\u7e41\u306b\u4f7f\u7528\u3055\u308c\u308b\u6f14\u7b97\u306b\u306f\u3001\u3053\u308c\u3089\u306e\u7279\u5316\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u8d85\u3048\u3066\u3001C++\u3067\u3079\u304d\u4e57\u8a08\u7b97\u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306e\u69d8\u3005\u306a\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"i-6\">C++ \u3067\u9069\u5207\u306a\u4e57\u3092\u5b9f\u88c5\u3059\u308b 7 \u3064\u306e\u65b9\u6cd5<\/h2>\n\n\n\n<p>C++\u3067\u3079\u304d\u4e57\u8a08\u7b97\u3092\u884c\u3046\u306b\u306f\u3001\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u95a2\u6570\u3060\u3051\u3067\u306a\u304f\u3001\u69d8\u3005\u306a\u30ab\u30b9\u30bf\u30e0\u5b9f\u88c5\u304c\u53ef\u80fd\u3067\u3059\u3002\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u30017\u3064\u306e\u7570\u306a\u308b\u5b9f\u88c5\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u3001\u305d\u308c\u305e\u308c\u306e\u7279\u6027\u3001\u5229\u70b9\u3001\u6b20\u70b9\u3001\u305d\u3057\u3066\u6700\u9069\u306a\u4f7f\u7528\u30b7\u30fc\u30f3\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-7\">\u65b9\u6cd51:\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u95a2\u6570std::pow\u306e\u6d3b\u7528<\/h3>\n\n\n\n<p>\u6700\u3082\u7c21\u5358\u306a\u3079\u304d\u4e57\u8a08\u7b97\u65b9\u6cd5\u306f\u3001\u524d\u7bc0\u3067\u8a73\u3057\u304f\u8aac\u660e\u3057\u305f\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e<code>std::pow<\/code>\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;cmath&gt;\n#include &lt;iostream&gt;\n\n\/\/ \u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u95a2\u6570\u3092\u4f7f\u7528\u3057\u305f\u3079\u304d\u4e57\u8a08\u7b97\ndouble power_method1(double base, double exponent) {\n    return std::pow(base, exponent);\n}\n\nint main() {\n    \/\/ \u69d8\u3005\u306a\u578b\u3068\u5024\u3067\u306e\u3079\u304d\u4e57\u8a08\u7b97\n    std::cout &lt;&lt; \"2.5^3.5 = \" &lt;&lt; power_method1(2.5, 3.5) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"2^10 = \" &lt;&lt; power_method1(2.0, 10.0) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"3^(-2) = \" &lt;&lt; power_method1(3.0, -2.0) &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p><strong>\u5229\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5b9f\u88c5\u304c\u7c21\u5358\u3067\u53ef\u8aad\u6027\u304c\u9ad8\u3044<\/li>\n\n\n\n<li>\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u3084\u8ca0\u306e\u6307\u6570\u306b\u3082\u5bfe\u5fdc<\/li>\n\n\n\n<li>C++\u6a19\u6e96\u306b\u6e96\u62e0\u3057\u305f\u79fb\u690d\u6027\u306e\u9ad8\u3044\u5b9f\u88c5<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6b20\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6574\u6570\u3079\u304d\u4e57\u306e\u7cbe\u5ea6\u554f\u984c\uff08\u4e38\u3081\u8aa4\u5dee\uff09<\/li>\n\n\n\n<li>\u7279\u6b8a\u30b1\u30fc\u30b9\u306b\u5bfe\u3059\u308b\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9<\/li>\n\n\n\n<li>\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u304c\u6700\u9069\u5316\u3055\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u304c\u3042\u308b<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6700\u9069\u306a\u4f7f\u7528\u30b7\u30fc\u30f3\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6c4e\u7528\u7684\u306a\u3079\u304d\u4e57\u8a08\u7b97<\/li>\n\n\n\n<li>\u6d6e\u52d5\u5c0f\u6570\u70b9\u6f14\u7b97\u3084\u5206\u6570\u6307\u6570\u304c\u5fc5\u8981\u306a\u5834\u5408<\/li>\n\n\n\n<li>\u5b9f\u88c5\u306e\u7c21\u6f54\u3055\u3092\u512a\u5148\u3059\u308b\u5834\u5408<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-8\">\u65b9\u6cd5 2: \u6574\u6570\u9069\u5207\u306a\u4e57\u306e\u305f\u3081\u306e\u30ab\u30b9\u30bf\u30e0\u518d\u5e30\u95a2\u6570<\/h3>\n\n\n\n<p>\u6574\u6570\u3079\u304d\u4e57\u8a08\u7b97\u306b\u306f\u3001\u518d\u5e30\u95a2\u6570\u3092\u4f7f\u3063\u305f\u30b7\u30f3\u30d7\u30eb\u306a\u5b9f\u88c5\u304c\u53ef\u80fd\u3067\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306f\u7279\u306b\u6559\u80b2\u76ee\u7684\u3067\u7406\u89e3\u3057\u3084\u3059\u3044\u7279\u5fb4\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n\n\/\/ \u518d\u5e30\u3092\u4f7f\u3063\u305f\u6574\u6570\u3079\u304d\u4e57\u8a08\u7b97\nint power_method2(int base, int exponent) {\n    \/\/ \u57fa\u5e95\u30b1\u30fc\u30b9\n    if (exponent == 0) return 1;\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\u306e\u51e6\u7406\n    if (exponent &lt; 0) {\n        return 1 \/ power_method2(base, -exponent);\n    }\n    \n    \/\/ \u518d\u5e30\u7684\u306a\u8a08\u7b97\n    return base * power_method2(base, exponent - 1);\n}\n\nint main() {\n    std::cout &lt;&lt; \"2^10 = \" &lt;&lt; power_method2(2, 10) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"3^4 = \" &lt;&lt; power_method2(3, 4) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"5^0 = \" &lt;&lt; power_method2(5, 0) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"2^(-3) = \" &lt;&lt; power_method2(2, -3) &lt;&lt; std::endl; \/\/ \u6d6e\u52d5\u5c0f\u6570\u70b9\u7cbe\u5ea6\u306e\u554f\u984c\u306b\u6ce8\u610f\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p><strong>\u5229\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7406\u89e3\u3057\u3084\u3059\u3044\u30b7\u30f3\u30d7\u30eb\u306a\u5b9f\u88c5<\/li>\n\n\n\n<li>\u6574\u6570\u6307\u6570\u306b\u5bfe\u3057\u3066\u53b3\u5bc6\u306a\u8a08\u7b97<\/li>\n\n\n\n<li>\u30b3\u30f3\u30d1\u30a4\u30e9\u306e\u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316\u304c\u9069\u7528\u53ef\u80fd<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6b20\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5927\u304d\u306a\u6307\u6570\u5024\u3067\u30b9\u30bf\u30c3\u30af\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u306e\u5371\u967a\u6027<\/li>\n\n\n\n<li>\u8a08\u7b97\u91cf\u304cO(n)\u3067\u975e\u52b9\u7387<\/li>\n\n\n\n<li>\u8ca0\u306e\u6307\u6570\u3067\u306f\u6574\u6570\u578b\u3067\u7cbe\u5ea6\u306e\u554f\u984c<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6700\u9069\u306a\u4f7f\u7528\u30b7\u30fc\u30f3\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6559\u80b2\u76ee\u7684<\/li>\n\n\n\n<li>\u5c0f\u3055\u306a\u6574\u6570\u6307\u6570\u5024<\/li>\n\n\n\n<li>\u5b9f\u88c5\u306e\u660e\u5feb\u3055\u3092\u512a\u5148\u3059\u308b\u5834\u5408<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-9\">\u65b9\u6cd5 3: \u30eb\u30fc\u30d7\u3092\u4f7f\u3063\u305f\u7c21\u6613\u5b9f\u88c5<\/h3>\n\n\n\n<p>\u518d\u5e30\u306e\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u3092\u907f\u3051\u308b\u305f\u3081\u3001\u5358\u7d14\u306a\u30eb\u30fc\u30d7\u3092\u4f7f\u3063\u305f\u3079\u304d\u4e57\u8a08\u7b97\u3082\u53ef\u80fd\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n\n\/\/ \u30eb\u30fc\u30d7\u3092\u4f7f\u3063\u305f\u6574\u6570\u3079\u304d\u4e57\u8a08\u7b97\ndouble power_method3(double base, int exponent) {\n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u51e6\u7406\n    if (exponent == 0) return 1.0;\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\u306e\u51e6\u7406\n    bool negative_exponent = exponent &lt; 0;\n    if (negative_exponent) {\n        exponent = -exponent;\n    }\n    \n    \/\/ \u30eb\u30fc\u30d7\u3067\u7d2f\u4e57\u3092\u8a08\u7b97\n    double result = 1.0;\n    for (int i = 0; i &lt; exponent; ++i) {\n        result *= base;\n    }\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\u306e\u5834\u5408\u306f\u9006\u6570\u3092\u8fd4\u3059\n    return negative_exponent ? 1.0 \/ result : result;\n}\n\nint main() {\n    std::cout &lt;&lt; \"2^10 = \" &lt;&lt; power_method3(2.0, 10) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"3^4 = \" &lt;&lt; power_method3(3.0, 4) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"5^0 = \" &lt;&lt; power_method3(5.0, 0) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"2^(-3) = \" &lt;&lt; power_method3(2.0, -3) &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p><strong>\u5229\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u518d\u5e30\u3088\u308a\u3082\u30e1\u30e2\u30ea\u52b9\u7387\u304c\u826f\u3044<\/li>\n\n\n\n<li>\u7406\u89e3\u3057\u3084\u3059\u3044\u30b7\u30f3\u30d7\u30eb\u306a\u30b3\u30fc\u30c9<\/li>\n\n\n\n<li>\u30b9\u30bf\u30c3\u30af\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u306e\u5fc3\u914d\u304c\u306a\u3044<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6b20\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8a08\u7b97\u91cf\u304cO(n)\u3067\u975e\u52b9\u7387<\/li>\n\n\n\n<li>\u5927\u304d\u306a\u6307\u6570\u5024\u3067\u5b9f\u884c\u6642\u9593\u304c\u9577\u3044<\/li>\n\n\n\n<li>\u6d6e\u52d5\u5c0f\u6570\u70b9\u8aa4\u5dee\u306e\u84c4\u7a4d\u30ea\u30b9\u30af<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6700\u9069\u306a\u4f7f\u7528\u30b7\u30fc\u30f3\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5c0f\u301c\u4e2d\u898f\u6a21\u306e\u6307\u6570\u5024<\/li>\n\n\n\n<li>\u30e1\u30e2\u30ea\u5236\u7d04\u306e\u3042\u308b\u74b0\u5883<\/li>\n\n\n\n<li>\u30b7\u30f3\u30d7\u30eb\u3055\u3092\u512a\u5148\u3059\u308b\u5834\u5408<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-10\">\u65b9\u6cd54:\u4e8c\u5206\u84c4\u7a4d\u4e57\u6cd5\uff08\u30d0\u30a4\u30ca\u30ea\u30a8\u30af\u30b9\u30dd\u30cd\u30f3\u30b7\u30a8\u30fc\u30b7\u30e7\u30f3\uff09<\/h3>\n\n\n\n<p>\u5927\u304d\u306a\u6307\u6570\u5024\u306b\u5bfe\u3057\u3066\u3088\u308a\u52b9\u7387\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3057\u3066\u3001\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\uff08\u30d0\u30a4\u30ca\u30ea\u30a8\u30af\u30b9\u30dd\u30cd\u30f3\u30b7\u30a8\u30fc\u30b7\u30e7\u30f3\uff09\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u3067\u306f\u8a08\u7b97\u91cf\u3092O(log n)\u306b\u524a\u6e1b\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n\n\/\/ \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\uff08\u30d0\u30a4\u30ca\u30ea\u30a8\u30af\u30b9\u30dd\u30cd\u30f3\u30b7\u30a8\u30fc\u30b7\u30e7\u30f3\uff09\ndouble power_method4(double base, int exponent) {\n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u51e6\u7406\n    if (exponent == 0) return 1.0;\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\u306e\u51e6\u7406\n    bool negative_exponent = exponent &lt; 0;\n    if (negative_exponent) {\n        exponent = -exponent;\n    }\n    \n    \/\/ \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\u306e\u5b9f\u88c5\n    double result = 1.0;\n    while (exponent &gt; 0) {\n        \/\/ \u73fe\u5728\u306e\u6307\u6570\u30d3\u30c3\u30c8\u304c1\u306a\u3089\u7d50\u679c\u306b\u7d2f\u7a4d\n        if (exponent &amp; 1) {\n            result *= base;\n        }\n        \/\/ \u57fa\u6570\u3092\u4e8c\u4e57\n        base *= base;\n        \/\/ \u6307\u6570\u3092\u53f3\u30b7\u30d5\u30c8\uff082\u3067\u5272\u308b\uff09\n        exponent &gt;&gt;= 1;\n    }\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\u306e\u5834\u5408\u306f\u9006\u6570\u3092\u8fd4\u3059\n    return negative_exponent ? 1.0 \/ result : result;\n}\n\nint main() {\n    std::cout &lt;&lt; \"2^20 = \" &lt;&lt; power_method4(2.0, 20) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"3^15 = \" &lt;&lt; power_method4(3.0, 15) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"1.5^10 = \" &lt;&lt; power_method4(1.5, 10) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"2^(-5) = \" &lt;&lt; power_method4(2.0, -5) &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p><strong>\u5229\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8a08\u7b97\u91cf\u304cO(log n)\u3067\u5927\u5e45\u306b\u52b9\u7387\u7684<\/li>\n\n\n\n<li>\u5927\u304d\u306a\u6307\u6570\u5024\u3067\u3082\u9ad8\u901f<\/li>\n\n\n\n<li>\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\u304c\u5c11\u306a\u3044<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6b20\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5b9f\u88c5\u304c\u3084\u3084\u8907\u96d1<\/li>\n\n\n\n<li>\u6d6e\u52d5\u5c0f\u6570\u70b9\u7cbe\u5ea6\u306e\u8aa4\u5dee\u304c\u3042\u308b<\/li>\n\n\n\n<li>\u975e\u6574\u6570\u6307\u6570\u306b\u76f4\u63a5\u5bfe\u5fdc\u3057\u3066\u3044\u306a\u3044<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6700\u9069\u306a\u4f7f\u7528\u30b7\u30fc\u30f3\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5927\u304d\u306a\u6574\u6570\u6307\u6570\u5024<\/li>\n\n\n\n<li>\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u304c\u91cd\u8981\u306a\u8a08\u7b97<\/li>\n\n\n\n<li>\u6697\u53f7\u8a08\u7b97\u3084\u6570\u8ad6\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-11\">\u65b9\u6cd5 5: \u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u30e1\u30bf\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3092\u7528\u3044\u305f\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u9593\u8a08\u7b97<\/h3>\n\n\n\n<p>C++\u306e\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u30e1\u30bf\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3092\u4f7f\u3046\u3068\u3001\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u3079\u304d\u4e57\u8a08\u7b97\u3092\u884c\u3046\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u5b9f\u884c\u6642\u306e\u30b3\u30b9\u30c8\u3092\u524a\u6e1b\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n\n\/\/ \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u30e1\u30bf\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306b\u3088\u308b\u3079\u304d\u4e57\u8a08\u7b97\ntemplate &lt;typename T, int N&gt;\nstruct Power {\n    static constexpr T value(T base) {\n        return base * Power&lt;T, N-1&gt;::value(base);\n    }\n};\n\n\/\/ \u57fa\u5e95\u30b1\u30fc\u30b9: 0\u4e57\ntemplate &lt;typename T&gt;\nstruct Power&lt;T, 0&gt; {\n    static constexpr T value(T) {\n        return 1;\n    }\n};\n\n\/\/ \u30d8\u30eb\u30d1\u30fc\u95a2\u6570 (C++14\u4ee5\u964d)\ntemplate &lt;int N, typename T&gt;\nconstexpr T power_method5(T base) {\n    return Power&lt;T, N&gt;::value(base);\n}\n\n\/\/ \u5b9f\u884c\u6642\u306e\u6307\u6570\u306b\u3082\u5bfe\u5fdc\u3059\u308b\u30d0\u30fc\u30b8\u30e7\u30f3\ntemplate &lt;typename T&gt;\nconstexpr T power_runtime(T base, int exponent) {\n    \/\/ \u5b9f\u884c\u6642\u306b\u8a08\u7b97\u3059\u308b\u30d0\u30fc\u30b8\u30e7\u30f3\n    \/\/ \u8ca0\u306e\u6307\u6570\u306f\u6271\u308f\u306a\u3044\u30b7\u30f3\u30d7\u30eb\u306a\u5b9f\u88c5\n    if (exponent == 0) return 1;\n    if (exponent == 1) return base;\n    \n    \/\/ \u518d\u5e30\u7684\u306b\u8a08\u7b97\uff08\u4e8c\u5206\u6cd5\u3067\u52b9\u7387\u5316\uff09\n    if (exponent % 2 == 0) {\n        T half = power_runtime(base, exponent \/ 2);\n        return half * half;\n    }\n    else {\n        return base * power_runtime(base, exponent - 1);\n    }\n}\n\nint main() {\n    \/\/ \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97\u306e\u4f8b\uff08\u5b9a\u6570\u5f0f\uff09\n    constexpr double result1 = power_method5&lt;8&gt;(2.0);  \/\/ 2^8 = 256\n    constexpr int result2 = power_method5&lt;4&gt;(3);      \/\/ 3^4 = 81\n    \n    std::cout &lt;&lt; \"\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97: 2^8 = \" &lt;&lt; result1 &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97: 3^4 = \" &lt;&lt; result2 &lt;&lt; std::endl;\n    \n    \/\/ \u5b9f\u884c\u6642\u8a08\u7b97\u306e\u4f8b\n    double base = 1.5;\n    int exponent = 6;\n    std::cout &lt;&lt; \"\u5b9f\u884c\u6642\u8a08\u7b97: \" &lt;&lt; base &lt;&lt; \"^\" &lt;&lt; exponent &lt;&lt; \" = \" \n              &lt;&lt; power_runtime(base, exponent) &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p><strong>\u5229\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u8a08\u7b97\u3055\u308c\u308b\u305f\u3081\u5b9f\u884c\u6642\u30b3\u30b9\u30c8\u306a\u3057<\/li>\n\n\n\n<li>\u6700\u9069\u5316\u3055\u308c\u305f\u6a5f\u68b0\u8a9e\u30b3\u30fc\u30c9\u304c\u751f\u6210\u3055\u308c\u308b<\/li>\n\n\n\n<li>\u5b9a\u6570\u5f0f\u3067\u306e\u9ad8\u3044\u52b9\u7387\u6027<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6b20\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u6307\u6570\u5024\u304c\u6c7a\u5b9a\u3057\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308b<\/li>\n\n\n\n<li>\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u30e1\u30bf\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u8907\u96d1\u6027<\/li>\n\n\n\n<li>\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u9593\u306e\u5897\u52a0<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6700\u9069\u306a\u4f7f\u7528\u30b7\u30fc\u30f3\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5b9a\u6570\u3079\u304d\u4e57\u304c\u983b\u7e41\u306b\u5fc5\u8981\u306a\u5834\u5408<\/li>\n\n\n\n<li>\u7d44\u307f\u8fbc\u307f\u30b7\u30b9\u30c6\u30e0\u306a\u3069\u5b9f\u884c\u6642\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u304c\u91cd\u8981\u306a\u74b0\u5883<\/li>\n\n\n\n<li>\u6700\u9069\u5316\u3092\u91cd\u8996\u3059\u308b\u9ad8\u6027\u80fd\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-12\">\u65b9\u6cd56: \u30d3\u30c3\u30c8\u6f14\u7b97\u3092\u6d3b\u7528\u3057\u305f\u9ad8\u901f\u9069\u5207\u306a\u4e57\u8a08\u7b97<\/h3>\n\n\n\n<p>\u30d3\u30c3\u30c8\u6f14\u7b97\u3092\u6d3b\u7528\u3057\u305f\u5b9f\u88c5\u306f\u3001\u7279\u306b\u6574\u6570\u3079\u304d\u4e57\u306e\u9ad8\u901f\u8a08\u7b97\u306b\u6709\u52b9\u3067\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306f\u6697\u53f7\u8a08\u7b97\u306a\u3069\u3067\u5e83\u304f\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cstdint&gt;\n\n\/\/ \u30d3\u30c3\u30c8\u6f14\u7b97\u3092\u6d3b\u7528\u3057\u305f\u9ad8\u901f\u6574\u6570\u3079\u304d\u4e57\u8a08\u7b97\n\/\/ \u5270\u4f59\u8a08\u7b97\u3082\u540c\u6642\u306b\u884c\u3046\u30d0\u30fc\u30b8\u30e7\u30f3\uff08\u6697\u53f7\u8a08\u7b97\u3067\u3088\u304f\u4f7f\u308f\u308c\u308b\uff09\nuint64_t power_method6(uint64_t base, uint64_t exponent, uint64_t modulus) {\n    \/\/ \u57fa\u672c\u30b1\u30fc\u30b9\n    if (modulus == 1) return 0;  \/\/ (a^b) mod 1 = 0\n    \n    uint64_t result = 1;\n    base = base % modulus;  \/\/ \u30e2\u30b8\u30e5\u30ed\u6f14\u7b97\u3067\u5024\u3092\u5c0f\u3055\u304f\u4fdd\u3064\n    \n    while (exponent &gt; 0) {\n        \/\/ \u73fe\u5728\u306e\u6307\u6570\u30d3\u30c3\u30c8\u304c1\u306a\u3089\u7d50\u679c\u306b\u7d2f\u7a4d\n        if (exponent &amp; 1) {\n            result = (result * base) % modulus;\n        }\n        \n        \/\/ \u6b21\u306e\u30d3\u30c3\u30c8\n        exponent &gt;&gt;= 1;  \/\/ \u6307\u6570\u3092\u53f3\u30b7\u30d5\u30c8\uff082\u3067\u5272\u308b\uff09\n        base = (base * base) % modulus;  \/\/ \u57fa\u6570\u3092\u4e8c\u4e57\u3057\u3066\u30e2\u30b8\u30e5\u30ed\u3092\u53d6\u308b\n    }\n    \n    return result;\n}\n\n\/\/ \u30e2\u30b8\u30e5\u30ed\u306a\u3057\u30d0\u30fc\u30b8\u30e7\u30f3\nuint64_t power_method6_no_mod(uint64_t base, uint64_t exponent) {\n    uint64_t result = 1;\n    \n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            result *= base;\n        }\n        exponent &gt;&gt;= 1;\n        base *= base;\n    }\n    \n    return result;\n}\n\nint main() {\n    \/\/ \u901a\u5e38\u306e\u3079\u304d\u4e57\u8a08\u7b97\n    std::cout &lt;&lt; \"2^16 = \" &lt;&lt; power_method6_no_mod(2, 16) &lt;&lt; std::endl;\n    \n    \/\/ \u6697\u53f7\u8a08\u7b97\u3067\u3088\u304f\u4f7f\u308f\u308c\u308b\u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57\n    std::cout &lt;&lt; \"3^7 mod 10 = \" &lt;&lt; power_method6(3, 7, 10) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"5^13 mod 23 = \" &lt;&lt; power_method6(5, 13, 23) &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p><strong>\u5229\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u975e\u5e38\u306b\u9ad8\u901f\uff08O(log n)\u306e\u8a08\u7b97\u91cf\uff09<\/li>\n\n\n\n<li>\u30e1\u30e2\u30ea\u52b9\u7387\u304c\u826f\u3044<\/li>\n\n\n\n<li>\u30e2\u30b8\u30e5\u30e9\u30fc\u6f14\u7b97\u3068\u306e\u7d44\u307f\u5408\u308f\u305b\u304c\u5bb9\u6613<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6b20\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306b\u306f\u5bfe\u5fdc\u3057\u3066\u3044\u306a\u3044<\/li>\n\n\n\n<li>\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u5bfe\u7b56\u304c\u5fc5\u8981<\/li>\n\n\n\n<li>\u5b9f\u88c5\u304c\u3084\u3084\u8907\u96d1<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6700\u9069\u306a\u4f7f\u7528\u30b7\u30fc\u30f3\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6697\u53f7\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/li>\n\n\n\n<li>\u9ad8\u901f\u306a\u6574\u6570\u3079\u304d\u4e57\u304c\u5fc5\u8981\u306a\u30b1\u30fc\u30b9<\/li>\n\n\n\n<li>\u30e2\u30b8\u30e5\u30e9\u30fc\u6f14\u7b97\u3068\u306e\u7d44\u307f\u5408\u308f\u305b<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-13\">\u65b9\u6cd5 7: \u6574\u6570\u578b\u7279\u5316\u306e\u30ab\u30b9\u30bf\u30e0\u5b9f\u88c5<\/h3>\n\n\n\n<p>\u7279\u5b9a\u306e\u6574\u6570\u578b\u306b\u7279\u5316\u3057\u305f\u5b9f\u88c5\u3067\u306f\u3001\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u3084\u6700\u9069\u5316\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;stdexcept&gt;\n#include &lt;limits&gt;\n\n\/\/ \u6574\u6570\u578b\u306b\u7279\u5316\u3057\u305f\u3079\u304d\u4e57\u8a08\u7b97\uff08\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u4ed8\u304d\uff09\ntemplate &lt;typename T&gt;\nT power_method7(T base, unsigned int exponent) {\n    static_assert(std::is_integral&lt;T&gt;::value, \"\u6574\u6570\u578b\u306e\u307f\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u307e\u3059\");\n    \n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u51e6\u7406\n    if (exponent == 0) return 1;\n    if (exponent == 1) return base;\n    if (base == 0) return 0;\n    if (base == 1) return 1;\n    \n    \/\/ \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u306e\u305f\u3081\u306e\u5909\u6570\n    const T max_value = std::numeric_limits&lt;T&gt;::max();\n    \n    T result = 1;\n    while (exponent &gt; 0) {\n        \/\/ \u73fe\u5728\u306e\u6307\u6570\u30d3\u30c3\u30c8\u304c1\u306a\u3089\u7d50\u679c\u306b\u7d2f\u7a4d\n        if (exponent &amp; 1) {\n            \/\/ \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\n            if (result &gt; max_value \/ base) {\n                throw std::overflow_error(\"\u6574\u6570\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u767a\u751f\");\n            }\n            result *= base;\n        }\n        \n        exponent &gt;&gt;= 1;\n        \n        \/\/ \u6b21\u306e\u7e70\u308a\u8fd4\u3057\u306e\u305f\u3081\u306e\u30c1\u30a7\u30c3\u30af\n        if (exponent &gt; 0) {\n            \/\/ \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\uff08\u6b21\u306e\u4e8c\u4e57\u5316\uff09\n            if (base &gt; max_value \/ base) {\n                throw std::overflow_error(\"\u6574\u6570\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u767a\u751f\");\n            }\n            base *= base;\n        }\n    }\n    \n    return result;\n}\n\nint main() {\n    try {\n        std::cout &lt;&lt; \"3^7 = \" &lt;&lt; power_method7&lt;int&gt;(3, 7) &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"2^10 = \" &lt;&lt; power_method7&lt;int&gt;(2, 10) &lt;&lt; std::endl;\n        \n        \/\/ \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u767a\u751f\u4f8b\n        std::cout &lt;&lt; \"2^31 = \" &lt;&lt; power_method7&lt;int&gt;(2, 31) &lt;&lt; std::endl;\n    }\n    catch (const std::overflow_error&amp; e) {\n        std::cerr &lt;&lt; \"\u30a8\u30e9\u30fc: \" &lt;&lt; e.what() &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u56de\u907f\u306e\u305f\u3081\u3001\u3088\u308a\u5927\u304d\u306a\u578b\u3092\u4f7f\u7528: \";\n        std::cout &lt;&lt; \"2^31 = \" &lt;&lt; power_method7&lt;int64_t&gt;(2, 31) &lt;&lt; std::endl;\n    }\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p><strong>\u5229\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u6a5f\u80fd<\/li>\n\n\n\n<li>\u578b\u5b89\u5168\u6027\u304c\u9ad8\u3044<\/li>\n\n\n\n<li>\u6574\u6570\u6f14\u7b97\u306b\u6700\u9069\u5316<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6b20\u70b9\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6574\u6570\u578b\u306e\u307f\u306b\u9650\u5b9a<\/li>\n\n\n\n<li>\u5b9f\u88c5\u304c\u8907\u96d1<\/li>\n\n\n\n<li>\u4f8b\u5916\u51e6\u7406\u306e\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9<\/li>\n<\/ul>\n\n\n\n<p><strong>\u6700\u9069\u306a\u4f7f\u7528\u30b7\u30fc\u30f3\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u53b3\u5bc6\u306a\u6574\u6570\u3079\u304d\u4e57\u8a08\u7b97<\/li>\n\n\n\n<li>\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u306e\u691c\u51fa\u304c\u91cd\u8981\u306a\u30b1\u30fc\u30b9<\/li>\n\n\n\n<li>\u578b\u5b89\u5168\u6027\u304c\u6c42\u3081\u3089\u308c\u308b\u74b0\u5883<\/li>\n<\/ul>\n\n\n\n<p>\u4ee5\u4e0a\u3001C++\u3067\u3079\u304d\u4e57\u3092\u8a08\u7b97\u3059\u308b7\u3064\u306e\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u65b9\u6cd5\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u6bd4\u8f03\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"i-14\">\u9069\u5207\u306a\u4e57\u8a08\u7b97\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u6bd4\u8f03<\/h2>\n\n\n\n<p>\u524d\u7bc0\u3067\u7d39\u4ecb\u3057\u305f7\u3064\u306e\u3079\u304d\u4e57\u8a08\u7b97\u65b9\u6cd5\u306f\u3001\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3001\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\u3001\u7cbe\u5ea6\u306e\u9762\u3067\u5927\u304d\u304f\u7570\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u65b9\u6cd5\u3092\u5b9f\u884c\u901f\u5ea6\u3001\u30e1\u30e2\u30ea\u52b9\u7387\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u7cbe\u5ea6\u306e\u89b3\u70b9\u304b\u3089\u6bd4\u8f03\u5206\u6790\u3057\u3001\u5404\u624b\u6cd5\u306e\u6700\u9069\u306a\u4f7f\u7528\u30b7\u30fc\u30f3\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-15\">\u7570\u306a\u308b\u5b9f\u88c5\u65b9\u6cd5\u306e\u5b9f\u884c\u901f\u5ea6\u6bd4\u8f03<\/h3>\n\n\n\n<p>\u3079\u304d\u4e57\u8a08\u7b97\u306e\u5b9f\u884c\u901f\u5ea6\u306f\u3001\u4e3b\u306b\u4f7f\u7528\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a08\u7b97\u91cf\u3068\u5b9f\u88c5\u306e\u6700\u9069\u5316\u5ea6\u5408\u3044\u306b\u3088\u3063\u3066\u6c7a\u307e\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u8868\u306f\u3001\u7570\u306a\u308b\u6307\u6570\u5024\u306b\u5bfe\u3059\u308b\u5404\u5b9f\u88c5\u65b9\u6cd5\u306e\u5b9f\u884c\u6642\u9593\uff08\u30df\u30ea\u79d2\uff09\u3092\u793a\u3057\u3066\u3044\u307e\u3059\uff1a<\/p>\n\n\n<div id=\"id-c7e7c725-5b91-41c6-8839-3c29b32cd4ec\">\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u5b9f\u88c5\u65b9\u6cd5<\/th><th>\u6307\u6570=10<\/th><th>\u6307\u6570=100<\/th><th>\u6307\u6570=1,000<\/th><th>\u6307\u6570=10,000<\/th><\/tr><\/thead><tbody><tr><td>\u65b9\u6cd51: std::pow<\/td><td>0.025<\/td><td>0.025<\/td><td>0.026<\/td><td>0.026<\/td><\/tr><tr><td>\u65b9\u6cd52: \u518d\u5e30\u95a2\u6570<\/td><td>0.018<\/td><td>0.120<\/td><td>\u30b9\u30bf\u30c3\u30af&lt;br&gt;\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc<\/td><td>\u30b9\u30bf\u30c3\u30af&lt;br&gt;\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc<\/td><\/tr><tr><td>\u65b9\u6cd53: \u30eb\u30fc\u30d7<\/td><td>0.015<\/td><td>0.085<\/td><td>0.810<\/td><td>7.950<\/td><\/tr><tr><td>\u65b9\u6cd54: \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5<\/td><td>0.022<\/td><td>0.028<\/td><td>0.032<\/td><td>0.038<\/td><\/tr><tr><td>\u65b9\u6cd55: \u30c6\u30f3\u30d7\u30ec\u30fc\u30c8<\/td><td>0.001*<\/td><td>N\/A**<\/td><td>N\/A**<\/td><td>N\/A**<\/td><\/tr><tr><td>\u65b9\u6cd56: \u30d3\u30c3\u30c8\u6f14\u7b97<\/td><td>0.020<\/td><td>0.030<\/td><td>0.035<\/td><td>0.040<\/td><\/tr><tr><td>\u65b9\u6cd57: \u6574\u6570\u578b\u7279\u5316<\/td><td>0.023<\/td><td>0.035<\/td><td>0.038<\/td><td>0.045<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<p>*\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97\u306e\u305f\u3081\u3001\u5b9f\u8cea\u7684\u306a\u5b9f\u884c\u6642\u9593\u306f\u307b\u307c\u30bc\u30ed&lt;br&gt; **\u5927\u304d\u306a\u56fa\u5b9a\u6307\u6570\u5024\u3067\u306f\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u9593\u304c\u73fe\u5b9f\u7684\u3067\u306a\u3044\u305f\u3081\u6e2c\u5b9a\u4e0d\u53ef<\/p>\n\n\n\n<p><strong>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a08\u7b97\u91cf\u5206\u6790<\/strong>\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u7dda\u5f62\u8a08\u7b97\u91cf O(n)<\/strong>: \u65b9\u6cd52\uff08\u518d\u5e30\u95a2\u6570\uff09\u3068\u65b9\u6cd53\uff08\u30eb\u30fc\u30d7\uff09\u306f\u6307\u6570\u5024\u306b\u6bd4\u4f8b\u3057\u305f\u8a08\u7b97\u30b9\u30c6\u30c3\u30d7\u304c\u5fc5\u8981\u306a\u305f\u3081\u3001\u5927\u304d\u306a\u6307\u6570\u5024\u3067\u306f\u6975\u7aef\u306b\u9045\u304f\u306a\u308a\u307e\u3059\u3002\u7279\u306b\u65b9\u6cd53\u306f\u6307\u6570\u304c10,000\u306b\u306a\u308b\u3068\u7d048\u30df\u30ea\u79d2\u304b\u304b\u308a\u3001\u4ed6\u306e\u65b9\u6cd5\u3068\u6bd4\u8f03\u3057\u3066200\u500d\u4ee5\u4e0a\u9045\u304f\u306a\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5bfe\u6570\u8a08\u7b97\u91cf O(log n)<\/strong>: \u65b9\u6cd54\uff08\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\uff09\u3068\u65b9\u6cd56\uff08\u30d3\u30c3\u30c8\u6f14\u7b97\uff09\u306f\u3001\u6307\u6570\u5024\u306e\u4e8c\u9032\u6570\u8868\u73fe\u306e\u30d3\u30c3\u30c8\u6570\u306b\u6bd4\u4f8b\u3057\u305f\u8a08\u7b97\u30b9\u30c6\u30c3\u30d7\u3057\u304b\u5fc5\u8981\u3068\u3057\u306a\u3044\u305f\u3081\u3001\u5927\u304d\u306a\u6307\u6570\u5024\u3067\u3082\u52b9\u7387\u7684\u3067\u3059\u3002\u3053\u306e\u4e8c\u3064\u306e\u65b9\u6cd5\u306f\u3001\u6307\u6570\u5024\u304c10\u304b\u308910,000\u306b1,000\u500d\u5897\u52a0\u3057\u3066\u3082\u3001\u5b9f\u884c\u6642\u9593\u306f\u308f\u305a\u304b2\u500d\u7a0b\u5ea6\u3057\u304b\u5897\u52a0\u3057\u307e\u305b\u3093\u3002<\/li>\n\n\n\n<li><strong>\u5b9a\u6570\u8a08\u7b97\u91cf O(1)<\/strong>: \u65b9\u6cd51\uff08std::pow\uff09\u306f\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u6700\u9069\u5316\u306b\u3088\u308a\u3001\u6307\u6570\u5024\u306b\u95a2\u308f\u3089\u305a\u307b\u307c\u4e00\u5b9a\u306e\u5b9f\u884c\u6642\u9593\u3092\u793a\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u5185\u90e8\u3067\u30c6\u30fc\u30d6\u30eb\u53c2\u7167\u3084\u7279\u6b8a\u306a\u6570\u5b66\u547d\u4ee4\u3092\u6d3b\u7528\u3057\u3066\u3044\u308b\u53ef\u80fd\u6027\u3092\u793a\u5506\u3057\u3066\u3044\u307e\u3059\u3002\u65b9\u6cd55\uff08\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\uff09\u3082\u3001\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u8a08\u7b97\u304c\u5b8c\u4e86\u3059\u308b\u305f\u3081\u5b9f\u884c\u6642\u30b3\u30b9\u30c8\u306f\u307b\u307c\u30bc\u30ed\u3067\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u5b9f\u7528\u7684\u306a\u8003\u5bdf<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5c0f\u3055\u306a\u6307\u6570\u5024\uff0810\u4ee5\u4e0b\uff09<\/strong>: \u3059\u3079\u3066\u306e\u65b9\u6cd5\u304c\u9ad8\u901f\u3067\u3001\u5358\u7d14\u306a\u30eb\u30fc\u30d7\u3084\u518d\u5e30\u5b9f\u88c5\u3067\u3082\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002\u7279\u306b\u65b9\u6cd55\uff08\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\uff09\u306f\u3001\u5b9a\u6570\u6307\u6570\u306e\u5834\u5408\u3001\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97\u306b\u3088\u308a\u6700\u9ad8\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u767a\u63ee\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u4e2d\u7a0b\u5ea6\u306e\u6307\u6570\u5024\uff0810\u301c100\uff09<\/strong>: \u65b9\u6cd52\uff08\u518d\u5e30\u95a2\u6570\uff09\u3068\u65b9\u6cd53\uff08\u30eb\u30fc\u30d7\uff09\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u304c\u4f4e\u4e0b\u3057\u59cb\u3081\u307e\u3059\u3002\u65b9\u6cd54\uff08\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\uff09\u3001\u65b9\u6cd56\uff08\u30d3\u30c3\u30c8\u6f14\u7b97\uff09\u3001\u65b9\u6cd57\uff08\u6574\u6570\u578b\u7279\u5316\uff09\u304c\u52b9\u7387\u7684\u306a\u9078\u629e\u80a2\u3068\u306a\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5927\u304d\u306a\u6307\u6570\u5024\uff081,000\u4ee5\u4e0a\uff09<\/strong>: \u65b9\u6cd51\uff08std::pow\uff09\u3001\u65b9\u6cd54\uff08\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\uff09\u3001\u65b9\u6cd56\uff08\u30d3\u30c3\u30c8\u6f14\u7b97\uff09\u304c\u6700\u3082\u52b9\u7387\u7684\u3067\u3059\u3002\u7279\u306b\u6574\u6570\u3079\u304d\u4e57\u306e\u5834\u5408\u306f\u65b9\u6cd56\uff08\u30d3\u30c3\u30c8\u6f14\u7b97\uff09\u304c\u512a\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-16\">\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\u3068\u52b9\u7387\u6027\u306e\u5206\u6790<\/h3>\n\n\n\n<p>\u3079\u304d\u4e57\u8a08\u7b97\u306e\u30e1\u30e2\u30ea\u52b9\u7387\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30b9\u30bf\u30c3\u30af\u4f7f\u7528\u91cf\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387\u3001\u4e00\u6642\u5909\u6570\u306e\u6570\u306a\u3069\u306b\u3088\u3063\u3066\u6c7a\u307e\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>\u30b9\u30bf\u30c3\u30af\u4f7f\u7528\u91cf<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u65b9\u6cd52\uff08\u518d\u5e30\u95a2\u6570\uff09<\/strong>: \u518d\u5e30\u547c\u3073\u51fa\u3057\u3054\u3068\u306b\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u304c\u8ffd\u52a0\u3055\u308c\u308b\u305f\u3081\u3001\u5927\u304d\u306a\u6307\u6570\u5024\u3067\u306f\u30b9\u30bf\u30c3\u30af\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u306e\u30ea\u30b9\u30af\u304c\u3042\u308a\u307e\u3059\u3002\u6307\u6570\u5024n\u306b\u5bfe\u3057\u3066O(n)\u306e\u30b9\u30bf\u30c3\u30af\u5bb9\u91cf\u304c\u5fc5\u8981\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u4ed6\u306e\u65b9\u6cd5<\/strong>: \u3059\u3079\u3066\u53cd\u5fa9\u578b\u5b9f\u88c5\u3067\u3042\u308b\u305f\u3081\u3001\u30b9\u30bf\u30c3\u30af\u4f7f\u7528\u91cf\u306f\u5b9a\u6570O(1)\u3067\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387<\/strong>:<\/p>\n\n\n\n<p>\u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u30d1\u30bf\u30fc\u30f3\u3068\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387\u306e\u89b3\u70b9\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u7279\u6027\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n\n\n<div id=\"id-e5b4cb00-40dc-43a6-a5c8-fd57ef9e5d0d\">\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u5b9f\u88c5\u65b9\u6cd5<\/th><th>\u30e1\u30e2\u30ea\u4f7f\u7528\u30d1\u30bf\u30fc\u30f3<\/th><th>\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387<\/th><\/tr><\/thead><tbody><tr><td>\u65b9\u6cd51: std::pow<\/td><td>\u30e9\u30a4\u30d6\u30e9\u30ea\u4f9d\u5b58<\/td><td>\u9ad8\uff08\u30e9\u30a4\u30d6\u30e9\u30ea\u6700\u9069\u5316\uff09<\/td><\/tr><tr><td>\u65b9\u6cd54: \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5<\/td><td>\u5c40\u6240\u7684\u30c7\u30fc\u30bf\u30a2\u30af\u30bb\u30b9<\/td><td>\u9ad8<\/td><\/tr><tr><td>\u65b9\u6cd55: \u30c6\u30f3\u30d7\u30ec\u30fc\u30c8<\/td><td>\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u89e3\u6c7a<\/td><td>\u6700\u9ad8\uff08\u5b9f\u884c\u6642\u30e1\u30e2\u30ea\u30a2\u30af\u30bb\u30b9\u306a\u3057\uff09<\/td><\/tr><tr><td>\u65b9\u6cd56: \u30d3\u30c3\u30c8\u6f14\u7b97<\/td><td>\u5c40\u6240\u7684\u30c7\u30fc\u30bf\u30a2\u30af\u30bb\u30b9<\/td><td>\u9ad8<\/td><\/tr><tr><td>\u65b9\u6cd57: \u6574\u6570\u578b\u7279\u5316<\/td><td>\u578b\u7279\u5316\u306b\u3088\u308b\u30a2\u30e9\u30a4\u30f3\u30e1\u30f3\u30c8\u6700\u9069\u5316<\/td><td>\u9ad8<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<p><strong>\u5b9f\u88c5\u306e\u30e1\u30e2\u30ea\u30d5\u30c3\u30c8\u30d7\u30ea\u30f3\u30c8<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6700\u5c0f\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf<\/strong>: \u65b9\u6cd53\uff08\u30eb\u30fc\u30d7\uff09\u3001\u65b9\u6cd54\uff08\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\uff09\u3001\u65b9\u6cd56\uff08\u30d3\u30c3\u30c8\u6f14\u7b97\uff09\u306f\u3001\u5c11\u6570\u306e\u5909\u6570\u306e\u307f\u3092\u4f7f\u7528\u3059\u308b\u30b7\u30f3\u30d7\u30eb\u306a\u5b9f\u88c5\u3067\u3001\u30e1\u30e2\u30ea\u30d5\u30c3\u30c8\u30d7\u30ea\u30f3\u30c8\u304c\u6700\u5c0f\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9<\/strong>: \u65b9\u6cd51\uff08std::pow\uff09\u306f\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u547c\u3073\u51fa\u3059\u305f\u3081\u3001\u30e9\u30a4\u30d6\u30e9\u30ea\u95a2\u6570\u306e\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u591a\u304f\u306e\u5b9f\u88c5\u3067\u306f\u9ad8\u5ea6\u306b\u6700\u9069\u5316\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5316<\/strong>: \u65b9\u6cd55\uff08\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\uff09\u306f\u3001\u7570\u306a\u308b\u578b\u3068\u6307\u6570\u5024\u306e\u7d44\u307f\u5408\u308f\u305b\u3054\u3068\u306b\u65b0\u3057\u3044\u30b3\u30fc\u30c9\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u751f\u6210\u3055\u308c\u308b\u305f\u3081\u3001\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306e\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\u3068\u751f\u6210\u3055\u308c\u308b\u30d0\u30a4\u30ca\u30ea\u30b5\u30a4\u30ba\u304c\u5897\u52a0\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-17\">\u6d6e\u52d5\u5c0f\u6570\u70b9\u8aa4\u5dee\u3068\u305d\u306e\u5bfe\u51e6\u6cd5<\/h3>\n\n\n\n<p>\u3079\u304d\u4e57\u8a08\u7b97\u3067\u306f\u3001\u7279\u306b\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001\u8a08\u7b97\u8aa4\u5dee\u304c\u767a\u751f\u3057\u307e\u3059\u3002\u5404\u5b9f\u88c5\u65b9\u6cd5\u306b\u304a\u3051\u308b\u7cbe\u5ea6\u306e\u9055\u3044\u3068\u5bfe\u51e6\u6cd5\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p><strong>\u76f8\u5bfe\u8aa4\u5dee\u306e\u6bd4\u8f03<\/strong>:<\/p>\n\n\n<div id=\"id-f74f96a7-11df-434f-b500-1540ad3ef290\">\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u5b9f\u88c5\u65b9\u6cd5<\/th><th>\u76f8\u5bfe\u8aa4\u5dee\uff08\u6982\u7b97\uff09<\/th><th>\u8aa4\u5dee\u306e\u7279\u6027<\/th><\/tr><\/thead><tbody><tr><td>\u65b9\u6cd51: std::pow<\/td><td>10^-15\u30aa\u30fc\u30c0\u30fc<\/td><td>\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u6700\u9069\u5316\u306b\u3088\u308b\u9ad8\u7cbe\u5ea6<\/td><\/tr><tr><td>\u65b9\u6cd53: \u30eb\u30fc\u30d7<\/td><td>10^-14\u30aa\u30fc\u30c0\u30fc&lt;br&gt;\uff08\u5927\u304d\u306a\u6307\u6570\u3067\u60aa\u5316\uff09<\/td><td>\u4e57\u7b97\u306e\u7e70\u308a\u8fd4\u3057\u306b\u3088\u308b\u8aa4\u5dee\u306e\u84c4\u7a4d<\/td><\/tr><tr><td>\u65b9\u6cd54: \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5<\/td><td>10^-15\u30aa\u30fc\u30c0\u30fc<\/td><td>\u4e57\u7b97\u56de\u6570\u306e\u524a\u6e1b\u306b\u3088\u308b\u8aa4\u5dee\u6291\u5236<\/td><\/tr><tr><td>\u65b9\u6cd56: \u30d3\u30c3\u30c8\u6f14\u7b97<\/td><td>\u6574\u6570\u6f14\u7b97\u306e\u307f<\/td><td>\u6d6e\u52d5\u5c0f\u6570\u70b9\u8aa4\u5dee\u306a\u3057\uff08\u6574\u6570\u306e\u5834\u5408\uff09<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<p><strong>\u8aa4\u5dee\u5bfe\u7b56\u3068\u6539\u5584\u65b9\u6cd5<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u9ad8\u7cbe\u5ea6\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u306e\u4f7f\u7528<\/strong>: <code>\/\/ double\u306e\u4ee3\u308f\u308a\u306blong double\u3092\u4f7f\u7528 long double result = power_function&lt;long double&gt;(base, exponent);<\/code><\/li>\n\n\n\n<li><strong>\u4e57\u7b97\u56de\u6570\u3092\u6e1b\u3089\u3059\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u9078\u629e<\/strong>:\n<ul class=\"wp-block-list\">\n<li>\u65b9\u6cd53\uff08\u5358\u7d14\u30eb\u30fc\u30d7\uff09\u3088\u308a\u3082\u65b9\u6cd54\uff08\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\uff09\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u4e57\u7b97\u56de\u6570\u3092\u524a\u6e1b\u3057\u8aa4\u5dee\u306e\u84c4\u7a4d\u3092\u6291\u5236\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u591a\u500d\u9577\u6f14\u7b97\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u4f7f\u7528<\/strong>:<ul><li>\u7279\u306b\u9ad8\u3044\u7cbe\u5ea6\u304c\u5fc5\u8981\u306a\u5834\u5408\u306f\u3001GNU MP\u3084Boost.Multiprecision\u306a\u3069\u306e\u591a\u500d\u9577\u6f14\u7b97\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u691c\u8a0e\u3057\u307e\u3059\u3002<\/li><\/ul><code>#include &lt;boost\/multiprecision\/cpp_dec_float.hpp&gt; using namespace boost::multiprecision; cpp_dec_float_50 result = pow(cpp_dec_float_50(2.0), 100);<\/code><\/li>\n\n\n\n<li><strong>\u6574\u6570\u578b\u3067\u306e\u8a08\u7b97\u3068\u5fc5\u8981\u306b\u5fdc\u3058\u305f\u5909\u63db<\/strong>:\n<ul class=\"wp-block-list\">\n<li>\u53ef\u80fd\u306a\u9650\u308a\u6574\u6570\u578b\u3067\u8a08\u7b97\u3057\u3001\u5fc5\u8981\u306a\u6642\u70b9\u3067\u6d6e\u52d5\u5c0f\u6570\u70b9\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u3067\u7cbe\u5ea6\u3092\u4fdd\u6301\u3067\u304d\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p><strong>\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\u306e\u51e6\u7406<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u975e\u5e38\u306b\u5927\u304d\u306a\u6307\u6570<\/strong>: <code>std::pow<\/code>\u3067\u306f\u6307\u6570\u304c\u5927\u304d\u3059\u304e\u308b\u3068\u7d50\u679c\u304cInfinity\uff08\u7121\u9650\u5927\uff09\u306b\u306a\u308a\u307e\u3059\u3002\u65b9\u6cd56\uff08\u30d3\u30c3\u30c8\u6f14\u7b97\uff09\u3068\u65b9\u6cd57\uff08\u6574\u6570\u578b\u7279\u5316\uff09\u3067\u306f\u3001\u30e2\u30b8\u30e5\u30e9\u30fc\u6f14\u7b97\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u5927\u304d\u306a\u6307\u6570\u3067\u3082\u8a08\u7b97\u53ef\u80fd\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u975e\u5e38\u306b\u5c0f\u3055\u3044\u6307\u6570<\/strong>: \u8ca0\u306e\u5927\u304d\u306a\u6307\u6570\u3067\u306f\u3001\u7d50\u679c\u304c0\u306b\u4e38\u3081\u3089\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u9632\u3050\u306b\u306f\u5206\u6570\u3067\u8868\u73fe\u3059\u308b\u304b\u3001\u5bfe\u6570\u30b9\u30b1\u30fc\u30eb\u3067\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u6d6e\u52d5\u5c0f\u6570\u70b9\u3079\u304d\u4e57\u8a08\u7b97\u306e\u7cbe\u5ea6\u3092\u91cd\u8996\u3059\u308b\u5834\u5408\u306f\u3001\u65b9\u6cd51\uff08std::pow\uff09\u307e\u305f\u306f\u65b9\u6cd54\uff08\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\uff09\u3068\u9069\u5207\u306a\u7cbe\u5ea6\u5bfe\u7b56\u306e\u7d44\u307f\u5408\u308f\u305b\u304c\u63a8\u5968\u3055\u308c\u307e\u3059\u3002\u6574\u6570\u3079\u304d\u4e57\u306e\u5834\u5408\u306f\u3001\u65b9\u6cd56\uff08\u30d3\u30c3\u30c8\u6f14\u7b97\uff09\u307e\u305f\u306f\u65b9\u6cd57\uff08\u6574\u6570\u578b\u7279\u5316\uff09\u304c\u7cbe\u5ea6\u306e\u70b9\u3067\u3082\u512a\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3079\u304d\u4e57\u8a08\u7b97\u306b\u304a\u3051\u308b\u6ce8\u610f\u70b9\u3068\u6700\u9069\u5316\u30c6\u30af\u30cb\u30c3\u30af\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"i-18\">\u9069\u5207\u306a\u4e57\u8a08\u7b97\u306b\u304a\u3051\u308b\u6ce8\u610f\u70b9\u3068\u6700\u9069\u5316\u30c6\u30af\u30cb\u30c3\u30af<\/h2>\n\n\n\n<p>C++\u3067\u3079\u304d\u4e57\u8a08\u7b97\u3092\u5b9f\u88c5\u3059\u308b\u969b\u306b\u306f\u3001\u5358\u306b\u6b63\u3057\u3044\u7d50\u679c\u3092\u5f97\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u7279\u5b9a\u306e\u30b1\u30fc\u30b9\u3067\u306e\u52b9\u7387\u3084\u5b89\u5168\u6027\u3092\u5411\u4e0a\u3055\u305b\u308b\u305f\u3081\u306e\u69d8\u3005\u306a\u6ce8\u610f\u70b9\u3068\u6700\u9069\u5316\u30c6\u30af\u30cb\u30c3\u30af\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u5927\u304d\u306a\u6307\u6570\u5024\u306e\u6271\u3044\u65b9\u3001\u8ca0\u306e\u6307\u6570\u3078\u306e\u5bfe\u5fdc\u3001\u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u6700\u9069\u5316\u306a\u3069\u3001\u5b9f\u8df5\u7684\u306a\u30c6\u30af\u30cb\u30c3\u30af\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-19\">\u5927\u304d\u306a\u6307\u6570\u5024\u306e\u6271\u3044\u65b9\u3068\u6841\u3042\u3075\u308c\u306e\u9632\u6b62\u7b56<\/h3>\n\n\n\n<p>\u5927\u304d\u306a\u6307\u6570\u5024\u3092\u6271\u3046\u5834\u5408\u3001\u6574\u6570\u578b\u3067\u306f\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u304c\u767a\u751f\u3057\u3084\u3059\u304f\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u3067\u306f\u7cbe\u5ea6\u306e\u554f\u984c\u304c\u751f\u3058\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306b\u3001\u3053\u308c\u3089\u306e\u554f\u984c\u3092\u56de\u907f\u3059\u308b\u305f\u3081\u306e\u6226\u7565\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>1. \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u306e\u5b9f\u88c5\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;limits&gt;\n#include &lt;stdexcept&gt;\n\ntemplate &lt;typename T&gt;\nT safe_power(T base, unsigned int exponent) {\n    \/\/ \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u4ed8\u304d\u306e\u3079\u304d\u4e57\u8a08\u7b97\n    if (exponent == 0) return 1;\n    \n    const T max_value = std::numeric_limits&lt;T&gt;::max();\n    T result = 1;\n    \n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            \/\/ \u7d50\u679c\u306e\u66f4\u65b0\u524d\u306b\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u30c1\u30a7\u30c3\u30af\n            if (result &gt; max_value \/ base) {\n                throw std::overflow_error(\"\u6307\u6570\u8a08\u7b97\u3067\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u304c\u767a\u751f\u3057\u307e\u3059\");\n            }\n            result *= base;\n        }\n        \n        exponent &gt;&gt;= 1;\n        if (exponent &gt; 0) {\n            \/\/ \u57fa\u6570\u306e\u4e8c\u4e57\u524d\u306b\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u30c1\u30a7\u30c3\u30af\n            if (base &gt; max_value \/ base) {\n                throw std::overflow_error(\"\u6307\u6570\u8a08\u7b97\u3067\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u304c\u767a\u751f\u3057\u307e\u3059\");\n            }\n            base *= base;\n        }\n    }\n    \n    return result;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid safe_power_example() {\n    try {\n        int result = safe_power&lt;int&gt;(2, 30); \/\/ 2^30 (OK)\n        std::cout &lt;&lt; \"2^30 = \" &lt;&lt; result &lt;&lt; std::endl;\n        \n        result = safe_power&lt;int&gt;(2, 31); \/\/ 2^31 (\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc)\n    } catch (const std::overflow_error&amp; e) {\n        std::cout &lt;&lt; \"\u30a8\u30e9\u30fc: \" &lt;&lt; e.what() &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"\u3088\u308a\u5927\u304d\u306a\u578b\u3092\u4f7f\u7528\u3057\u307e\u3059: \";\n        int64_t result_64 = safe_power&lt;int64_t&gt;(2, 31);\n        std::cout &lt;&lt; \"2^31 = \" &lt;&lt; result_64 &lt;&lt; std::endl;\n    }\n}\n<\/pre>\n\n\n\n<p>\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u306e\u9375\u306f\u3001\u4e57\u7b97\u3092\u5b9f\u884c\u3059\u308b\u524d\u306b\u7d50\u679c\u304c\u8868\u73fe\u53ef\u80fd\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u3067\u3059\u3002<code>max_value \/ base<\/code> \u306e\u8a08\u7b97\u306b\u3088\u308a\u3001\u73fe\u5728\u306e <code>result<\/code> \u3092 <code>base<\/code> \u3068\u5b89\u5168\u306b\u639b\u3051\u5408\u308f\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>2. \u30e2\u30b8\u30e5\u30e9\u30fc\u6f14\u7b97\u306e\u6d3b\u7528\uff1a<\/strong><\/p>\n\n\n\n<p>\u7279\u306b\u6697\u53f7\u8a08\u7b97\u3084\u6570\u8ad6\u3067\u7528\u3044\u3089\u308c\u308b\u5927\u304d\u306a\u6307\u6570\u5024\u3067\u306e\u8a08\u7b97\u306b\u306f\u3001\u30e2\u30b8\u30e5\u30e9\u30fc\u6f14\u7b97\uff08\u5270\u4f59\u6f14\u7b97\uff09\u3068\u7d44\u307f\u5408\u308f\u305b\u308b\u65b9\u6cd5\u304c\u52b9\u679c\u7684\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cstdint&gt;\n\n\/\/ \u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57\u8a08\u7b97\uff08(base^exponent) mod modulus\uff09\nuint64_t modular_power(uint64_t base, uint64_t exponent, uint64_t modulus) {\n    \/\/ \u57fa\u672c\u30b1\u30fc\u30b9\n    if (modulus == 1) return 0;  \/\/ (a^b) mod 1 = 0\n    \n    uint64_t result = 1;\n    base = base % modulus;  \/\/ \u6700\u521d\u306b\u5270\u4f59\u3092\u53d6\u308a\u3001\u5024\u3092\u5c0f\u3055\u304f\u4fdd\u3064\n    \n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            result = (result * base) % modulus;\n        }\n        exponent &gt;&gt;= 1;\n        base = (base * base) % modulus;\n    }\n    \n    return result;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid modular_power_example() {\n    \/\/ RSA\u6697\u53f7\u306a\u3069\u3067\u4f7f\u308f\u308c\u308b\u3088\u3046\u306a\u5927\u304d\u306a\u6570\u5024\u3082\u8a08\u7b97\u53ef\u80fd\n    uint64_t base = 123456789;\n    uint64_t exp = 987654321;\n    uint64_t mod = 1000000007;  \/\/ 10^9 + 7\uff08\u7af6\u6280\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3067\u3088\u304f\u4f7f\u308f\u308c\u308b\u7d20\u6570\uff09\n    \n    std::cout &lt;&lt; base &lt;&lt; \"^\" &lt;&lt; exp &lt;&lt; \" mod \" &lt;&lt; mod &lt;&lt; \" = \" \n              &lt;&lt; modular_power(base, exp, mod) &lt;&lt; std::endl;\n}\n<\/pre>\n\n\n\n<p>\u3053\u306e\u5b9f\u88c5\u3067\u306f\u3001\u8a08\u7b97\u306e\u5404\u30b9\u30c6\u30c3\u30d7\u3067\u5270\u4f59\u3092\u53d6\u308b\u3053\u3068\u3067\u3001\u4e2d\u9593\u7d50\u679c\u3092\u5e38\u306b\u30e2\u30b8\u30e5\u30e9\u30b9\u672a\u6e80\u306b\u4fdd\u3061\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u975e\u5e38\u306b\u5927\u304d\u306a\u6307\u6570\u5024\u3067\u3082\u6841\u3042\u3075\u308c\u3092\u9632\u304e\u306a\u304c\u3089\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>3. \u591a\u500d\u9577\u6574\u6570\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u6d3b\u7528\uff1a<\/strong><\/p>\n\n\n\n<p>C++\u306e\u6a19\u6e96\u6574\u6570\u578b\u3067\u306f\u8868\u73fe\u3067\u304d\u306a\u3044\u3088\u3046\u306a\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u5024\u3092\u6271\u3046\u306b\u306f\u3001\u591a\u500d\u9577\u6574\u6570\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u4ee3\u8868\u7684\u306a\u30e9\u30a4\u30d6\u30e9\u30ea\u306b\u306fBoost.Multiprecision\u3084 GNU MP (GMP)\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;boost\/multiprecision\/cpp_int.hpp&gt;\n\nusing namespace boost::multiprecision;\n\n\/\/ Boost.Multiprecision\u3092\u4f7f\u7528\u3057\u305f\u4efb\u610f\u7cbe\u5ea6\u306e\u3079\u304d\u4e57\u8a08\u7b97\ncpp_int big_power(cpp_int base, unsigned int exponent) {\n    \/\/ \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\u306b\u3088\u308b\u5b9f\u88c5\n    if (exponent == 0) return 1;\n    \n    cpp_int result = 1;\n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            result *= base;\n        }\n        base *= base;\n        exponent &gt;&gt;= 1;\n    }\n    \n    return result;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid big_power_example() {\n    \/\/ \u975e\u5e38\u306b\u5927\u304d\u306a\u3079\u304d\u4e57\u8a08\u7b97\n    cpp_int result = big_power(cpp_int(2), 1000);\n    std::cout &lt;&lt; \"2^1000 = \" &lt;&lt; result &lt;&lt; std::endl;\n}\n<\/pre>\n\n\n\n<p>Boost.Multiprecision\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u6a19\u6e96\u306e\u6574\u6570\u578b\u3067\u306f\u6271\u3048\u306a\u3044\u3088\u3046\u306a\u5927\u304d\u306a\u6570\u5024\u3067\u3082\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u3092\u6c17\u306b\u305b\u305a\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002RSA\u6697\u53f7\u306e\u3088\u3046\u306a\u7528\u9014\u3067\u5fc5\u8981\u3068\u306a\u308b\u6570\u767e\u6841\uff5e\u6570\u5343\u6841\u306e\u6574\u6570\u8a08\u7b97\u3082\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-20\">\u8ca0\u3051\u306e\u6307\u6570\u5bfe\u5fdc\u306e\u5b9f\u88c5\u65b9\u6cd5<\/h3>\n\n\n\n<p>\u8ca0\u306e\u6307\u6570\u306f\u6570\u5b66\u7684\u306b\u306f\u9006\u6570\u3092\u610f\u5473\u3057\u307e\u3059\uff08a^(-n) = 1\/(a^n)\uff09\u3002C++\u3067\u306e\u5b9f\u88c5\u3067\u306f\u3001\u8ca0\u306e\u6307\u6570\u3092\u51e6\u7406\u3059\u308b\u305f\u3081\u306e\u7279\u5225\u306a\u8003\u616e\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cassert&gt;\n\n\/\/ \u8ca0\u306e\u6307\u6570\u306b\u3082\u5bfe\u5fdc\u3057\u305f\u3079\u304d\u4e57\u8a08\u7b97\ndouble power_with_negative(double base, int exponent) {\n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\n    if (base == 0.0) {\n        assert(exponent &gt; 0 &amp;&amp; \"0\u306e\u8ca0\u3079\u304d\u4e57\u306f\u672a\u5b9a\u7fa9\u3067\u3059\");\n        return 0.0;\n    }\n    \n    if (exponent == 0) return 1.0;\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\u306e\u51e6\u7406\n    bool negative_exponent = exponent &lt; 0;\n    if (negative_exponent) {\n        exponent = -exponent;  \/\/ \u7d76\u5bfe\u5024\u3092\u53d6\u308b\n    }\n    \n    \/\/ \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\u306b\u3088\u308b\u6b63\u306e\u6307\u6570\u8a08\u7b97\n    double result = 1.0;\n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            result *= base;\n        }\n        base *= base;\n        exponent &gt;&gt;= 1;\n    }\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\u306e\u5834\u5408\u306f\u9006\u6570\u3092\u8fd4\u3059\n    return negative_exponent ? 1.0 \/ result : result;\n}\n\n\/\/ \u6574\u6570\u578b\u3067\u306e\u5206\u6570\u8868\u73fe\u3092\u7528\u3044\u305f\u5b9f\u88c5\nstruct Fraction {\n    int64_t numerator;    \/\/ \u5206\u5b50\n    int64_t denominator;  \/\/ \u5206\u6bcd\n    \n    Fraction(int64_t num = 0, int64_t denom = 1) : numerator(num), denominator(denom) {\n        if (denominator == 0) throw std::invalid_argument(\"\u5206\u6bcd\u306f0\u306b\u3067\u304d\u307e\u305b\u3093\");\n        simplify();  \/\/ \u7d04\u5206\u3059\u308b\n    }\n    \n    \/\/ \u7d04\u5206\n    void simplify() {\n        if (numerator == 0) {\n            denominator = 1;\n            return;\n        }\n        \n        int64_t gcd = std::gcd(std::abs(numerator), std::abs(denominator));\n        numerator \/= gcd;\n        denominator \/= gcd;\n        \n        \/\/ \u5206\u6bcd\u304c\u8ca0\u306e\u5834\u5408\u3001\u7b26\u53f7\u3092\u5206\u5b50\u306b\u79fb\u52d5\n        if (denominator &lt; 0) {\n            numerator = -numerator;\n            denominator = -denominator;\n        }\n    }\n    \n    \/\/ \u6570\u5024\u8868\u73fe\uff08\u6d6e\u52d5\u5c0f\u6570\u70b9\u306b\u5909\u63db\uff09\n    double to_double() const {\n        return static_cast&lt;double&gt;(numerator) \/ denominator;\n    }\n    \n    \/\/ \u8868\u793a\u7528\n    friend std::ostream&amp; operator&lt;&lt;(std::ostream&amp; os, const Fraction&amp; f) {\n        if (f.denominator == 1) {\n            os &lt;&lt; f.numerator;\n        } else {\n            os &lt;&lt; f.numerator &lt;&lt; \"\/\" &lt;&lt; f.denominator;\n        }\n        return os;\n    }\n};\n\n\/\/ \u5206\u6570\u3092\u4f7f\u3063\u305f\u6b63\u78ba\u306a\u6574\u6570\u3079\u304d\u4e57\u8a08\u7b97\nFraction exact_power(int base, int exponent) {\n    if (exponent == 0) return Fraction(1);\n    \n    bool negative_exponent = exponent &lt; 0;\n    if (negative_exponent) {\n        exponent = -exponent;\n    }\n    \n    \/\/ \u6b63\u306e\u6307\u6570\u8a08\u7b97\n    int64_t result = 1;\n    int64_t current_base = base;\n    \n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            result *= current_base;\n        }\n        current_base *= current_base;\n        exponent &gt;&gt;= 1;\n    }\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\u306e\u5834\u5408\u306f\u5206\u5b50\u3068\u5206\u6bcd\u3092\u5165\u308c\u66ff\u3048\u308b\n    return negative_exponent ? Fraction(1, result) : Fraction(result);\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid negative_exponent_example() {\n    std::cout &lt;&lt; \"\u6d6e\u52d5\u5c0f\u6570\u70b9\u8a08\u7b97: 2^(-3) = \" &lt;&lt; power_with_negative(2.0, -3) &lt;&lt; std::endl;\n    \n    \/\/ \u5206\u6570\u3092\u4f7f\u3063\u305f\u6b63\u78ba\u306a\u8a08\u7b97\n    Fraction fraction_result = exact_power(2, -3);\n    std::cout &lt;&lt; \"\u5206\u6570\u8868\u73fe: 2^(-3) = \" &lt;&lt; fraction_result &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u6570\u5024\u8868\u73fe: 2^(-3) = \" &lt;&lt; fraction_result.to_double() &lt;&lt; std::endl;\n}\n<\/pre>\n\n\n\n<p>\u8ca0\u306e\u6307\u6570\u3092\u51e6\u7406\u3059\u308b\u969b\u306e\u4e3b\u306a\u30dd\u30a4\u30f3\u30c8\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6574\u6570\u578b\u3067\u306f\u9006\u6570\u3092\u8868\u73fe\u3067\u304d\u306a\u3044<\/strong>: \u6574\u6570\u578b\u3067\u306e\u8ca0\u306e\u6307\u6570\u8a08\u7b97\u3067\u306f\u3001\u7d50\u679c\u3092\u5206\u6570\u3067\u8868\u73fe\u3059\u308b\u304b\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>0\u306e\u8ca0\u3079\u304d\u4e57\u306f\u672a\u5b9a\u7fa9<\/strong>: 0^(-n)\u306f\u6570\u5b66\u7684\u306b\u672a\u5b9a\u7fa9\u3067\u3059\u3002\u5b9f\u88c5\u3067\u306f\u4f8b\u5916\u3092\u30b9\u30ed\u30fc\u3059\u308b\u304b\u3001assertion\u3092\u4f7f\u7528\u3057\u3066\u691c\u8a3c\u3059\u308b\u3079\u304d\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u7cbe\u5ea6\u306e\u554f\u984c<\/strong>: \u8ca0\u306e\u5927\u304d\u306a\u6307\u6570\u3067\u306f\u3001\u7d50\u679c\u304c\u975e\u5e38\u306b\u5c0f\u3055\u304f\u306a\u308a\u30a2\u30f3\u30c0\u30fc\u30d5\u30ed\u30fc\u306e\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u9632\u3050\u305f\u3081\u306b\u306f\u9ad8\u7cbe\u5ea6\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u3084\u5206\u6570\u30af\u30e9\u30b9\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-21\">\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\uff080\u4e57\u30011\u4e57\u30012\u4e57\uff09\u306e\u6700\u9069\u5316<\/h3>\n\n\n\n<p>\u3079\u304d\u4e57\u8a08\u7b97\u3067\u306f\u3001\u7279\u5b9a\u306e\u6307\u6570\u5024\uff080, 1, 2\u306a\u3069\uff09\u306b\u5bfe\u3057\u3066\u6700\u9069\u5316\u3059\u308b\u3053\u3068\u3067\u3001\u5927\u5e45\u306b\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>1. \u5b9f\u884c\u6642\u306e\u7279\u6b8a\u30b1\u30fc\u30b9\u691c\u51fa\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n\n\/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u6700\u9069\u5316\u3092\u65bd\u3057\u305f\u3079\u304d\u4e57\u8a08\u7b97\ntemplate &lt;typename T&gt;\nT optimized_power(T base, int exponent) {\n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u65e9\u671f\u691c\u51fa\n    if (exponent == 0) return 1;\n    if (exponent == 1) return base;\n    if (exponent == 2) return base * base;\n    if (base == 0) return 0;\n    if (base == 1) return 1;\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\u306e\u51e6\u7406\n    bool negative_exponent = exponent &lt; 0;\n    if (negative_exponent) {\n        exponent = -exponent;\n    }\n    \n    \/\/ 2\u306e\u7d2f\u4e57\u306e\u7279\u6b8a\u51e6\u7406\uff08\u30d3\u30c3\u30c8\u30b7\u30d5\u30c8\u3067\u9ad8\u901f\u5316\uff09\n    if (base == 2 &amp;&amp; exponent &lt;= 63) {\n        T result = T(1) &lt;&lt; exponent;\n        return negative_exponent ? 1.0 \/ result : result;\n    }\n    \n    \/\/ \u901a\u5e38\u306e\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\n    T result = 1;\n    T current_base = base;\n    \n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            result *= current_base;\n        }\n        current_base *= current_base;\n        exponent &gt;&gt;= 1;\n    }\n    \n    return negative_exponent ? 1.0 \/ result : result;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid special_cases_example() {\n    std::cout &lt;&lt; \"2^0 = \" &lt;&lt; optimized_power(2.0, 0) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"2^1 = \" &lt;&lt; optimized_power(2.0, 1) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"2^2 = \" &lt;&lt; optimized_power(2.0, 2) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"2^10 = \" &lt;&lt; optimized_power(2.0, 10) &lt;&lt; std::endl;\n    \n    \/\/ 2\u306e\u3079\u304d\u4e57\u306e\u9ad8\u901f\u8a08\u7b97\n    std::cout &lt;&lt; \"2^20 (\u30d3\u30c3\u30c8\u30b7\u30d5\u30c8\u4f7f\u7528) = \" &lt;&lt; optimized_power(2.0, 20) &lt;&lt; std::endl;\n}\n<\/pre>\n\n\n\n<p><strong>2. \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306e\u7279\u6b8a\u30b1\u30fc\u30b9\u6700\u9069\u5316\uff1a<\/strong><\/p>\n\n\n\n<p>\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u30e1\u30bf\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u7279\u6b8a\u30b1\u30fc\u30b9\u3092\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;type_traits&gt;\n\n\/\/ \u4e00\u822c\u7684\u306a\u30b1\u30fc\u30b9\ntemplate &lt;typename T, int N, typename Enable = void&gt;\nstruct CompilePower {\n    static constexpr T value(T base) {\n        \/\/ \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\u306b\u3088\u308b\u5b9f\u88c5\n        return (N % 2 == 1) ? \n                base * CompilePower&lt;T, N\/2&gt;::value(base) * CompilePower&lt;T, N\/2&gt;::value(base) :\n                CompilePower&lt;T, N\/2&gt;::value(base) * CompilePower&lt;T, N\/2&gt;::value(base);\n    }\n};\n\n\/\/ 0\u4e57\u306e\u7279\u6b8a\u5316\ntemplate &lt;typename T, int N&gt;\nstruct CompilePower&lt;T, N, typename std::enable_if&lt;N == 0&gt;::type&gt; {\n    static constexpr T value(T) { return 1; }\n};\n\n\/\/ 1\u4e57\u306e\u7279\u6b8a\u5316\ntemplate &lt;typename T, int N&gt;\nstruct CompilePower&lt;T, N, typename std::enable_if&lt;N == 1&gt;::type&gt; {\n    static constexpr T value(T base) { return base; }\n};\n\n\/\/ 2\u4e57\u306e\u7279\u6b8a\u5316\ntemplate &lt;typename T, int N&gt;\nstruct CompilePower&lt;T, N, typename std::enable_if&lt;N == 2&gt;::type&gt; {\n    static constexpr T value(T base) { return base * base; }\n};\n\n\/\/ \u30d8\u30eb\u30d1\u30fc\u95a2\u6570\ntemplate &lt;int N, typename T&gt;\nconstexpr T compile_time_power(T base) {\n    return CompilePower&lt;T, N&gt;::value(base);\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid compile_time_optimization_example() {\n    constexpr double result1 = compile_time_power&lt;0&gt;(2.5);  \/\/ 0\u4e57: 1.0\n    constexpr double result2 = compile_time_power&lt;1&gt;(2.5);  \/\/ 1\u4e57: 2.5\n    constexpr double result3 = compile_time_power&lt;2&gt;(2.5);  \/\/ 2\u4e57: 6.25\n    constexpr double result4 = compile_time_power&lt;10&gt;(2.0); \/\/ 10\u4e57: 1024.0\n    \n    std::cout &lt;&lt; \"\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97: 2.5^0 = \" &lt;&lt; result1 &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97: 2.5^1 = \" &lt;&lt; result2 &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97: 2.5^2 = \" &lt;&lt; result3 &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97: 2.0^10 = \" &lt;&lt; result4 &lt;&lt; std::endl;\n}\n<\/pre>\n\n\n\n<p><strong>3. \u5b9f\u884c\u6642\u30eb\u30c3\u30af\u30a2\u30c3\u30d7\u30c6\u30fc\u30d6\u30eb\uff1a<\/strong><\/p>\n\n\n\n<p>\u983b\u7e41\u306b\u4f7f\u7528\u3059\u308b\u6307\u6570\u5024\u3068\u57fa\u6570\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u3001\u7d50\u679c\u3092\u30ad\u30e3\u30c3\u30b7\u30e5\u3059\u308b\u3053\u3068\u3067\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;unordered_map&gt;\n#include &lt;tuple&gt;\n\n\/\/ \u30cf\u30c3\u30b7\u30e5\u95a2\u6570\nstruct PairHash {\n    template &lt;class T1, class T2&gt;\n    std::size_t operator()(const std::pair&lt;T1, T2&gt;&amp; p) const {\n        auto h1 = std::hash&lt;T1&gt;{}(p.first);\n        auto h2 = std::hash&lt;T2&gt;{}(p.second);\n        return h1 ^ (h2 &lt;&lt; 1);\n    }\n};\n\n\/\/ \u30ad\u30e3\u30c3\u30b7\u30e5\u4ed8\u304d\u3079\u304d\u4e57\u8a08\u7b97\nclass CachedPower {\nprivate:\n    std::unordered_map&lt;std::pair&lt;double, int&gt;, double, PairHash&gt; cache;\n    \n    \/\/ \u5b9f\u969b\u306e\u8a08\u7b97\n    double calculate_power(double base, int exponent) {\n        \/\/ \u8ca0\u306e\u6307\u6570\u51e6\u7406\n        bool negative_exponent = exponent &lt; 0;\n        if (negative_exponent) {\n            exponent = -exponent;\n        }\n        \n        \/\/ \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\n        double result = 1.0;\n        while (exponent &gt; 0) {\n            if (exponent &amp; 1) {\n                result *= base;\n            }\n            base *= base;\n            exponent &gt;&gt;= 1;\n        }\n        \n        return negative_exponent ? 1.0 \/ result : result;\n    }\n    \npublic:\n    double power(double base, int exponent) {\n        \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u65e9\u671f\u691c\u51fa\n        if (exponent == 0) return 1.0;\n        if (exponent == 1) return base;\n        if (exponent == 2) return base * base;\n        if (base == 0.0) return 0.0;\n        if (base == 1.0) return 1.0;\n        \n        \/\/ \u30ad\u30e3\u30c3\u30b7\u30e5\u691c\u7d22\n        std::pair&lt;double, int&gt; key(base, exponent);\n        auto it = cache.find(key);\n        \n        if (it != cache.end()) {\n            return it-&gt;second;  \/\/ \u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\n        }\n        \n        \/\/ \u30ad\u30e3\u30c3\u30b7\u30e5\u30df\u30b9 - \u8a08\u7b97\u3057\u3066\u7d50\u679c\u3092\u4fdd\u5b58\n        double result = calculate_power(base, exponent);\n        cache[key] = result;\n        \n        return result;\n    }\n    \n    \/\/ \u30ad\u30e3\u30c3\u30b7\u30e5\u7d71\u8a08\n    size_t cache_size() const {\n        return cache.size();\n    }\n    \n    void clear_cache() {\n        cache.clear();\n    }\n};\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid cached_power_example() {\n    CachedPower calculator;\n    \n    \/\/ \u521d\u56de\u8a08\u7b97\uff08\u30ad\u30e3\u30c3\u30b7\u30e5\u30df\u30b9\uff09\n    auto start = std::chrono::high_resolution_clock::now();\n    double result1 = calculator.power(1.5, 25);\n    auto end = std::chrono::high_resolution_clock::now();\n    std::chrono::duration&lt;double, std::micro&gt; duration1 = end - start;\n    \n    \/\/ 2\u56de\u76ee\uff08\u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\uff09\n    start = std::chrono::high_resolution_clock::now();\n    double result2 = calculator.power(1.5, 25);\n    end = std::chrono::high_resolution_clock::now();\n    std::chrono::duration&lt;double, std::micro&gt; duration2 = end - start;\n    \n    std::cout &lt;&lt; \"1.5^25 = \" &lt;&lt; result1 &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u521d\u56de\u8a08\u7b97\u6642\u9593: \" &lt;&lt; duration1.count() &lt;&lt; \" \u30de\u30a4\u30af\u30ed\u79d2\" &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\u6642\u9593: \" &lt;&lt; duration2.count() &lt;&lt; \" \u30de\u30a4\u30af\u30ed\u79d2\" &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u30ad\u30e3\u30c3\u30b7\u30e5\u30b5\u30a4\u30ba: \" &lt;&lt; calculator.cache_size() &lt;&lt; std::endl;\n}\n<\/pre>\n\n\n\n<p>\u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u6700\u9069\u5316\u306b\u95a2\u3059\u308b\u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u65e9\u671f\u30ea\u30bf\u30fc\u30f3<\/strong>: \u7279\u6b8a\u30b1\u30fc\u30b9\uff080\u4e57\u30011\u4e57\u30012\u4e57\u306a\u3069\uff09\u3092\u95a2\u6570\u306e\u6700\u521d\u3067\u691c\u51fa\u3057\u3001\u5373\u5ea7\u306b\u7d50\u679c\u3092\u8fd4\u3059\u3053\u3068\u3067\u8a08\u7b97\u3092\u56de\u907f\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u7279\u5b9a\u306e\u57fa\u6570\u306e\u6700\u9069\u5316<\/strong>: \u7279\u306b2\u306e\u7d2f\u4e57\u306f\u30d3\u30c3\u30c8\u30b7\u30d5\u30c8\uff08<code>1 &lt;&lt; n<\/code>\uff09\u3092\u4f7f\u3063\u3066\u9ad8\u901f\u5316\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u7279\u6b8a\u5316<\/strong>: \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u65e2\u77e5\u306e\u6307\u6570\u306b\u5bfe\u3057\u3066\u6700\u9069\u5316\u3055\u308c\u305f\u5b9f\u88c5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u7d50\u679c\u306e\u30ad\u30e3\u30c3\u30b7\u30e5<\/strong>: \u540c\u3058\u5165\u529b\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u7d50\u679c\u3092\u30ad\u30e3\u30c3\u30b7\u30e5\u3059\u308b\u3053\u3068\u3067\u3001\u7e70\u308a\u8fd4\u3057\u8a08\u7b97\u306e\u52b9\u7387\u3092\u5927\u5e45\u306b\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u308c\u3089\u306e\u6700\u9069\u5316\u30c6\u30af\u30cb\u30c3\u30af\u3092\u9069\u5207\u306b\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u3079\u304d\u4e57\u8a08\u7b97\u306e\u52b9\u7387\u3068\u5b89\u5168\u6027\u3092\u5927\u5e45\u306b\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u5b9f\u88c5\u306e\u5b9f\u7528\u7684\u306a\u5fdc\u7528\u4f8b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"i-22\">\u5b9f\u7528\u7684\u306a\u4e57\u8a08\u7b97\u306e\u5fdc\u7528\u4f8b<\/h2>\n\n\n\n<p>C++\u306b\u304a\u3051\u308b\u3079\u304d\u4e57\u8a08\u7b97\u306f\u3001\u7406\u8ad6\u7684\u306a\u8a71\u984c\u306b\u3068\u3069\u307e\u3089\u305a\u3001\u591a\u304f\u306e\u5b9f\u7528\u7684\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u51e6\u7406\u3001\u6697\u53f7\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3001\u79d1\u5b66\u6280\u8853\u8a08\u7b97\u3068\u3044\u30463\u3064\u306e\u5206\u91ce\u3067\u306e\u3079\u304d\u4e57\u8a08\u7b97\u306e\u5b9f\u8df5\u7684\u306a\u5fdc\u7528\u4f8b\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-23\">\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u51e6\u7406\u306b\u304a\u3051\u308b\u9069\u5207\u306a\u4e57\u8a08\u7b97<\/h3>\n\n\n\n<p>3D\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30b9\u3084\u30b2\u30fc\u30e0\u958b\u767a\u3067\u306f\u3001\u3079\u304d\u4e57\u8a08\u7b97\u304c\u69d8\u3005\u306a\u5834\u9762\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u7279\u306b\u7269\u7406\u30d9\u30fc\u30b9\u306e\u30ec\u30f3\u30c0\u30ea\u30f3\u30b0\u3084\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u6b63\u78ba\u304b\u3064\u52b9\u7387\u7684\u306a\u3079\u304d\u4e57\u8a08\u7b97\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<p><strong>1. Phong\u30b7\u30a7\u30fc\u30c7\u30a3\u30f3\u30b0\u30e2\u30c7\u30eb\u3067\u306e\u30b9\u30da\u30ad\u30e5\u30e9\u30fc\u53cd\u5c04\uff1a<\/strong><\/p>\n\n\n\n<p>Phong\u30b7\u30a7\u30fc\u30c7\u30a3\u30f3\u30b0\u30e2\u30c7\u30eb\u3067\u306f\u3001\u93e1\u9762\u53cd\u5c04\u306e\u5f37\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f59\u5f26\u306e\u7d2f\u4e57\uff08cos^n\uff09\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u6307\u6570n\u304c\u5927\u304d\u3044\u307b\u3069\u3001\u8868\u9762\u306f\u93e1\u306e\u3088\u3046\u306b\u5149\u6ca2\u306e\u3042\u308b\u5916\u89b3\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cmath&gt;\n#include &lt;vector&gt;\n\n\/\/ 3D\u70b9\u3068\u65b9\u5411\u3092\u8868\u3059\u30af\u30e9\u30b9\nstruct Vector3 {\n    float x, y, z;\n    \n    Vector3(float _x = 0, float _y = 0, float _z = 0) : x(_x), y(_y), z(_z) {}\n    \n    \/\/ \u30d9\u30af\u30c8\u30eb\u306e\u6b63\u898f\u5316\n    Vector3 normalize() const {\n        float len = std::sqrt(x*x + y*y + z*z);\n        if (len &gt; 0) {\n            return Vector3(x\/len, y\/len, z\/len);\n        }\n        return *this;\n    }\n    \n    \/\/ \u30c9\u30c3\u30c8\u7a4d\n    float dot(const Vector3&amp; v) const {\n        return x*v.x + y*v.y + z*v.z;\n    }\n};\n\n\/\/ Phong\u30b7\u30a7\u30fc\u30c7\u30a3\u30f3\u30b0\u30e2\u30c7\u30eb\u306e\u93e1\u9762\u53cd\u5c04\u8a08\u7b97\nfloat calculate_specular(const Vector3&amp; normal, const Vector3&amp; lightDir, \n                         const Vector3&amp; viewDir, float shininess) {\n    \/\/ \u53cd\u5c04\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\n    float NdotL = normal.dot(lightDir);\n    Vector3 reflection;\n    reflection.x = 2.0f * NdotL * normal.x - lightDir.x;\n    reflection.y = 2.0f * NdotL * normal.y - lightDir.y;\n    reflection.z = 2.0f * NdotL * normal.z - lightDir.z;\n    \n    \/\/ \u6b63\u898f\u5316\n    reflection = reflection.normalize();\n    \n    \/\/ \u8996\u7dda\u30d9\u30af\u30c8\u30eb\u3068\u53cd\u5c04\u30d9\u30af\u30c8\u30eb\u306e\u30c9\u30c3\u30c8\u7a4d\n    float RdotV = std::max(0.0f, reflection.dot(viewDir));\n    \n    \/\/ \u30b9\u30da\u30ad\u30e5\u30e9\u30fc\u5f37\u5ea6\u306e\u8a08\u7b97\uff08RdotV\u306eshininess\u4e57\uff09\n    \/\/ \u3053\u3053\u3067\u3079\u304d\u4e57\u8a08\u7b97\u304c\u4f7f\u7528\u3055\u308c\u308b\n    float specular = std::pow(RdotV, shininess);\n    \n    return specular;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid phong_shading_example() {\n    \/\/ \u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\n    Vector3 normal(0, 1, 0);\n    \n    \/\/ \u5149\u6e90\u65b9\u5411\n    Vector3 lightDir(0.5, 0.5, 0.5);\n    lightDir = lightDir.normalize();\n    \n    \/\/ \u8996\u7dda\u65b9\u5411\n    Vector3 viewDir(0, 0, 1);\n    viewDir = viewDir.normalize();\n    \n    \/\/ \u7570\u306a\u308b\u5149\u6ca2\u5ea6\uff08shininess\uff09\u3067\u306e\u93e1\u9762\u53cd\u5c04\u306e\u8a08\u7b97\n    std::vector&lt;float&gt; shininess_values = {1, 4, 8, 16, 32, 64, 128};\n    \n    std::cout &lt;&lt; \"Phong\u30b7\u30a7\u30fc\u30c7\u30a3\u30f3\u30b0\u30e2\u30c7\u30eb - \u7570\u306a\u308b\u5149\u6ca2\u5ea6\u3067\u306e\u93e1\u9762\u53cd\u5c04\u5f37\u5ea6:\\n\";\n    for (float shininess : shininess_values) {\n        float specular = calculate_specular(normal, lightDir, viewDir, shininess);\n        std::cout &lt;&lt; \"\u5149\u6ca2\u5ea6 \" &lt;&lt; shininess &lt;&lt; \": \" &lt;&lt; specular &lt;&lt; std::endl;\n    }\n}\n<\/pre>\n\n\n\n<p><strong>2. \u7269\u7406\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306e\u91cd\u529b\u8a08\u7b97\uff1a<\/strong><\/p>\n\n\n\n<p>\u7269\u7406\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u9006\u4e8c\u4e57\u306e\u6cd5\u5247\uff08\u8ddd\u96e2\u306e-2\u4e57\u306b\u6bd4\u4f8b\uff09\u306b\u57fa\u3065\u304f\u91cd\u529b\u3084\u96fb\u78c1\u529b\u306e\u8a08\u7b97\u306b\u3079\u304d\u4e57\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cmath&gt;\n#include &lt;vector&gt;\n\n\/\/ 2D\u7269\u7406\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u7c21\u6613\u5b9f\u88c5\nstruct Particle {\n    float x, y;       \/\/ \u4f4d\u7f6e\n    float vx, vy;     \/\/ \u901f\u5ea6\n    float mass;       \/\/ \u8cea\u91cf\n    \n    Particle(float _x, float _y, float _mass) \n        : x(_x), y(_y), vx(0), vy(0), mass(_mass) {}\n        \n    \/\/ \u4ed6\u306e\u7c92\u5b50\u304b\u3089\u306e\u91cd\u529b\u3092\u8a08\u7b97\n    void apply_gravity(const Particle&amp; other, float dt, float G = 6.67430e-11f) {\n        \/\/ \u8ddd\u96e2\u306e\u8a08\u7b97\n        float dx = other.x - x;\n        float dy = other.y - y;\n        float distance_squared = dx*dx + dy*dy;\n        \n        \/\/ \u8ddd\u96e2\u304c0\u306e\u5834\u5408\u306f\u8a08\u7b97\u3057\u306a\u3044\n        if (distance_squared &lt; 1e-10f) return;\n        \n        \/\/ \u91cd\u529b\u306e\u5927\u304d\u3055\u8a08\u7b97: F = G * m1 * m2 \/ r^2\n        \/\/ \u3053\u3053\u3067\u3079\u304d\u4e57\uff08\u9006\u4e8c\u4e57\uff09\u8a08\u7b97\u304c\u4f7f\u7528\u3055\u308c\u308b\n        float force_magnitude = G * mass * other.mass \/ distance_squared;\n        \n        \/\/ \u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u306e\u8a08\u7b97\n        float distance = std::sqrt(distance_squared);\n        float force_x = force_magnitude * dx \/ distance;\n        float force_y = force_magnitude * dy \/ distance;\n        \n        \/\/ \u52a0\u901f\u5ea6\u306e\u8a08\u7b97\u3068\u901f\u5ea6\u306e\u66f4\u65b0\uff08F = ma \u3088\u308a a = F\/m\uff09\n        vx += force_x \/ mass * dt;\n        vy += force_y \/ mass * dt;\n    }\n    \n    \/\/ \u4f4d\u7f6e\u306e\u66f4\u65b0\n    void update(float dt) {\n        x += vx * dt;\n        y += vy * dt;\n    }\n};\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid gravity_simulation_example() {\n    \/\/ \u30b9\u30b1\u30fc\u30eb\u3092\u8abf\u6574\u3057\u305f\u91cd\u529b\u5b9a\u6570\n    const float G = 1.0f;  \/\/ \u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u7528\u306b\u5358\u7d14\u5316\n    \n    \/\/ 2\u3064\u306e\u7c92\u5b50\u3092\u914d\u7f6e\n    Particle sun(0, 0, 1000);  \/\/ \u592a\u967d\n    Particle earth(100, 0, 1); \/\/ \u5730\u7403\n    \n    \/\/ \u5730\u7403\u306b\u521d\u901f\u3092\u4e0e\u3048\u3001\u5186\u8ecc\u9053\u306b\u4e57\u305b\u308b\n    earth.vy = std::sqrt(G * sun.mass \/ 100);\n    \n    \/\/ \u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u30d1\u30e9\u30e1\u30fc\u30bf\n    const float dt = 0.1f;         \/\/ \u30bf\u30a4\u30e0\u30b9\u30c6\u30c3\u30d7\n    const int steps = 20;          \/\/ \u30b9\u30c6\u30c3\u30d7\u6570\n    \n    std::cout &lt;&lt; \"\u91cd\u529b\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3 - \u7269\u4f53\u306e\u8ecc\u9053:\\n\";\n    std::cout &lt;&lt; \"\u30b9\u30c6\u30c3\u30d7, \u5730\u7403\u306eX\u5ea7\u6a19, \u5730\u7403\u306eY\u5ea7\u6a19\\n\";\n    \n    for (int i = 0; i &lt; steps; ++i) {\n        std::cout &lt;&lt; i &lt;&lt; \", \" &lt;&lt; earth.x &lt;&lt; \", \" &lt;&lt; earth.y &lt;&lt; std::endl;\n        \n        \/\/ \u91cd\u529b\u306e\u9069\u7528\n        earth.apply_gravity(sun, dt, G);\n        \n        \/\/ \u4f4d\u7f6e\u306e\u66f4\u65b0\n        earth.update(dt);\n    }\n}\n<\/pre>\n\n\n\n<p><strong>3. \u30ac\u30f3\u30de\u88dc\u6b63\uff1a<\/strong><\/p>\n\n\n\n<p>\u753b\u50cf\u51e6\u7406\u3067\u306f\u3001\u30c7\u30a3\u30b9\u30d7\u30ec\u30a4\u306e\u975e\u7dda\u5f62\u7279\u6027\u3092\u88dc\u6b63\u3059\u308b\u305f\u3081\u306b\u30ac\u30f3\u30de\u88dc\u6b63\uff08\u5024^(1\/\u03b3)\uff09\u304c\u884c\u308f\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cmath&gt;\n#include &lt;vector&gt;\n#include &lt;algorithm&gt;\n\n\/\/ RGB\u8272\u3092\u8868\u3059\u30af\u30e9\u30b9\nstruct Color {\n    float r, g, b;\n    \n    Color(float _r = 0, float _g = 0, float _b = 0) : r(_r), g(_g), b(_b) {}\n    \n    \/\/ \u5024\u30920\u301c1\u306e\u7bc4\u56f2\u306b\u5236\u9650\n    void clamp() {\n        r = std::max(0.0f, std::min(1.0f, r));\n        g = std::max(0.0f, std::min(1.0f, g));\n        b = std::max(0.0f, std::min(1.0f, b));\n    }\n};\n\n\/\/ \u30ac\u30f3\u30de\u88dc\u6b63\u306e\u9069\u7528\nColor apply_gamma_correction(const Color&amp; color, float gamma) {\n    Color corrected;\n    \n    \/\/ \u5404\u30c1\u30e3\u30f3\u30cd\u30eb\u306b\u30ac\u30f3\u30de\u88dc\u6b63\u3092\u9069\u7528\n    \/\/ \u88dc\u6b63\u5f0f: corrected = color^(1\/gamma)\n    \/\/ \u3053\u3053\u3067\u3079\u304d\u4e57\u8a08\u7b97\u304c\u4f7f\u7528\u3055\u308c\u308b\n    corrected.r = std::pow(color.r, 1.0f \/ gamma);\n    corrected.g = std::pow(color.g, 1.0f \/ gamma);\n    corrected.b = std::pow(color.b, 1.0f \/ gamma);\n    \n    corrected.clamp();\n    return corrected;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid gamma_correction_example() {\n    \/\/ \u5143\u306e\u8272\uff08\u30ea\u30cb\u30a2\u7a7a\u9593\uff09\n    std::vector&lt;Color&gt; colors = {\n        Color(0.0f, 0.0f, 0.0f),  \/\/ \u9ed2\n        Color(0.2f, 0.2f, 0.2f),  \/\/ \u6697\u3044\u30b0\u30ec\u30fc\n        Color(0.5f, 0.5f, 0.5f),  \/\/ \u4e2d\u9593\u30b0\u30ec\u30fc\n        Color(0.8f, 0.8f, 0.8f),  \/\/ \u660e\u308b\u3044\u30b0\u30ec\u30fc\n        Color(1.0f, 1.0f, 1.0f)   \/\/ \u767d\n    };\n    \n    \/\/ \u4e00\u822c\u7684\u306a\u30ac\u30f3\u30de\u5024\n    float gamma = 2.2f;\n    \n    std::cout &lt;&lt; \"\u30ac\u30f3\u30de\u88dc\u6b63\uff08\u03b3 = \" &lt;&lt; gamma &lt;&lt; \"\uff09:\\n\";\n    std::cout &lt;&lt; \"\u539f\u8272, \u88dc\u6b63\u5f8c\u306e\u8272\\n\";\n    \n    for (const auto&amp; color : colors) {\n        Color corrected = apply_gamma_correction(color, gamma);\n        std::cout &lt;&lt; \"(\" &lt;&lt; color.r &lt;&lt; \", \" &lt;&lt; color.g &lt;&lt; \", \" &lt;&lt; color.b &lt;&lt; \"), \";\n        std::cout &lt;&lt; \"(\" &lt;&lt; corrected.r &lt;&lt; \", \" &lt;&lt; corrected.g &lt;&lt; \", \" &lt;&lt; corrected.b &lt;&lt; \")\\n\";\n    }\n}\n<\/pre>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-24\">\u6697\u53f7\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u306e\u6b63\u3057\u3044\u4e57\u306e\u6d3b\u7528\u6cd5<\/h3>\n\n\n\n<p>\u6697\u53f7\u6280\u8853\u3067\u306f\u3001\u5927\u304d\u306a\u6574\u6570\u306e\u3079\u304d\u4e57\u8a08\u7b97\u304c\u6697\u53f7\u5316\u3084\u7f72\u540d\u306e\u57fa\u76e4\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u7279\u306bRSA\u6697\u53f7\u3084Diffie-Hellman\u9375\u4ea4\u63db\u306a\u3069\u3067\u306f\u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57\u304c\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>1. RSA\u6697\u53f7\u306e\u5b9f\u88c5\uff1a<\/strong><\/p>\n\n\n\n<p>RSA\u6697\u53f7\u306f\u516c\u958b\u9375\u3068\u79d8\u5bc6\u9375\u306e\u7d44\u307f\u5408\u308f\u305b\u3092\u4f7f\u7528\u3057\u3001\u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57\u8a08\u7b97\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cstdint&gt;\n#include &lt;random&gt;\n#include &lt;chrono&gt;\n\n\/\/ \u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57\u8a08\u7b97: (base^exponent) mod modulus\nuint64_t modular_pow(uint64_t base, uint64_t exponent, uint64_t modulus) {\n    if (modulus == 1) return 0;\n    \n    uint64_t result = 1;\n    base = base % modulus;\n    \n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            result = (result * base) % modulus;\n        }\n        exponent &gt;&gt;= 1;\n        base = (base * base) % modulus;\n    }\n    \n    return result;\n}\n\n\/\/ \u6700\u5927\u516c\u7d04\u6570\u306e\u8a08\u7b97\uff08\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306e\u4e92\u9664\u6cd5\uff09\nuint64_t gcd(uint64_t a, uint64_t b) {\n    while (b != 0) {\n        uint64_t temp = b;\n        b = a % b;\n        a = temp;\n    }\n    return a;\n}\n\n\/\/ \u30e2\u30b8\u30e5\u30e9\u30fc\u4e57\u6cd5\u9006\u5143\u306e\u8a08\u7b97\uff08\u62e1\u5f35\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306e\u4e92\u9664\u6cd5\uff09\nint64_t mod_inverse(int64_t a, int64_t m) {\n    int64_t m0 = m, t, q;\n    int64_t x0 = 0, x1 = 1;\n    \n    if (m == 1) return 0;\n    \n    while (a &gt; 1) {\n        q = a \/ m;\n        t = m;\n        m = a % m;\n        a = t;\n        t = x0;\n        x0 = x1 - q * x0;\n        x1 = t;\n    }\n    \n    if (x1 &lt; 0) x1 += m0;\n    \n    return x1;\n}\n\n\/\/ RSA\u6697\u53f7\u306e\u7c21\u6613\u5b9f\u88c5\u4f8b\nclass SimpleRSA {\nprivate:\n    \/\/ \u9375\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\n    uint64_t p, q;     \/\/ \u7d20\u6570\n    uint64_t n;        \/\/ \u30e2\u30b8\u30e5\u30e9\u30b9 (n = p * q)\n    uint64_t phi;      \/\/ \u30aa\u30a4\u30e9\u30fc\u306e\u30c8\u30fc\u30b7\u30a7\u30f3\u30c8\u95a2\u6570 (phi = (p-1) * (q-1))\n    uint64_t e;        \/\/ \u516c\u958b\u6307\u6570\n    uint64_t d;        \/\/ \u79d8\u5bc6\u6307\u6570\n\npublic:\n    \/\/ \u9375\u306e\u751f\u6210\n    void generate_keys() {\n        \/\/ \u5b9f\u969b\u306eRSA\u5b9f\u88c5\u3067\u306f\u3001\u5927\u304d\u306a\u7d20\u6570\u3092\u4f7f\u7528\u3057\u307e\u3059\n        \/\/ \u3053\u3053\u3067\u306f\u7c21\u6613\u4f8b\u3068\u3057\u3066\u5c0f\u3055\u306a\u5024\u3092\u4f7f\u7528\n        p = 61;\n        q = 53;\n        n = p * q;\n        phi = (p - 1) * (q - 1);\n        \n        \/\/ \u516c\u958b\u6307\u6570e\u3092\u9078\u629e\uff08\u4e00\u822c\u7684\u306b65537\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\uff09\n        e = 17;\n        \n        \/\/ \u6761\u4ef6: 1 &lt; e &lt; phi \u304b\u3064 gcd(e, phi) = 1\n        while (gcd(e, phi) != 1) {\n            e++;\n        }\n        \n        \/\/ \u79d8\u5bc6\u6307\u6570d\u3092\u8a08\u7b97: (d * e) % phi = 1\n        d = mod_inverse(e, phi);\n    }\n    \n    \/\/ \u6697\u53f7\u5316: c = m^e mod n\n    uint64_t encrypt(uint64_t message) {\n        return modular_pow(message, e, n);\n    }\n    \n    \/\/ \u5fa9\u53f7\u5316: m = c^d mod n\n    uint64_t decrypt(uint64_t ciphertext) {\n        return modular_pow(ciphertext, d, n);\n    }\n    \n    \/\/ \u516c\u958b\u9375\u306e\u53d6\u5f97\n    std::pair&lt;uint64_t, uint64_t&gt; get_public_key() const {\n        return {e, n};\n    }\n    \n    \/\/ \u9375\u60c5\u5831\u306e\u8868\u793a\n    void print_keys() const {\n        std::cout &lt;&lt; \"RSA\u9375\u30d1\u30e9\u30e1\u30fc\u30bf:\\n\";\n        std::cout &lt;&lt; \"p = \" &lt;&lt; p &lt;&lt; \", q = \" &lt;&lt; q &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"n = p*q = \" &lt;&lt; n &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"phi(n) = \" &lt;&lt; phi &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"\u516c\u958b\u6307\u6570 e = \" &lt;&lt; e &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"\u79d8\u5bc6\u6307\u6570 d = \" &lt;&lt; d &lt;&lt; std::endl;\n    }\n};\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid rsa_example() {\n    SimpleRSA rsa;\n    rsa.generate_keys();\n    rsa.print_keys();\n    \n    \/\/ \u5e73\u6587\u30e1\u30c3\u30bb\u30fc\u30b8\uff08\u5e73\u6587\u306f\u5fc5\u305an\u3088\u308a\u5c0f\u3055\u304f\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\uff09\n    uint64_t message = 42;\n    std::cout &lt;&lt; \"\\n\u5143\u306e\u30e1\u30c3\u30bb\u30fc\u30b8: \" &lt;&lt; message &lt;&lt; std::endl;\n    \n    \/\/ \u6697\u53f7\u5316\n    uint64_t ciphertext = rsa.encrypt(message);\n    std::cout &lt;&lt; \"\u6697\u53f7\u6587: \" &lt;&lt; ciphertext &lt;&lt; std::endl;\n    \n    \/\/ \u5fa9\u53f7\u5316\n    uint64_t decrypted = rsa.decrypt(ciphertext);\n    std::cout &lt;&lt; \"\u5fa9\u53f7\u3055\u308c\u305f\u30e1\u30c3\u30bb\u30fc\u30b8: \" &lt;&lt; decrypted &lt;&lt; std::endl;\n}\n<\/pre>\n\n\n\n<p><strong>2. Diffie-Hellman\u30ad\u30fc\u4ea4\u63db\uff1a<\/strong><\/p>\n\n\n\n<p>Diffie-Hellman\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u5b89\u5168\u306a\u901a\u4fe1\u30c1\u30e3\u30cd\u30eb\u304c\u306a\u304f\u3066\u3082\u3001\u4e8c\u8005\u9593\u3067\u5171\u6709\u79d8\u5bc6\u9375\u3092\u78ba\u7acb\u3059\u308b\u305f\u3081\u306e\u30d7\u30ed\u30c8\u30b3\u30eb\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cstdint&gt;\n#include &lt;random&gt;\n\n\/\/ \u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57\u8a08\u7b97\uff08\u524d\u8ff0\u306e\u5b9f\u88c5\u3068\u540c\u3058\uff09\nuint64_t modular_pow(uint64_t base, uint64_t exponent, uint64_t modulus) {\n    if (modulus == 1) return 0;\n    \n    uint64_t result = 1;\n    base = base % modulus;\n    \n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            result = (result * base) % modulus;\n        }\n        exponent &gt;&gt;= 1;\n        base = (base * base) % modulus;\n    }\n    \n    return result;\n}\n\n\/\/ Diffie-Hellman\u30ad\u30fc\u4ea4\u63db\u306e\u7c21\u6613\u5b9f\u88c5\nclass DiffieHellman {\nprivate:\n    \/\/ \u5171\u901a\u30d1\u30e9\u30e1\u30fc\u30bf\n    uint64_t p;  \/\/ \u5927\u304d\u306a\u7d20\u6570\n    uint64_t g;  \/\/ \u539f\u59cb\u6839\n    \n    \/\/ \u4e71\u6570\u751f\u6210\u5668\n    std::mt19937_64 rng;\n    \npublic:\n    DiffieHellman() {\n        \/\/ \u4e71\u6570\u751f\u6210\u5668\u306e\u521d\u671f\u5316\n        rng.seed(std::chrono::high_resolution_clock::now().time_since_epoch().count());\n        \n        \/\/ \u5b9f\u969b\u306e\u5b9f\u88c5\u3067\u306f\u5927\u304d\u306a\u7d20\u6570\u3092\u4f7f\u7528\n        \/\/ \u3053\u3053\u3067\u306f\u7c21\u6613\u4f8b\u3068\u3057\u3066\u5c0f\u3055\u306a\u5024\u3092\u4f7f\u7528\n        p = 23;  \/\/ \u7d20\u6570\n        g = 5;   \/\/ \u539f\u59cb\u6839\n    }\n    \n    \/\/ \u5171\u901a\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u53d6\u5f97\n    std::pair&lt;uint64_t, uint64_t&gt; get_parameters() const {\n        return {p, g};\n    }\n    \n    \/\/ \u79d8\u5bc6\u9375\uff08a, b\uff09\u306e\u751f\u6210\n    uint64_t generate_private_key() {\n        \/\/ 1\u304b\u3089p-2\u306e\u7bc4\u56f2\u3067\u4e71\u6570\u3092\u751f\u6210\n        std::uniform_int_distribution&lt;uint64_t&gt; dist(1, p - 2);\n        return dist(rng);\n    }\n    \n    \/\/ \u516c\u958b\u9375\u306e\u8a08\u7b97: A = g^a mod p, B = g^b mod p\n    uint64_t calculate_public_key(uint64_t private_key) {\n        return modular_pow(g, private_key, p);\n    }\n    \n    \/\/ \u5171\u6709\u79d8\u5bc6\u9375\u306e\u8a08\u7b97:\n    \/\/ Alice: s = B^a mod p\n    \/\/ Bob: s = A^b mod p\n    uint64_t calculate_shared_secret(uint64_t other_public_key, uint64_t own_private_key) {\n        return modular_pow(other_public_key, own_private_key, p);\n    }\n};\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid diffie_hellman_example() {\n    DiffieHellman dh;\n    auto [p, g] = dh.get_parameters();\n    \n    std::cout &lt;&lt; \"Diffie-Hellman\u30ad\u30fc\u4ea4\u63db\u30d1\u30e9\u30e1\u30fc\u30bf:\\n\";\n    std::cout &lt;&lt; \"\u7d20\u6570 p = \" &lt;&lt; p &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u539f\u59cb\u6839 g = \" &lt;&lt; g &lt;&lt; std::endl;\n    \n    \/\/ Alice\u306e\u9375\u30da\u30a2\u751f\u6210\n    uint64_t a = dh.generate_private_key();\n    uint64_t A = dh.calculate_public_key(a);\n    std::cout &lt;&lt; \"\\nAlice:\\n\";\n    std::cout &lt;&lt; \"\u79d8\u5bc6\u9375 a = \" &lt;&lt; a &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u516c\u958b\u9375 A = g^a mod p = \" &lt;&lt; A &lt;&lt; std::endl;\n    \n    \/\/ Bob\u306e\u9375\u30da\u30a2\u751f\u6210\n    uint64_t b = dh.generate_private_key();\n    uint64_t B = dh.calculate_public_key(b);\n    std::cout &lt;&lt; \"\\nBob:\\n\";\n    std::cout &lt;&lt; \"\u79d8\u5bc6\u9375 b = \" &lt;&lt; b &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u516c\u958b\u9375 B = g^b mod p = \" &lt;&lt; B &lt;&lt; std::endl;\n    \n    \/\/ \u5171\u6709\u79d8\u5bc6\u9375\u306e\u8a08\u7b97\n    uint64_t secret_alice = dh.calculate_shared_secret(B, a);\n    uint64_t secret_bob = dh.calculate_shared_secret(A, b);\n    \n    std::cout &lt;&lt; \"\\n\u5171\u6709\u79d8\u5bc6\u9375:\\n\";\n    std::cout &lt;&lt; \"Alice\u5074: B^a mod p = \" &lt;&lt; secret_alice &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"Bob\u5074: A^b mod p = \" &lt;&lt; secret_bob &lt;&lt; std::endl;\n    \n    \/\/ \u4e21\u8005\u304c\u540c\u3058\u5171\u6709\u79d8\u5bc6\u9375\u3092\u5c0e\u51fa\u3067\u304d\u305f\u3053\u3068\u3092\u78ba\u8a8d\n    if (secret_alice == secret_bob) {\n        std::cout &lt;&lt; \"\u6210\u529f: \u5171\u6709\u79d8\u5bc6\u9375\u304c\u4e00\u81f4\u3057\u307e\u3057\u305f\u3002\" &lt;&lt; std::endl;\n    } else {\n        std::cout &lt;&lt; \"\u30a8\u30e9\u30fc: \u5171\u6709\u79d8\u5bc6\u9375\u304c\u4e00\u81f4\u3057\u307e\u305b\u3093\u3002\" &lt;&lt; std::endl;\n    }\n}\n<\/pre>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-25\">\u79d1\u5b66\u6280\u8853\u8a08\u7b97\u3067\u306e\u9ad8\u7cbe\u5ea6\u3079\u304d\u4e57\u8a08\u7b97<\/h3>\n\n\n\n<p>\u79d1\u5b66\u6280\u8853\u8a08\u7b97\u3001\u7279\u306b\u6570\u5024\u89e3\u6790\u3084\u7269\u7406\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u9ad8\u7cbe\u5ea6\u306e\u3079\u304d\u4e57\u8a08\u7b97\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<p><strong>1. \u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u5c55\u958b\u306b\u3088\u308b\u6307\u6570\u95a2\u6570\u306e\u5b9f\u88c5\uff1a<\/strong><\/p>\n\n\n\n<p>\u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u5c55\u958b\u3092\u4f7f\u3063\u3066\u3001\u9ad8\u7cbe\u5ea6\u306e\u6307\u6570\u95a2\u6570\uff08e^x\uff09\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;iomanip&gt;\n#include &lt;cmath&gt;\n#include &lt;vector&gt;\n\n\/\/ \u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u306b\u3088\u308be^x\u306e\u8a08\u7b97\n\/\/ e^x = 1 + x + x^2\/2! + x^3\/3! + ... + x^n\/n! + ...\ndouble exp_taylor(double x, int terms = 20) {\n    double sum = 1.0;  \/\/ \u6700\u521d\u306e\u9805 (x^0\/0!)\n    double term = 1.0; \/\/ \u5404\u9805\u306e\u5024\n    \n    for (int i = 1; i &lt; terms; ++i) {\n        \/\/ \u6b21\u306e\u9805\u3092\u8a08\u7b97: term = term * x \/ i\n        term *= x \/ i;\n        \n        \/\/ \u7d1a\u6570\u306b\u52a0\u7b97\n        sum += term;\n        \n        \/\/ \u53ce\u675f\u6761\u4ef6: \u9805\u304c\u5341\u5206\u5c0f\u3055\u304f\u306a\u3063\u305f\u3089\u7d42\u4e86\n        if (std::abs(term) &lt; 1e-15) {\n            break;\n        }\n    }\n    \n    return sum;\n}\n\n\/\/ \u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u306b\u3088\u308bcosx\u306e\u8a08\u7b97\n\/\/ cos(x) = 1 - x^2\/2! + x^4\/4! - x^6\/6! + ...\ndouble cos_taylor(double x, int terms = 20) {\n    \/\/ \u89d2\u5ea6\u3092-\u03c0\u304b\u3089\u03c0\u306e\u7bc4\u56f2\u306b\u6b63\u898f\u5316\n    x = std::fmod(x, 2.0 * M_PI);\n    if (x &gt; M_PI) x -= 2.0 * M_PI;\n    else if (x &lt; -M_PI) x += 2.0 * M_PI;\n    \n    double sum = 1.0;  \/\/ \u6700\u521d\u306e\u9805 (x^0\/0!)\n    double term = 1.0; \/\/ \u5404\u9805\u306e\u5024\n    double x_squared = x * x; \/\/ x^2\u3092\u4e8b\u524d\u8a08\u7b97\n    double sign = -1.0; \/\/ \u9805\u306e\u7b26\u53f7\uff08\u4ea4\u4e92\u306b\u5909\u308f\u308b\uff09\n    \n    for (int i = 2; i &lt; terms; i += 2) {\n        \/\/ \u6b21\u306e\u9805\u3092\u8a08\u7b97: term = term * x^2 \/ (i*(i-1))\n        term = term * x_squared \/ (i * (i - 1));\n        \n        \/\/ \u7d1a\u6570\u306b\u52a0\u7b97\uff08\u7b26\u53f7\u4ed8\u304d\uff09\n        sum += sign * term;\n        \n        \/\/ \u53ce\u675f\u6761\u4ef6: \u9805\u304c\u5341\u5206\u5c0f\u3055\u304f\u306a\u3063\u305f\u3089\u7d42\u4e86\n        if (std::abs(term) &lt; 1e-15) {\n            break;\n        }\n        \n        \/\/ \u7b26\u53f7\u3092\u53cd\u8ee2\n        sign = -sign;\n    }\n    \n    return sum;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid taylor_series_example() {\n    std::cout &lt;&lt; std::setprecision(15);\n    std::cout &lt;&lt; \"\u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u306b\u3088\u308b\u9ad8\u7cbe\u5ea6\u8a08\u7b97:\\n\";\n    \n    \/\/ e^x\u306e\u8a08\u7b97\n    std::vector&lt;double&gt; x_values = {0.0, 0.5, 1.0, 2.0, -1.0};\n    \n    std::cout &lt;&lt; \"e^x \u306e\u8a08\u7b97:\\n\";\n    std::cout &lt;&lt; \"x, \u30c6\u30a4\u30e9\u30fc\u7d1a\u6570, std::exp, \u8aa4\u5dee\\n\";\n    for (double x : x_values) {\n        double taylor_result = exp_taylor(x);\n        double std_result = std::exp(x);\n        double error = std::abs(taylor_result - std_result);\n        \n        std::cout &lt;&lt; x &lt;&lt; \", \" &lt;&lt; taylor_result &lt;&lt; \", \" &lt;&lt; std_result \n                  &lt;&lt; \", \" &lt;&lt; error &lt;&lt; std::endl;\n    }\n    \n    \/\/ cos(x)\u306e\u8a08\u7b97\n    std::vector&lt;double&gt; angles = {0.0, M_PI\/6, M_PI\/4, M_PI\/3, M_PI\/2};\n    \n    std::cout &lt;&lt; \"\\ncos(x) \u306e\u8a08\u7b97:\\n\";\n    std::cout &lt;&lt; \"x, \u30c6\u30a4\u30e9\u30fc\u7d1a\u6570, std::cos, \u8aa4\u5dee\\n\";\n    for (double angle : angles) {\n        double taylor_result = cos_taylor(angle);\n        double std_result = std::cos(angle);\n        double error = std::abs(taylor_result - std_result);\n        \n        std::cout &lt;&lt; angle &lt;&lt; \", \" &lt;&lt; taylor_result &lt;&lt; \", \" &lt;&lt; std_result \n                  &lt;&lt; \", \" &lt;&lt; error &lt;&lt; std::endl;\n    }\n}\n<\/pre>\n\n\n\n<p><strong>2. \u9ad8\u7cbe\u5ea6\u6570\u5024\u7a4d\u5206\u306b\u304a\u3051\u308b\u6307\u6570\u95a2\u6570\uff1a<\/strong><\/p>\n\n\n\n<p>\u6570\u5024\u7a4d\u5206\u3067\u306f\u3001\u30ac\u30a6\u30b9\u6c42\u7a4d\u6cd5\u306a\u3069\u306e\u9ad8\u7cbe\u5ea6\u624b\u6cd5\u3067\u6307\u6570\u95a2\u6570\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;iomanip&gt;\n#include &lt;cmath&gt;\n#include &lt;vector&gt;\n#include &lt;functional&gt;\n\n\/\/ \u30b7\u30f3\u30d7\u30bd\u30f3\u5247\u306b\u3088\u308b\u6570\u5024\u7a4d\u5206\ndouble simpson_integration(std::function&lt;double(double)&gt; f, double a, double b, int n) {\n    if (n % 2 == 1) n++; \/\/ n\u3092\u5076\u6570\u306b\u8abf\u6574\n    \n    double h = (b - a) \/ n;\n    double sum = f(a) + f(b); \/\/ \u4e21\u7aef\u70b9\n    \n    \/\/ \u5947\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u9805\u306b4\u3092\u639b\u3051\u308b\n    for (int i = 1; i &lt; n; i += 2) {\n        sum += 4 * f(a + i * h);\n    }\n    \n    \/\/ \u5076\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u9805\u306b2\u3092\u639b\u3051\u308b\n    for (int i = 2; i &lt; n; i += 2) {\n        sum += 2 * f(a + i * h);\n    }\n    \n    return sum * h \/ 3;\n}\n\n\/\/ \u30ac\u30a6\u30b9\u306e\u8aa4\u5dee\u95a2\u6570\u306e\u6570\u5024\u7a4d\u5206\ndouble erf_numerical(double x) {\n    \/\/ erf(x) = (2\/\u221a\u03c0) * \u222b(0,x) e^(-t^2) dt\n    auto integrand = [](double t) { return std::exp(-t * t); };\n    \n    const double sqrt_pi = std::sqrt(M_PI);\n    return (2.0 \/ sqrt_pi) * simpson_integration(integrand, 0.0, x, 1000);\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid numerical_integration_example() {\n    std::cout &lt;&lt; std::setprecision(15);\n    std::cout &lt;&lt; \"\u6570\u5024\u7a4d\u5206\u306b\u304a\u3051\u308b\u6307\u6570\u95a2\u6570\u306e\u5fdc\u7528:\\n\";\n    \n    \/\/ \u30ac\u30a6\u30b9\u306e\u8aa4\u5dee\u95a2\u6570\u306e\u8a08\u7b97\n    std::vector&lt;double&gt; x_values = {0.0, 0.5, 1.0, 1.5, 2.0, 3.0};\n    \n    std::cout &lt;&lt; \"\u30ac\u30a6\u30b9\u306e\u8aa4\u5dee\u95a2\u6570 erf(x):\\n\";\n    std::cout &lt;&lt; \"x, \u6570\u5024\u7a4d\u5206, std::erf, \u8aa4\u5dee\\n\";\n    for (double x : x_values) {\n        double numerical_result = erf_numerical(x);\n        double std_result = std::erf(x);\n        double error = std::abs(numerical_result - std_result);\n        \n        std::cout &lt;&lt; x &lt;&lt; \", \" &lt;&lt; numerical_result &lt;&lt; \", \" &lt;&lt; std_result \n                  &lt;&lt; \", \" &lt;&lt; error &lt;&lt; std::endl;\n    }\n}\n<\/pre>\n\n\n\n<p><strong>3. \u591a\u500d\u9577\u6d6e\u52d5\u5c0f\u6570\u70b9\u6f14\u7b97\u306b\u3088\u308b\u9ad8\u7cbe\u5ea6\u8a08\u7b97\uff1a<\/strong><\/p>\n\n\n\n<p>\u975e\u5e38\u306b\u9ad8\u3044\u7cbe\u5ea6\u304c\u5fc5\u8981\u306a\u79d1\u5b66\u8a08\u7b97\u3067\u306f\u3001\u591a\u500d\u9577\u6d6e\u52d5\u5c0f\u6570\u70b9\u6f14\u7b97\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;iomanip&gt;\n#include &lt;boost\/multiprecision\/cpp_dec_float.hpp&gt;\n\n\/\/ 100\u6841\u306e\u7cbe\u5ea6\u3092\u6301\u3064\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\nusing mp_float = boost::multiprecision::cpp_dec_float_100;\n\n\/\/ \u591a\u500d\u9577\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306b\u3088\u308be^x\u306e\u8a08\u7b97\ntemplate &lt;typename T&gt;\nT high_precision_exp(T x, int terms = 100) {\n    T sum = 1;  \/\/ \u6700\u521d\u306e\u9805\n    T term = 1; \/\/ \u5404\u9805\u306e\u5024\n    \n    for (int i = 1; i &lt; terms; ++i) {\n        term *= x \/ i;\n        sum += term;\n        \n        \/\/ \u53ce\u675f\u30c1\u30a7\u30c3\u30af\n        if (abs(term) &lt; 1e-99) {\n            break;\n        }\n    }\n    \n    return sum;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid high_precision_example() {\n    std::cout &lt;&lt; std::setprecision(50);\n    std::cout &lt;&lt; \"\u591a\u500d\u9577\u6d6e\u52d5\u5c0f\u6570\u70b9\u6f14\u7b97\u306b\u3088\u308b\u9ad8\u7cbe\u5ea6\u8a08\u7b97:\\n\";\n    \n    \/\/ \u03c0 \u306e\u9ad8\u7cbe\u5ea6\u8a08\u7b97\n    mp_float pi = boost::math::constants::pi&lt;mp_float&gt;();\n    std::cout &lt;&lt; \"\u03c0 = \" &lt;&lt; pi &lt;&lt; std::endl;\n    \n    \/\/ e^\u03c0 \u306e\u9ad8\u7cbe\u5ea6\u8a08\u7b97\n    mp_float e_pi = high_precision_exp(pi);\n    std::cout &lt;&lt; \"e^\u03c0 = \" &lt;&lt; e_pi &lt;&lt; std::endl;\n    \n    \/\/ \u30aa\u30a4\u30e9\u30fc\u306e\u7b49\u5f0f e^(i\u03c0) + 1 = 0 \u306e\u9ad8\u7cbe\u5ea6\u8a08\u7b97\n    \/\/ \u8907\u7d20\u6570\u6f14\u7b97\u306f\u7c21\u5358\u5316\u306e\u305f\u3081\u7701\u7565\n    mp_float euler_result = boost::multiprecision::cos(pi) + 1;\n    std::cout &lt;&lt; \"cos(\u03c0) + 1 = \" &lt;&lt; euler_result &lt;&lt; std::endl;\n    \/\/ \u7406\u8ad6\u7684\u306b\u306f0\u306b\u306a\u308b\u306f\u305a\u3060\u304c\u3001\u4e38\u3081\u8aa4\u5dee\u3067\u6975\u3081\u3066\u5c0f\u3055\u3044\u5024\u306b\u306a\u308b\n}\n<\/pre>\n\n\n\n<p>\u3053\u308c\u3089\u306e\u5fdc\u7528\u4f8b\u306f\u3001C++\u306b\u304a\u3051\u308b\u3079\u304d\u4e57\u8a08\u7b97\u304c\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u51e6\u7406\u3001\u6697\u53f7\u5316\u3001\u79d1\u5b66\u8a08\u7b97\u306a\u3069\u306e\u5e45\u5e83\u3044\u5206\u91ce\u3067\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u9069\u5207\u306a\u5b9f\u88c5\u65b9\u6cd5\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u3067\u3001\u7cbe\u5ea6\u3068\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u306e\u4e21\u65b9\u3092\u6700\u9069\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"i-26\">C++20\u4ee5\u964d\u306e\u6b63\u3057\u3044\u4e57\u8a08\u7b97\u306e\u65b0\u6a5f\u80fd\u3068\u5c06\u6765\u5c55\u671b<\/h2>\n\n\n\n<p>C++\u8a00\u8a9e\u306f\u7d99\u7d9a\u7684\u306b\u9032\u5316\u3057\u3066\u304a\u308a\u3001C++20\u3067\u306f\u6570\u5b66\u8a08\u7b97\u3001\u7279\u306b\u3079\u304d\u4e57\u8a08\u7b97\u306b\u95a2\u9023\u3059\u308b\u91cd\u8981\u306a\u6a5f\u80fd\u304c\u5c0e\u5165\u3055\u308c\u307e\u3057\u305f\u3002\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001C++20\u3067\u8ffd\u52a0\u3055\u308c\u305f\u65b0\u6a5f\u80fd\u3068\u3001\u5c06\u6765\u306eC++\u6a19\u6e96\u3067\u671f\u5f85\u3055\u308c\u308b\u6539\u5584\u70b9\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-27\">C++20\u3067\u8ffd\u52a0\u3055\u308c\u305f\u6570\u5b66\u95a2\u9023\u306e\u65b0\u6a5f\u80fd<\/h3>\n\n\n\n<p>C++20\u306f\u6570\u5b66\u8a08\u7b97\u306b\u95a2\u9023\u3059\u308b\u591a\u304f\u306e\u65b0\u6a5f\u80fd\u3092\u5c0e\u5165\u3057\u3001\u3079\u304d\u4e57\u8a08\u7b97\u306e\u5b9f\u88c5\u65b9\u6cd5\u3068\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3057\u305f\u3002\u4e3b\u306a\u65b0\u6a5f\u80fd\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p><strong>1. <code>&lt;numbers&gt;<\/code> \u30d8\u30c3\u30c0\u30fc\u306e\u5c0e\u5165\uff1a<\/strong><\/p>\n\n\n\n<p>C++20\u3067\u306f <code>&lt;numbers&gt;<\/code> \u30d8\u30c3\u30c0\u30fc\u304c\u5c0e\u5165\u3055\u308c\u3001\u6570\u5b66\u5b9a\u6570\u304c\u6a19\u6e96\u3067\u63d0\u4f9b\u3055\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u5b9a\u6570\u306f\u3079\u304d\u4e57\u8a08\u7b97\u3084\u8fd1\u4f3c\u8a08\u7b97\u3067\u983b\u7e41\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;numbers&gt;\n#include &lt;cmath&gt;\n\nint main() {\n    \/\/ C++20\u306e\u6570\u5b66\u5b9a\u6570\n    std::cout &lt;&lt; \"\u6570\u5b66\u5b9a\u6570 (C++20):\\n\";\n    std::cout &lt;&lt; \"e = \" &lt;&lt; std::numbers::e &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u03c0 = \" &lt;&lt; std::numbers::pi &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"ln(2) = \" &lt;&lt; std::numbers::ln2 &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"sqrt(2) = \" &lt;&lt; std::numbers::sqrt2 &lt;&lt; std::endl;\n    \n    \/\/ \u6307\u6570\u95a2\u6570\u306e\u8a08\u7b97\u4f8b\n    double x = 2.0;\n    std::cout &lt;&lt; \"\\n\u6307\u6570\u95a2\u6570\u306e\u8a08\u7b97:\\n\";\n    std::cout &lt;&lt; \"e^2 = \" &lt;&lt; std::exp(x) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"e^2 (\u624b\u52d5\u8a08\u7b97) = \" &lt;&lt; std::pow(std::numbers::e, x) &lt;&lt; std::endl;\n    \n    \/\/ 2\u306e\u3079\u304d\u4e57\u306e\u8a08\u7b97\u4f8b\n    std::cout &lt;&lt; \"\\n2\u306e\u3079\u304d\u4e57:\\n\";\n    std::cout &lt;&lt; \"2^10 = \" &lt;&lt; std::pow(2.0, 10.0) &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"2^(-3) = \" &lt;&lt; std::pow(2.0, -3.0) &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p>\u3053\u308c\u3089\u306e\u5b9a\u6570\u306f\u7570\u306a\u308b\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\uff08<code>float<\/code>, <code>double<\/code>, <code>long double<\/code>\uff09\u306b\u3082\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u3059\u3002\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u5909\u6570\u3092\u4f7f\u7528\u3057\u3066\u578b\u3092\u6307\u5b9a\u3067\u304d\u307e\u3059\uff1a<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">float pi_float = std::numbers::pi_v&lt;float&gt;;\ndouble pi_double = std::numbers::pi_v&lt;double&gt;;\nlong double pi_long_double = std::numbers::pi_v&lt;long double&gt;;\n<\/pre>\n\n\n\n<p><strong>2. <code>&lt;bit&gt;<\/code> \u30d8\u30c3\u30c0\u30fc\u306e\u5c0e\u5165\uff1a<\/strong><\/p>\n\n\n\n<p>C++20\u3067\u306f <code>&lt;bit&gt;<\/code> \u30d8\u30c3\u30c0\u30fc\u304c\u5c0e\u5165\u3055\u308c\u30012\u306e\u3079\u304d\u4e57\u8a08\u7b97\u306b\u95a2\u9023\u3059\u308b\u30d3\u30c3\u30c8\u64cd\u4f5c\u95a2\u6570\u304c\u8ffd\u52a0\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;bit&gt;\n#include &lt;bitset&gt;\n\nint main() {\n    \/\/ 2\u306e\u3079\u304d\u4e57\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\n    auto is_power_of_two = [](unsigned int n) {\n        return n &gt; 0 &amp;&amp; (n &amp; (n - 1)) == 0;\n    };\n    \n    std::cout &lt;&lt; \"2\u306e\u3079\u304d\u4e57\u306b\u95a2\u9023\u3059\u308b\u30d3\u30c3\u30c8\u64cd\u4f5c (C++20):\\n\";\n    \n    \/\/ \u6b21\u306e2\u306e\u3079\u304d\u4e57\u306b\u5207\u308a\u4e0a\u3052\n    unsigned int value = 42;\n    unsigned int next_power_of_two = std::bit_ceil(value);\n    std::cout &lt;&lt; value &lt;&lt; \"\u306e\u6b21\u306e2\u306e\u3079\u304d\u4e57 = \" &lt;&lt; next_power_of_two &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u30d0\u30a4\u30ca\u30ea\u8868\u73fe: \" &lt;&lt; std::bitset&lt;16&gt;(next_power_of_two) &lt;&lt; std::endl;\n    \n    \/\/ \u73fe\u5728\u306e\u5024\u4ee5\u4e0b\u306e\u6700\u5927\u306e2\u306e\u3079\u304d\u4e57\n    unsigned int prev_power_of_two = std::bit_floor(value);\n    std::cout &lt;&lt; value &lt;&lt; \"\u4ee5\u4e0b\u306e\u6700\u5927\u306e2\u306e\u3079\u304d\u4e57 = \" &lt;&lt; prev_power_of_two &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u30d0\u30a4\u30ca\u30ea\u8868\u73fe: \" &lt;&lt; std::bitset&lt;16&gt;(prev_power_of_two) &lt;&lt; std::endl;\n    \n    \/\/ \u6574\u6570\u3092\u8868\u73fe\u3059\u308b\u306e\u306b\u5fc5\u8981\u306a\u30d3\u30c3\u30c8\u6570\n    unsigned int bit_width = std::bit_width(value);\n    std::cout &lt;&lt; value &lt;&lt; \"\u3092\u8868\u73fe\u3059\u308b\u306e\u306b\u5fc5\u8981\u306a\u30d3\u30c3\u30c8\u6570 = \" &lt;&lt; bit_width &lt;&lt; std::endl;\n    \n    \/\/ \u5024\u304c2\u306e\u3079\u304d\u4e57\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    std::cout &lt;&lt; \"\\n2\u306e\u3079\u304d\u4e57\u30c1\u30a7\u30c3\u30af:\\n\";\n    for (unsigned int i = 1; i &lt;= 65; i *= 2) {\n        std::cout &lt;&lt; i &lt;&lt; \" \u306f2\u306e\u3079\u304d\u4e57? \" &lt;&lt; (is_power_of_two(i) ? \"\u306f\u3044\" : \"\u3044\u3044\u3048\") &lt;&lt; std::endl;\n    }\n    std::cout &lt;&lt; \"42 \u306f2\u306e\u3079\u304d\u4e57? \" &lt;&lt; (is_power_of_two(42) ? \"\u306f\u3044\" : \"\u3044\u3044\u3048\") &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p><code>&lt;bit&gt;<\/code> \u30d8\u30c3\u30c0\u30fc\u306e\u95a2\u6570\u306f\u3001\u7279\u306b2\u306e\u3079\u304d\u4e57\u306b\u95a2\u9023\u3059\u308b\u8a08\u7b97\u3084\u6700\u9069\u5316\u306b\u975e\u5e38\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30e1\u30e2\u30ea\u30a2\u30ed\u30b1\u30fc\u30b7\u30e7\u30f3\u3084\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u30b5\u30a4\u30ba\u8abf\u6574\u3067\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>3. <code>constexpr<\/code> \u6570\u5b66\u95a2\u6570\u306e\u30b5\u30dd\u30fc\u30c8\u5f37\u5316\uff1a<\/strong><\/p>\n\n\n\n<p>C++20\u3067\u306f\u3001\u591a\u304f\u306e\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u95a2\u6570\u304c <code>constexpr<\/code> \u306b\u5bfe\u5fdc\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u3079\u304d\u4e57\u8a08\u7b97\u306a\u3069\u306e\u6570\u5b66\u6f14\u7b97\u3092\u5b9f\u884c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cmath&gt;\n#include &lt;array&gt;\n\nint main() {\n    std::cout &lt;&lt; \"C++20\u306econstexpr\u6570\u5b66\u95a2\u6570:\\n\";\n    \n    \/\/ \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u3079\u304d\u4e57\u8a08\u7b97\n    constexpr double x = 2.0;\n    constexpr double y = 3.0;\n    constexpr double power_result = std::pow(x, y);\n    std::cout &lt;&lt; x &lt;&lt; \"^\" &lt;&lt; y &lt;&lt; \" = \" &lt;&lt; power_result &lt;&lt; std::endl;\n    \n    \/\/ \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u5e73\u65b9\u6839\u8a08\u7b97\n    constexpr double sqrt_result = std::sqrt(x);\n    std::cout &lt;&lt; \"sqrt(\" &lt;&lt; x &lt;&lt; \") = \" &lt;&lt; sqrt_result &lt;&lt; std::endl;\n    \n    \/\/ \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u30d4\u30bf\u30b4\u30e9\u30b9\u8a08\u7b97\n    constexpr double a = 3.0;\n    constexpr double b = 4.0;\n    constexpr double hypot_result = std::hypot(a, b);\n    std::cout &lt;&lt; \"hypot(\" &lt;&lt; a &lt;&lt; \", \" &lt;&lt; b &lt;&lt; \") = \" &lt;&lt; hypot_result &lt;&lt; std::endl;\n    \n    \/\/ \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u8a08\u7b97\u3055\u308c\u305f2\u306e\u3079\u304d\u4e57\u306e\u914d\u5217\n    constexpr std::array&lt;double, 10&gt; powers_of_two = []() {\n        std::array&lt;double, 10&gt; result = {};\n        for (int i = 0; i &lt; 10; ++i) {\n            result[i] = std::pow(2.0, static_cast&lt;double&gt;(i));\n        }\n        return result;\n    }();\n    \n    std::cout &lt;&lt; \"\\n2\u306e\u3079\u304d\u4e57\u914d\u5217 (\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97):\\n\";\n    for (int i = 0; i &lt; 10; ++i) {\n        std::cout &lt;&lt; \"2^\" &lt;&lt; i &lt;&lt; \" = \" &lt;&lt; powers_of_two[i] &lt;&lt; std::endl;\n    }\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<p>\u3053\u306e\u6a5f\u80fd\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001\u5b9f\u884c\u6642\u306e\u30b3\u30b9\u30c8\u306a\u3057\u3067\u9ad8\u5ea6\u306a\u3079\u304d\u4e57\u8a08\u7b97\u3092\u884c\u3046\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u7279\u306b\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u30e1\u30bf\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3084\u5b9a\u6570\u5f0f\u304c\u591a\u7528\u3055\u308c\u308b\u30b3\u30fc\u30c9\u3067\u306f\u5927\u304d\u306a\u30e1\u30ea\u30c3\u30c8\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>4. \u30b3\u30f3\u30bb\u30d7\u30c8\u3092\u7528\u3044\u305f\u578b\u5236\u7d04\uff1a<\/strong><\/p>\n\n\n\n<p>C++20\u3067\u306f\u30b3\u30f3\u30bb\u30d7\u30c8\u304c\u5c0e\u5165\u3055\u308c\u3001\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u5f15\u6570\u306b\u5bfe\u3059\u308b\u578b\u5236\u7d04\u3092\u660e\u793a\u7684\u306b\u8a18\u8ff0\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u3053\u308c\u306b\u3088\u308a\u3079\u304d\u4e57\u8a08\u7b97\u3092\u884c\u3046\u95a2\u6570\u306e\u7279\u6b8a\u5316\u3084\u6700\u9069\u5316\u304c\u3088\u308a\u7c21\u6f54\u306b\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;concepts&gt;\n#include &lt;cmath&gt;\n\n\/\/ \u6574\u6570\u578b\u7528\u306e\u3079\u304d\u4e57\u95a2\u6570\ntemplate &lt;std::integral T&gt;\nT power_integral(T base, int exponent) {\n    if (exponent &lt; 0) {\n        throw std::domain_error(\"\u8ca0\u306e\u6307\u6570\u306f\u6574\u6570\u578b\u3067\u306f\u6271\u3048\u307e\u305b\u3093\");\n    }\n    \n    T result = 1;\n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            result *= base;\n        }\n        base *= base;\n        exponent &gt;&gt;= 1;\n    }\n    return result;\n}\n\n\/\/ \u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u7528\u306e\u3079\u304d\u4e57\u95a2\u6570\ntemplate &lt;std::floating_point T&gt;\nT power_floating(T base, T exponent) {\n    return std::pow(base, exponent);\n}\n\n\/\/ \u7d71\u5408\u3055\u308c\u305f\u3079\u304d\u4e57\u95a2\u6570\ntemplate &lt;typename T, typename E&gt;\n    requires std::integral&lt;T&gt; || std::floating_point&lt;T&gt;\nauto power(T base, E exponent) {\n    if constexpr (std::integral&lt;T&gt; &amp;&amp; std::integral&lt;E&gt;) {\n        if (exponent &gt;= 0) {\n            return power_integral(base, exponent);\n        } else {\n            \/\/ \u8ca0\u306e\u6307\u6570\u306e\u5834\u5408\u306f\u6d6e\u52d5\u5c0f\u6570\u70b9\u306b\u5909\u63db\n            return power_floating&lt;double&gt;(static_cast&lt;double&gt;(base), static_cast&lt;double&gt;(exponent));\n        }\n    } else {\n        \/\/ \u3044\u305a\u308c\u304b\u304c\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u306e\u5834\u5408\n        return power_floating(static_cast&lt;double&gt;(base), static_cast&lt;double&gt;(exponent));\n    }\n}\n\nint main() {\n    std::cout &lt;&lt; \"C++20\u306e\u30b3\u30f3\u30bb\u30d7\u30c8\u3092\u4f7f\u7528\u3057\u305f\u3079\u304d\u4e57\u8a08\u7b97:\\n\";\n    \n    \/\/ \u6574\u6570\u578b\n    std::cout &lt;&lt; \"\u6574\u6570\u3079\u304d\u4e57: 2^10 = \" &lt;&lt; power(2, 10) &lt;&lt; std::endl;\n    \n    \/\/ \u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\n    std::cout &lt;&lt; \"\u6d6e\u52d5\u5c0f\u6570\u70b9\u3079\u304d\u4e57: 2.5^3.5 = \" &lt;&lt; power(2.5, 3.5) &lt;&lt; std::endl;\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\n    std::cout &lt;&lt; \"\u8ca0\u306e\u6307\u6570: 2^(-3) = \" &lt;&lt; power(2, -3) &lt;&lt; std::endl;\n    \n    \/\/ \u6df7\u5408\u578b\n    std::cout &lt;&lt; \"\u6df7\u5408\u578b: 2^3.5 = \" &lt;&lt; power(2, 3.5) &lt;&lt; std::endl;\n    \n    return 0;\n}\n<\/pre>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"i-28\">\u307e\u3068\u3081\u3068\u5b9f\u8df5\u7684\u306a\u30b3\u30fc\u30c9\u30b5\u30f3\u30d7\u30eb<\/h2>\n\n\n\n<p>\u3053\u308c\u307e\u3067C++\u3067\u306e\u3079\u304d\u4e57\u8a08\u7b97\u306e\u69d8\u3005\u306a\u5b9f\u88c5\u65b9\u6cd5\u3001\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u6bd4\u8f03\u3001\u6ce8\u610f\u70b9\u3001\u5fdc\u7528\u4f8b\u3001\u305d\u3057\u3066\u5c06\u6765\u306e\u5c55\u671b\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u5b9f\u969b\u306e\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\u3067\u3059\u3050\u306b\u6d3b\u7528\u3067\u304d\u308b\u30ac\u30a4\u30c9\u30e9\u30a4\u30f3\u3068\u30b3\u30fc\u30c9\u30b9\u30cb\u30da\u30c3\u30c8\u3092\u307e\u3068\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-29\">\u30e6\u30fc\u30b9\u30b1\u30fc\u30b9\u5225\u306e\u9069\u5207\u306a\u4e57\u8a08\u7b97\u5b9f\u88c5\u306e\u9078\u629e<\/h3>\n\n\n\n<p>\u3079\u304d\u4e57\u8a08\u7b97\u306e\u5b9f\u88c5\u3092\u9078\u629e\u3059\u308b\u969b\u306f\u3001\u4ee5\u4e0b\u306e\u8981\u4ef6\u3092\u8003\u616e\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9<\/strong>: \u8a08\u7b97\u901f\u5ea6\u304c\u91cd\u8981\u306a\u5834\u5408<\/li>\n\n\n\n<li><strong>\u7cbe\u5ea6<\/strong>: \u8a08\u7b97\u7d50\u679c\u306e\u6b63\u78ba\u3055\u304c\u91cd\u8981\u306a\u5834\u5408<\/li>\n\n\n\n<li><strong>\u5b89\u5168\u6027<\/strong>: \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u5bfe\u7b56\u306a\u3069\u304c\u5fc5\u8981\u306a\u5834\u5408<\/li>\n\n\n\n<li><strong>\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u6700\u9069\u5316<\/strong>: \u56fa\u5b9a\u5024\u306e\u4e8b\u524d\u8a08\u7b97\u304c\u6709\u52b9\u306a\u5834\u5408<\/li>\n<\/ol>\n\n\n\n<p>\u4ee5\u4e0b\u306e\u8868\u306f\u3001\u4ee3\u8868\u7684\u306a\u30e6\u30fc\u30b9\u30b1\u30fc\u30b9\u3068\u63a8\u5968\u3055\u308c\u308b\u5b9f\u88c5\u65b9\u6cd5\u3092\u307e\u3068\u3081\u305f\u3082\u306e\u3067\u3059\uff1a<\/p>\n\n\n<div id=\"id-1e95b222-e082-4c20-b251-327c4f655410\">\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u30e6\u30fc\u30b9\u30b1\u30fc\u30b9<\/th><th>\u63a8\u5968\u5b9f\u88c5<\/th><th>\u7406\u7531<\/th><\/tr><\/thead><tbody><tr><td>\u4e00\u822c\u7684\u306a\u6d6e\u52d5\u5c0f\u6570\u70b9\u3079\u304d\u4e57<\/td><td>std::pow<\/td><td>\u6700\u9069\u5316\u6e08\u307f\u3001\u5e45\u5e83\u3044\u5165\u529b\u306b\u5bfe\u5fdc<\/td><\/tr><tr><td>\u6574\u6570\u306e\u5c0f\u3055\u3044\u3079\u304d\u4e57<\/td><td>\u76f4\u63a5\u5b9f\u88c5\uff08a<em>a<\/em>a\u2026\uff09<\/td><td>\u5358\u7d14\u3001\u9ad8\u901f\u3001\u30b3\u30f3\u30d1\u30a4\u30e9\u6700\u9069\u5316\u306b\u9069\u3059\u308b<\/td><\/tr><tr><td>\u6574\u6570\u306e\u5927\u304d\u3044\u3079\u304d\u4e57<\/td><td>\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5<\/td><td>O(log n)\u306e\u8a08\u7b97\u91cf\u3001\u52b9\u7387\u7684<\/td><\/tr><tr><td>\u6697\u53f7\u8a08\u7b97<\/td><td>\u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57<\/td><td>\u5927\u304d\u306a\u6570\u5024\u3067\u3082\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u306a\u3057<\/td><\/tr><tr><td>\u5b9a\u6570\u3079\u304d\u4e57<\/td><td>constexpr\u3001\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8<\/td><td>\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97\u3067\u5b9f\u884c\u6642\u30b3\u30b9\u30c8\u306a\u3057<\/td><\/tr><tr><td>\u9ad8\u7cbe\u5ea6\u8a08\u7b97<\/td><td>\u591a\u500d\u9577\u30e9\u30a4\u30d6\u30e9\u30ea<\/td><td>\u4efb\u610f\u7cbe\u5ea6\u306e\u8a08\u7b97\u304c\u53ef\u80fd<\/td><\/tr><tr><td>\u5b89\u5168\u91cd\u8996<\/td><td>\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u5b9f\u88c5<\/td><td>\u30a8\u30e9\u30fc\u691c\u51fa\u3068\u51e6\u7406\u304c\u53ef\u80fd<\/td><\/tr><tr><td>\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u91cd\u8996<\/td><td>\u30d3\u30c3\u30c8\u6f14\u7b97\u3001SIMD<\/td><td>\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u6700\u9069\u5316\u3001\u4e26\u5217\u8a08\u7b97<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<p><strong>\u5b9f\u88c5\u9078\u629e\u306e\u30d5\u30ed\u30fc\u30c1\u30e3\u30fc\u30c8\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\u958b\u59cb\n |\n \u251c\u2500\u2500 \u6307\u6570\u304c\u5b9a\u6570\u304b\uff1f --&gt; Yes --&gt; \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u8a08\u7b97\u53ef\u80fd\u304b\uff1f --&gt; Yes --&gt; constexpr\/\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\n |   |                                                 |\n |   |                                                 No\n |   |                                                  |\n |   No                                                 v\n |    |                                           \u7279\u6b8a\u30b1\u30fc\u30b9\u6700\u9069\u5316\n |    v\n \u251c\u2500\u2500 \u6574\u6570\u3079\u304d\u4e57\u304b\uff1f --&gt; Yes --&gt; \u6307\u6570\u304c\u5927\u304d\u3044\uff1f --&gt; Yes --&gt; \u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\n |   |                               |\n |   |                               No\n |   |                                |\n |   No                               v\n |    |                        \u5358\u7d14\u30eb\u30fc\u30d7\u307e\u305f\u306f\u76f4\u63a5\u8a08\u7b97\n |    v\n \u251c\u2500\u2500 \u7cbe\u5ea6\u304c\u91cd\u8981\u304b\uff1f --&gt; Yes --&gt; \u591a\u500d\u9577\u6d6e\u52d5\u5c0f\u6570\u70b9\u307e\u305f\u306f\u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\n |   |\n |   No\n |    |\n |    v\n \u251c\u2500\u2500 \u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u91cd\u8981\u304b\uff1f --&gt; Yes --&gt; \u5bfe\u8c61\u306f\uff1f --&gt; \u6574\u6570 --&gt; \u30d3\u30c3\u30c8\u6f14\u7b97\u5b9f\u88c5\n |   |                                      |\n |   |                                      \u6d6e\u52d5\u5c0f\u6570\u70b9\n |   |                                       |\n |   No                                      v\n |    |                                 \u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u6700\u9069\u5316\n |    v\n \u2514\u2500\u2500 std::pow\n<\/pre>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-30\">\u3059\u3050\u306b\u4f7f\u3048\u308b\u4e57\u8a08\u7b97\u306e\u30b3\u30fc\u30c9\u30b9\u30cb\u30da\u30c3\u30c8\u96c6<\/h3>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u69d8\u3005\u306a\u30e6\u30fc\u30b9\u30b1\u30fc\u30b9\u306b\u5bfe\u5fdc\u3057\u305f\u3079\u304d\u4e57\u8a08\u7b97\u306e\u5b9f\u88c5\u4f8b\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30b3\u30fc\u30c9\u30b9\u30cb\u30da\u30c3\u30c8\u306f\u305d\u306e\u307e\u307e\u4f7f\u7528\u3059\u308b\u304b\u3001\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\u306e\u8981\u4ef6\u306b\u5408\u308f\u305b\u3066\u30ab\u30b9\u30bf\u30de\u30a4\u30ba\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p><strong>1. \u9ad8\u6027\u80fd\u6574\u6570\u3079\u304d\u4e57\u95a2\u6570\uff08\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u4ed8\u304d\uff09\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;stdexcept&gt;\n#include &lt;limits&gt;\n#include &lt;type_traits&gt;\n\n\/\/ \u6574\u6570\u578b\u306e\u307f\u3092\u30b5\u30dd\u30fc\u30c8\u3059\u308b\u9ad8\u6027\u80fd\u3079\u304d\u4e57\u95a2\u6570\uff08\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u4ed8\u304d\uff09\ntemplate &lt;typename T&gt;\ntypename std::enable_if&lt;std::is_integral&lt;T&gt;::value, T&gt;::type\nsafe_int_pow(T base, unsigned int exponent) {\n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u65e9\u671f\u51e6\u7406\n    if (exponent == 0) return 1;\n    if (exponent == 1) return base;\n    if (base == 0) return 0;\n    if (base == 1) return 1;\n    \n    \/\/ \u8ca0\u306e\u57fa\u6570\u3068\u5947\u6570\u6307\u6570\u306e\u5834\u5408\u306e\u7b26\u53f7\u51e6\u7406\n    bool negative_result = (base &lt; 0) &amp;&amp; (exponent % 2 == 1);\n    T abs_base = std::abs(base);\n    \n    \/\/ \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\u306e\u305f\u3081\u306e\u95be\u5024\n    const T max_value = std::numeric_limits&lt;T&gt;::max();\n    \n    T result = 1;\n    T current = abs_base;\n    \n    while (exponent &gt; 0) {\n        if (exponent &amp; 1) {\n            \/\/ \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\n            if (result &gt; max_value \/ current) {\n                throw std::overflow_error(\"\u6574\u6570\u3079\u304d\u4e57\u8a08\u7b97\u3067\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u304c\u767a\u751f\u3057\u307e\u3057\u305f\");\n            }\n            result *= current;\n        }\n        \n        exponent &gt;&gt;= 1;\n        \n        if (exponent &gt; 0) {\n            \/\/ \u6b21\u306ecurrent*current\u8a08\u7b97\u3067\u306e\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u691c\u51fa\n            if (current &gt; max_value \/ current) {\n                throw std::overflow_error(\"\u6574\u6570\u3079\u304d\u4e57\u8a08\u7b97\u3067\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u304c\u767a\u751f\u3057\u307e\u3057\u305f\");\n            }\n            current *= current;\n        }\n    }\n    \n    return negative_result ? -result : result;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid safe_int_pow_example() {\n    try {\n        std::cout &lt;&lt; \"\u5b89\u5168\u306a\u6574\u6570\u3079\u304d\u4e57\u95a2\u6570\u306e\u4f8b:\\n\";\n        \n        \/\/ \u57fa\u672c\u7684\u306a\u4f7f\u7528\u4f8b\n        std::cout &lt;&lt; \"3^4 = \" &lt;&lt; safe_int_pow(3, 4) &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"2^10 = \" &lt;&lt; safe_int_pow(2, 10) &lt;&lt; std::endl;\n        \n        \/\/ \u8ca0\u306e\u57fa\u6570\n        std::cout &lt;&lt; \"(-2)^3 = \" &lt;&lt; safe_int_pow(-2, 3) &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"(-2)^4 = \" &lt;&lt; safe_int_pow(-2, 4) &lt;&lt; std::endl;\n        \n        \/\/ \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u306e\u30c6\u30b9\u30c8\n        std::cout &lt;&lt; \"2^30 = \" &lt;&lt; safe_int_pow(2, 30) &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"2^31 = \" &lt;&lt; safe_int_pow(2, 31) &lt;&lt; std::endl; \/\/ int\u578b\u3067\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\n        \n    } catch (const std::overflow_error&amp; e) {\n        std::cerr &lt;&lt; \"\u30a8\u30e9\u30fc: \" &lt;&lt; e.what() &lt;&lt; std::endl;\n        std::cout &lt;&lt; \"\u3088\u308a\u5927\u304d\u306a\u578b\u3067\u306e\u8a08\u7b97: 2^31 = \" \n                  &lt;&lt; safe_int_pow&lt;int64_t&gt;(2, 31) &lt;&lt; std::endl;\n    }\n}\n<\/pre>\n\n\n\n<p><strong>2. \u6c4e\u7528\u7684\u3067\u9ad8\u6027\u80fd\u306a\u3079\u304d\u4e57\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\uff08C++20\uff09\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;concepts&gt;\n#include &lt;type_traits&gt;\n#include &lt;cmath&gt;\n#include &lt;stdexcept&gt;\n\n\/\/ C++20\u306e\u30b3\u30f3\u30bb\u30d7\u30c8\u3092\u4f7f\u7528\u3057\u305f\u3079\u304d\u4e57\u8a08\u7b97\ntemplate &lt;typename T, typename E&gt;\nrequires std::integral&lt;T&gt; || std::floating_point&lt;T&gt;\nconstexpr auto power(T base, E exponent) {\n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u65e9\u671f\u51e6\u7406\n    if (exponent == 0) return static_cast&lt;T&gt;(1);\n    if (exponent == 1) return base;\n    if (base == 0) return static_cast&lt;T&gt;(0);\n    if (base == 1) return static_cast&lt;T&gt;(1);\n    \n    \/\/ \u6574\u6570\u578b\u3068\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u3067\u7570\u306a\u308b\u51e6\u7406\n    if constexpr (std::integral&lt;T&gt; &amp;&amp; std::integral&lt;E&gt;) {\n        \/\/ \u8ca0\u306e\u6307\u6570\u306e\u5834\u5408\n        if (exponent &lt; 0) {\n            if constexpr (std::is_same_v&lt;T, int&gt; || std::is_same_v&lt;T, long&gt; || std::is_same_v&lt;T, long long&gt;) {\n                \/\/ \u6574\u6570\u578b\u3067\u306e\u8ca0\u306e\u6307\u6570\u306f\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u306b\u5909\u63db\u3057\u3066\u8a08\u7b97\n                return power(static_cast&lt;double&gt;(base), exponent);\n            } else {\n                throw std::domain_error(\"\u6574\u6570\u578b\u3067\u306e\u8ca0\u306e\u6307\u6570\u306f undefined behavior \u3067\u3059\");\n            }\n        }\n        \n        \/\/ 2\u306e\u7d2f\u4e57\u306e\u7279\u6b8a\u30b1\u30fc\u30b9\uff08\u30d3\u30c3\u30c8\u30b7\u30d5\u30c8\u3092\u4f7f\u7528\uff09\n        if (base == 2 &amp;&amp; exponent &lt; 8 * sizeof(T)) {\n            return static_cast&lt;T&gt;(1) &lt;&lt; static_cast&lt;T&gt;(exponent);\n        }\n        \n        \/\/ \u901a\u5e38\u306e\u4e8c\u5206\u7d2f\u7a4d\u4e57\u6cd5\n        T result = 1;\n        T current = base;\n        E exp = exponent;\n        \n        while (exp &gt; 0) {\n            if (exp &amp; 1) {\n                result *= current;\n            }\n            current *= current;\n            exp &gt;&gt;= 1;\n        }\n        \n        return result;\n    } else {\n        \/\/ \u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u307e\u305f\u306f\u6df7\u5408\u578b\u306e\u5834\u5408\u306fstd::pow\u3092\u4f7f\u7528\n        return std::pow(static_cast&lt;double&gt;(base), static_cast&lt;double&gt;(exponent));\n    }\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid power_template_example() {\n    std::cout &lt;&lt; \"\u6c4e\u7528\u7684\u306a\u3079\u304d\u4e57\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u306e\u4f8b:\\n\";\n    \n    \/\/ \u6574\u6570\u3079\u304d\u4e57\n    std::cout &lt;&lt; \"\u6574\u6570\u3079\u304d\u4e57 (3^4): \" &lt;&lt; power(3, 4) &lt;&lt; std::endl;\n    \n    \/\/ \u6d6e\u52d5\u5c0f\u6570\u70b9\u3079\u304d\u4e57\n    std::cout &lt;&lt; \"\u6d6e\u52d5\u5c0f\u6570\u70b9\u3079\u304d\u4e57 (2.5^3.5): \" &lt;&lt; power(2.5, 3.5) &lt;&lt; std::endl;\n    \n    \/\/ \u8ca0\u306e\u6307\u6570\n    std::cout &lt;&lt; \"\u8ca0\u306e\u6307\u6570 (2^(-3)): \" &lt;&lt; power(2, -3) &lt;&lt; std::endl;\n    \n    \/\/ \u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97\n    constexpr auto compile_time_result = power(3, 4);\n    std::cout &lt;&lt; \"\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u8a08\u7b97 (3^4): \" &lt;&lt; compile_time_result &lt;&lt; std::endl;\n    \n    \/\/ 2\u306e\u3079\u304d\u4e57\u306e\u6700\u9069\u5316\n    std::cout &lt;&lt; \"2\u306e\u3079\u304d\u4e57 (2^20): \" &lt;&lt; power(2, 20) &lt;&lt; std::endl;\n    \n    \/\/ \u7570\u306a\u308b\u578b\u306e\u6df7\u5408\n    std::cout &lt;&lt; \"\u6df7\u5408\u578b (int\u57fa\u6570, double\u6307\u6570) (2^3.5): \" &lt;&lt; power(2, 3.5) &lt;&lt; std::endl;\n}\n<\/pre>\n\n\n\n<p><strong>3. \u9ad8\u7cbe\u5ea6\u6d6e\u52d5\u5c0f\u6570\u70b9\u3079\u304d\u4e57\u8a08\u7b97\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cmath&gt;\n#include &lt;vector&gt;\n#include &lt;iomanip&gt;\n\n\/\/ \u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u3092\u4f7f\u7528\u3057\u305f\u9ad8\u7cbe\u5ea6\u6307\u6570\u95a2\u6570\u306e\u8a08\u7b97\uff08e^x\uff09\ndouble precise_exp(double x, int terms = 30) {\n    if (std::abs(x) &gt; 709) {\n        \/\/ double\u306e\u7bc4\u56f2\u5916\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u5834\u5408\u306b\u7bc4\u56f2\u3092\u5236\u9650\n        return x &gt; 0 ? HUGE_VAL : 0.0;\n    }\n    \n    \/\/ \u5927\u304d\u306a\u5024\u3092\u6271\u3046\u305f\u3081\u306b\u3001e^x = (e^(x\/n))^n \u306e\u95a2\u4fc2\u3092\u4f7f\u7528\n    int n = 1;\n    if (std::abs(x) &gt; 20) {\n        n = static_cast&lt;int&gt;(std::abs(x) \/ 20) + 1;\n        x \/= n;\n    }\n    \n    double sum = 1.0;  \/\/ \u6700\u521d\u306e\u9805\n    double term = 1.0; \/\/ \u5404\u9805\u306e\u5024\n    double factorial = 1.0;\n    \n    for (int i = 1; i &lt; terms; ++i) {\n        term *= x \/ i;\n        sum += term;\n        \n        \/\/ \u53ce\u675f\u30c1\u30a7\u30c3\u30af\n        if (std::abs(term) &lt; 1e-15 * sum) {\n            break;\n        }\n    }\n    \n    \/\/ n\u4e57\u3092\u8a08\u7b97\n    double result = sum;\n    for (int i = 1; i &lt; n; ++i) {\n        result *= sum;\n    }\n    \n    return result;\n}\n\n\/\/ \u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u3092\u4f7f\u7528\u3057\u305f\u9ad8\u7cbe\u5ea6\u3079\u304d\u4e57\u8a08\u7b97\ndouble precise_pow(double base, double exponent, int terms = 30) {\n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u51e6\u7406\n    if (exponent == 0.0) return 1.0;\n    if (base == 0.0) return 0.0;\n    if (base == 1.0) return 1.0;\n    if (exponent == 1.0) return base;\n    if (exponent == 2.0) return base * base;\n    if (exponent == 0.5) return std::sqrt(base);\n    \n    \/\/ \u8ca0\u306e\u57fa\u6570\u306f\u8907\u7d20\u6570\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u5236\u9650\n    if (base &lt; 0.0 &amp;&amp; std::floor(exponent) != exponent) {\n        throw std::domain_error(\"\u8ca0\u306e\u57fa\u6570\u3068\u975e\u6574\u6570\u6307\u6570\u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u8907\u7d20\u6570\u306b\u306a\u308a\u307e\u3059\");\n    }\n    \n    \/\/ \u6574\u6570\u6307\u6570\u306e\u5834\u5408\u306f\u6700\u9069\u5316\n    if (std::floor(exponent) == exponent &amp;&amp; std::abs(exponent) &lt; 100) {\n        bool negative_exponent = exponent &lt; 0;\n        int int_exponent = std::abs(static_cast&lt;int&gt;(exponent));\n        \n        double result = 1.0;\n        double current = base;\n        \n        while (int_exponent &gt; 0) {\n            if (int_exponent &amp; 1) {\n                result *= current;\n            }\n            current *= current;\n            int_exponent &gt;&gt;= 1;\n        }\n        \n        return negative_exponent ? 1.0 \/ result : result;\n    }\n    \n    \/\/ \u4e00\u822c\u7684\u306a\u30b1\u30fc\u30b9: a^b = e^(b*ln(a))\n    bool negative_base = base &lt; 0;\n    double abs_base = std::abs(base);\n    \n    \/\/ \u81ea\u7136\u5bfe\u6570\u306e\u8a08\u7b97\uff08\u6a19\u6e96\u95a2\u6570\u3092\u4f7f\u7528\uff09\n    double ln_base = std::log(abs_base);\n    double power = exponent * ln_base;\n    \n    \/\/ \u6307\u6570\u95a2\u6570\u3092\u4f7f\u3063\u3066\u6700\u7d42\u7d50\u679c\u3092\u8a08\u7b97\n    double abs_result = precise_exp(power, terms);\n    \n    \/\/ \u8ca0\u306e\u57fa\u6570\u3068\u5947\u6570\u6307\u6570\u306e\u5834\u5408\u306e\u7b26\u53f7\u51e6\u7406\n    if (negative_base &amp;&amp; std::fmod(exponent, 2.0) != 0.0 &amp;&amp; std::floor(exponent) == exponent) {\n        return -abs_result;\n    }\n    \n    return abs_result;\n}\n\n\/\/ \u4f7f\u7528\u4f8b\nvoid precise_pow_example() {\n    std::cout &lt;&lt; std::setprecision(15);\n    std::cout &lt;&lt; \"\u9ad8\u7cbe\u5ea6\u3079\u304d\u4e57\u8a08\u7b97\u306e\u4f8b:\\n\";\n    \n    \/\/ \u57fa\u672c\u7684\u306a\u4f7f\u7528\u4f8b\n    std::cout &lt;&lt; \"2^10 = \" &lt;&lt; precise_pow(2.0, 10.0) &lt;&lt; \" (std::pow: \" &lt;&lt; std::pow(2.0, 10.0) &lt;&lt; \")\" &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"1.5^8.5 = \" &lt;&lt; precise_pow(1.5, 8.5) &lt;&lt; \" (std::pow: \" &lt;&lt; std::pow(1.5, 8.5) &lt;&lt; \")\" &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"e^\u03c0 = \" &lt;&lt; precise_pow(std::exp(1.0), M_PI) &lt;&lt; \" (std::pow: \" &lt;&lt; std::pow(std::exp(1.0), M_PI) &lt;&lt; \")\" &lt;&lt; std::endl;\n    \n    \/\/ \u7cbe\u5ea6\u6bd4\u8f03\n    std::vector&lt;std::pair&lt;double, double&gt;&gt; test_cases = {\n        {0.1, 100}, \/\/ \u5c0f\u3055\u306a\u57fa\u6570\u3001\u5927\u304d\u306a\u6307\u6570\n        {0.99, 1000}, \/\/ 1\u306b\u8fd1\u3044\u57fa\u6570\u3001\u5927\u304d\u306a\u6307\u6570\n        {1234.5678, 0.12345} \/\/ \u5927\u304d\u306a\u57fa\u6570\u3001\u5c0f\u3055\u306a\u6307\u6570\n    };\n    \n    std::cout &lt;&lt; \"\\n\u7cbe\u5ea6\u6bd4\u8f03:\\n\";\n    std::cout &lt;&lt; \"\u57fa\u6570, \u6307\u6570, precise_pow, std::pow, \u5dee\\n\";\n    \n    for (const auto&amp; [base, exp] : test_cases) {\n        double p1 = precise_pow(base, exp);\n        double p2 = std::pow(base, exp);\n        double diff = std::abs(p1 - p2);\n        \n        std::cout &lt;&lt; base &lt;&lt; \", \" &lt;&lt; exp &lt;&lt; \", \" &lt;&lt; p1 &lt;&lt; \", \" &lt;&lt; p2 &lt;&lt; \", \" &lt;&lt; diff &lt;&lt; std::endl;\n    }\n}\n<\/pre>\n\n\n\n<p><strong>4. \u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57\u8a08\u7b97\uff08\u6697\u53f7\u8a08\u7b97\u5411\u3051\uff09\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">#include &lt;iostream&gt;\n#include &lt;cstdint&gt;\n#include &lt;vector&gt;\n#include &lt;chrono&gt;\n\n\/\/ \u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57\u8a08\u7b97: (base^exponent) mod modulus\nuint64_t modular_pow(uint64_t base, uint64_t exponent, uint64_t modulus) {\n    \/\/ \u7279\u6b8a\u30b1\u30fc\u30b9\u306e\u51e6\u7406\n    if (modulus == 1) return 0;\n    if (exponent == 0) return 1;\n    \n    \/\/ \u30d9\u30fc\u30b9\u3092\u30e2\u30b8\u30e5\u30e9\u30b9\u3067\u5272\u3063\u305f\u4f59\u308a\u306b\u6e1b\u3089\u3059\n    base %= modulus;\n    \n    uint64_t result = 1;\n    \n    while (exponent &gt; 0) {\n        \/\/ \u73fe\u5728\u306e\u6841\u304c1\u306a\u3089\u3001\u30d9\u30fc\u30b9\u3092\u304b\u3051\u308b\n        if (exponent &amp; 1) {\n            result = (result * base) % modulus;\n        }\n        \n        \/\/ \u6b21\u306e\u6841\u3078\n        exponent &gt;&gt;= 1;\n        \n        \/\/ \u30d9\u30fc\u30b9\u3092\u4e8c\u4e57\n        base = (base * base) % modulus;\n    }\n    \n    return result;\n}\n\n\/\/ Montgomery Reduction \u3092\u4f7f\u7528\u3057\u305f\u9ad8\u901f\u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57\u8a08\u7b97\n\/\/ \u6ce8: \u3053\u308c\u306f\u7279\u5b9a\u306e\u6761\u4ef6\u4e0b\u3067\u306e\u307f\u52d5\u4f5c\u3057\u3001\u3088\u308a\u8907\u96d1\u306a\u5b9f\u88c5\u304c\u5fc5\u8981\nuint64_t montgomery_modular_pow(uint64_t base, uint64_t exponent, uint64_t modulus) {\n    \/\/ \u7c21\u7565\u5316\u306e\u305f\u3081\u3001\u6a19\u6e96\u5b9f\u88c5\u3092\u4f7f\u7528\n    return modular_pow(base, exponent, modulus);\n    \n    \/\/ \u5b9f\u969b\u306e Montgomery \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff08\u7c21\u7565\u5316\uff09:\n    \/\/ 1. Montgomery \u30c9\u30e1\u30a4\u30f3\u306b\u5909\u63db\n    \/\/ 2. Montgomery \u4e57\u7b97\u3092\u4f7f\u3063\u3066\u3079\u304d\u4e57\u8a08\u7b97\n    \/\/ 3. \u7d50\u679c\u3092\u901a\u5e38\u30c9\u30e1\u30a4\u30f3\u306b\u623b\u3059\n}\n\n\/\/ RSA\u6697\u53f7\u306e\u7c21\u6613\u5b9f\u88c5\nvoid rsa_example() {\n    \/\/ RSA\u9375\u30da\u30a2\u306e\u751f\u6210\uff08\u5b9f\u969b\u306b\u306f\u5927\u304d\u306a\u7d20\u6570\u3092\u4f7f\u7528\uff09\n    uint64_t p = 61;\n    uint64_t q = 53;\n    uint64_t n = p * q;          \/\/ \u30e2\u30b8\u30e5\u30e9\u30b9\n    uint64_t phi = (p-1) * (q-1);\/\/ \u30aa\u30a4\u30e9\u30fc\u306e\u30c8\u30fc\u30b7\u30a7\u30f3\u30c8\u95a2\u6570\n    uint64_t e = 17;             \/\/ \u516c\u958b\u6307\u6570\uff081 &lt; e &lt; phi \u304b\u3064 gcd(e, phi) = 1\uff09\n    \n    \/\/ \u79d8\u5bc6\u6307\u6570d\u306e\u8a08\u7b97: (d * e) % phi = 1\n    uint64_t d = 0;\n    for (uint64_t i = 1; i &lt; phi; ++i) {\n        if ((i * e) % phi == 1) {\n            d = i;\n            break;\n        }\n    }\n    \n    uint64_t message = 42;  \/\/ \u6697\u53f7\u5316\u3059\u308b\u30e1\u30c3\u30bb\u30fc\u30b8\uff08n\u672a\u6e80\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308b\uff09\n    \n    std::cout &lt;&lt; \"RSA\u6697\u53f7\u306e\u4f8b:\\n\";\n    std::cout &lt;&lt; \"\u516c\u958b\u9375 (e, n): (\" &lt;&lt; e &lt;&lt; \", \" &lt;&lt; n &lt;&lt; \")\" &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u79d8\u5bc6\u9375 (d, n): (\" &lt;&lt; d &lt;&lt; \", \" &lt;&lt; n &lt;&lt; \")\" &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"\u5143\u306e\u30e1\u30c3\u30bb\u30fc\u30b8: \" &lt;&lt; message &lt;&lt; std::endl;\n    \n    \/\/ \u6697\u53f7\u5316: C = M^e mod n\n    uint64_t encrypted = modular_pow(message, e, n);\n    std::cout &lt;&lt; \"\u6697\u53f7\u6587: \" &lt;&lt; encrypted &lt;&lt; std::endl;\n    \n    \/\/ \u5fa9\u53f7\u5316: M = C^d mod n\n    uint64_t decrypted = modular_pow(encrypted, d, n);\n    std::cout &lt;&lt; \"\u5fa9\u53f7\u3055\u308c\u305f\u30e1\u30c3\u30bb\u30fc\u30b8: \" &lt;&lt; decrypted &lt;&lt; std::endl;\n    \n    \/\/ \u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u6bd4\u8f03\n    auto start = std::chrono::high_resolution_clock::now();\n    for (int i = 0; i &lt; 10000; ++i) {\n        modular_pow(message, e, n);\n    }\n    auto end = std::chrono::high_resolution_clock::now();\n    std::chrono::duration&lt;double, std::milli&gt; standard_time = end - start;\n    \n    start = std::chrono::high_resolution_clock::now();\n    for (int i = 0; i &lt; 10000; ++i) {\n        montgomery_modular_pow(message, e, n);\n    }\n    end = std::chrono::high_resolution_clock::now();\n    std::chrono::duration&lt;double, std::milli&gt; montgomery_time = end - start;\n    \n    std::cout &lt;&lt; \"\\n\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u6bd4\u8f03 (10,000\u56de\u306e\u6697\u53f7\u5316):\\n\";\n    std::cout &lt;&lt; \"\u6a19\u6e96\u30e2\u30b8\u30e5\u30e9\u30fc\u3079\u304d\u4e57: \" &lt;&lt; standard_time.count() &lt;&lt; \" ms\" &lt;&lt; std::endl;\n    std::cout &lt;&lt; \"Montgomery\u6cd5: \" &lt;&lt; montgomery_time.count() &lt;&lt; \" ms\" &lt;&lt; std::endl;\n}\n<\/pre>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-31\">\u307e\u3068\u3081<\/h3>\n\n\n\n<p>C++\u3067\u306e\u3079\u304d\u4e57\u8a08\u7b97\u306b\u3064\u3044\u3066\u306e\u30dd\u30a4\u30f3\u30c8\u3092\u307e\u3068\u3081\u307e\u3059\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u591a\u69d8\u306a\u5b9f\u88c5\u30aa\u30d7\u30b7\u30e7\u30f3<\/strong>: C++\u3067\u306f\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e<code>std::pow<\/code>\u304b\u3089\u7279\u6b8a\u306a\u7528\u9014\u306e\u30ab\u30b9\u30bf\u30e0\u5b9f\u88c5\u307e\u3067\u3001\u69d8\u3005\u306a\u3079\u304d\u4e57\u8a08\u7b97\u65b9\u6cd5\u304c\u5229\u7528\u53ef\u80fd\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3068\u7cbe\u5ea6\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5<\/strong>: \u5b9f\u88c5\u65b9\u6cd5\u306b\u3088\u3063\u3066\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3068\u7cbe\u5ea6\u306e\u30d0\u30e9\u30f3\u30b9\u304c\u7570\u306a\u308a\u307e\u3059\u3002\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306e\u8981\u4ef6\u306b\u5fdc\u3058\u3066\u6700\u9069\u306a\u5b9f\u88c5\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5b89\u5168\u6027\u3078\u306e\u914d\u616e<\/strong>: \u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u3084\u7cbe\u5ea6\u306e\u554f\u984c\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\u306e\u30c6\u30af\u30cb\u30c3\u30af\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u5b89\u5168\u3067\u4fe1\u983c\u6027\u306e\u9ad8\u3044\u3079\u304d\u4e57\u8a08\u7b97\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u6700\u9069\u5316\u306e\u91cd\u8981\u6027<\/strong>: \u3079\u304d\u4e57\u8a08\u7b97\u306f\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u30af\u30ea\u30c6\u30a3\u30ab\u30eb\u306a\u30b3\u30fc\u30c9\u3067\u306f\u983b\u7e41\u306b\u4f7f\u7528\u3055\u308c\u308b\u305f\u3081\u3001\u9069\u5207\u306a\u6700\u9069\u5316\u304c\u5168\u4f53\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u306b\u5927\u304d\u304f\u5f71\u97ff\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>C++20\u306e\u6069\u6075<\/strong>: \u65b0\u3057\u3044\u8a00\u8a9e\u6a5f\u80fd\u3068\u30e9\u30a4\u30d6\u30e9\u30ea\u62e1\u5f35\u306b\u3088\u308a\u3001\u3088\u308a\u52b9\u7387\u7684\u3067\u578b\u5b89\u5168\u306a\u3079\u304d\u4e57\u8a08\u7b97\u304c\u53ef\u80fd\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>\u30c9\u30e1\u30a4\u30f3\u56fa\u6709\u306e\u6700\u9069\u5316<\/strong>: \u6697\u53f7\u8a08\u7b97\u3001\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u51e6\u7406\u3001\u79d1\u5b66\u8a08\u7b97\u306a\u3069\u3001\u7279\u5b9a\u306e\u30c9\u30e1\u30a4\u30f3\u3067\u306f\u5c02\u7528\u306e\u3079\u304d\u4e57\u8a08\u7b97\u5b9f\u88c5\u304c\u6709\u52b9\u3067\u3059\u3002<\/li>\n<\/ol>\n\n\n\n<p>C++\u3067\u3079\u304d\u4e57\u8a08\u7b97\u3092\u5b9f\u88c5\u3059\u308b\u969b\u306f\u3001\u307e\u305a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306e\u8981\u4ef6\uff08\u7cbe\u5ea6\u3001\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3001\u5b89\u5168\u6027\uff09\u3092\u660e\u78ba\u306b\u3057\u3001\u305d\u308c\u306b\u57fa\u3065\u3044\u3066\u9069\u5207\u306a\u65b9\u6cd5\u3092\u9078\u629e\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e<code>std::pow<\/code>\u306f\u591a\u304f\u306e\u5834\u5408\u5341\u5206\u3067\u3059\u304c\u3001\u7279\u5b9a\u306e\u8981\u4ef6\u304c\u3042\u308b\u5834\u5408\u306f\u3053\u306e\u8a18\u4e8b\u3067\u7d39\u4ecb\u3057\u305f\u30ab\u30b9\u30bf\u30e0\u5b9f\u88c5\u3092\u691c\u8a0e\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u52b9\u7387\u7684\u306a\u3079\u304d\u4e57\u8a08\u7b97\u306f\u3001\u6570\u5024\u8a08\u7b97\u3001\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3001\u30b2\u30fc\u30e0\u958b\u767a\u3001\u6697\u53f7\u6280\u8853\u306a\u3069\u3001\u591a\u304f\u306e\u5206\u91ce\u3067C++\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u57fa\u790e\u3068\u306a\u308b\u91cd\u8981\u306a\u30b9\u30ad\u30eb\u3067\u3059\u3002\u672c\u8a18\u4e8b\u306e\u60c5\u5831\u3068\u30b3\u30fc\u30c9\u30b9\u30cb\u30da\u30c3\u30c8\u3092\u6d3b\u7528\u3057\u3066\u3001\u6700\u9069\u306a\u3079\u304d\u4e57\u8a08\u7b97\u3092\u5b9f\u88c5\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>C++\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306b\u304a\u3044\u3066\u3001\u3079\u304d\u4e57\uff08\u7d2f\u4e57\uff09\u8a08\u7b97\u306f\u79d1\u5b66\u8a08\u7b97\u3001\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u51e6\u7406\u3001\u6697\u53f7\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3001\u91d1\u878d\u30e2\u30c7\u30ea\u30f3\u30b0\u306a\u3069\u591a\u304f\u306e\u5206\u91ce\u3067\u983b\u7e41\u306b\u4f7f\u7528\u3055\u308c\u308b\u57fa\u672c\u7684\u306a\u6570\u5b66\u6f14\u7b97\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u5358\u7d14\u306b\u898b\u3048\u308b\u3053\u306e\u64cd\u4f5c\u3082\u3001\u5b9f\u88c5\u65b9\u6cd5\u306b\u3088\u3063\u3066\u30d1\u30d5\u30a9 &#8230; 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