{"id":299535,"date":"2024-05-20T17:19:47","date_gmt":"2024-05-20T09:19:47","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/299535.html"},"modified":"2024-05-20T17:20:11","modified_gmt":"2024-05-20T09:20:11","slug":"%e5%a6%82%e4%bd%95%e9%80%9a%e8%bf%87%e8%ae%a1%e7%ae%97%e6%9c%ba%e7%a8%8b%e5%ba%8f%e6%9d%a5%e8%a1%a8%e7%a4%ba%e6%97%a0%e7%90%86%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/299535.html","title":{"rendered":"\u5982\u4f55\u901a\u8fc7\u8ba1\u7b97\u673a\u7a0b\u5e8f\u6765\u8868\u793a\u65e0\u7406\u6570"},"content":{"rendered":"<p style=\"text-align:center\"><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/27151715\/f1baa574-81ce-428a-8c64-bab6dd2ba880.webp\" alt=\"\u5982\u4f55\u901a\u8fc7\u8ba1\u7b97\u673a\u7a0b\u5e8f\u6765\u8868\u793a\u65e0\u7406\u6570\" \/><\/p>\n<p><p>\u901a\u8fc7\u8ba1\u7b97\u673a\u7a0b\u5e8f\u6765\u8868\u793a\u65e0\u7406\u6570\uff0c\u6838\u5fc3\u6280\u5de7\u5728\u4e8e\u91c7\u7528<strong>\u6570\u503c\u8fd1\u4f3c\u3001\u6570\u503c\u7c7b\u578b\u6269\u5c55\u3001\u7b26\u53f7\u8ba1\u7b97<\/strong>\u548c<strong>\u533a\u95f4\u4f30\u8ba1<\/strong>\u3002\u8fd9\u4e9b\u65b9\u6cd5\u4f7f\u5f97\u65e0\u7406\u6570\u5728\u8ba1\u7b97\u673a\u7a0b\u5e8f\u4e2d\u5f97\u4ee5\u6709\u6548\u8868\u8fbe\u548c\u5904\u7406\uff0c\u5c3d\u7ba1\u8ba1\u7b97\u673a\u65e0\u6cd5\u7cbe\u786e\u8868\u793a\u65e0\u7406\u6570\u3002\u5176\u4e2d\uff0c<strong>\u6570\u503c\u8fd1\u4f3c<\/strong>\u662f\u6700\u5e38\u7528\u7684\u65b9\u6cd5\uff0c\u5b83\u901a\u8fc7\u6709\u9650\u7684\u5c0f\u6570\u6765\u903c\u8fd1\u65e0\u7406\u6570\uff0c\u4f7f\u5f97\u5728\u5927\u591a\u6570\u5e94\u7528\u573a\u666f\u4e2d\u80fd\u591f\u6ee1\u8db3\u7cbe\u5ea6\u8981\u6c42\u3002<\/p>\n<\/p>\n<p><h3>\u4e00\u3001\u6570\u503c\u8fd1\u4f3c<\/h3>\n<\/p>\n<p><p>\u6570\u503c\u8fd1\u4f3c\u662f\u5904\u7406\u65e0\u7406\u6570\u7684\u6700\u76f4\u63a5\u4e5f\u662f\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u3002\u901a\u5e38\uff0c\u6211\u4eec\u4f1a\u4f7f\u7528\u6d6e\u70b9\u6570\u6765\u8fd1\u4f3c\u65e0\u7406\u6570\uff0c\u4f8b\u5982\uff0c\u03c0\u53ef\u4ee5\u88ab\u8fd1\u4f3c\u4e3a3.14159\uff0c\u221a2\u53ef\u4ee5\u88ab\u8fd1\u4f3c\u4e3a1.41421\u3002\u5728\u7f16\u7a0b\u5b9e\u8df5\u4e2d\uff0c\u6211\u4eec\u901a\u5e38\u91c7\u7528\u53cc\u7cbe\u5ea6\uff08double\uff09\u6216\u9ad8\u7cbe\u5ea6\uff08BigDecimal in Java, decimal in C#\uff09\u6d6e\u70b9\u6570\u6765\u8868\u793a\u8fd9\u4e9b\u8fd1\u4f3c\u503c\uff0c\u4ee5\u4fbf\u4e8e\u63d0\u9ad8\u8868\u793a\u7684\u7cbe\u786e\u5ea6\u3002<\/p>\n<\/p>\n<p><p>\u5bf9\u4e8e\u5927\u591a\u6570\u5e94\u7528\u573a\u666f\uff0c\u8fd9\u79cd\u8fd1\u4f3c\u662f\u8db3\u591f\u7684\u3002\u4f46\u5f53\u7cbe\u5ea6\u8981\u6c42\u975e\u5e38\u9ad8\u65f6\uff0c\u5c31\u9700\u8981\u4f7f\u7528\u66f4\u591a\u4f4d\u6570\u6765\u8868\u793a\u8fd9\u4e9b\u6570\u503c\u4e86\u3002\u4f8b\u5982\uff0c\u5728\u79d1\u5b66\u8ba1\u7b97\u548c\u52a0\u5bc6\u9886\u57df\uff0c\u53ef\u80fd\u9700\u8981\u6570\u767e\u3001\u751a\u81f3\u6570\u5343\u4f4d\u7684\u7cbe\u5ea6\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u4f7f\u7528\u7279\u5b9a\u5e93\uff0c\u5982Python\u7684<code>decimal<\/code>\u6216C++\u7684<code>boost::multiprecision<\/code>\u6765\u5b9e\u73b0\u9ad8\u7cbe\u5ea6\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<p><h3>\u4e8c\u3001\u6570\u503c\u7c7b\u578b\u6269\u5c55<\/h3>\n<\/p>\n<p><p>\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u901a\u8fc7\u6570\u503c\u7c7b\u578b\u7684\u6269\u5c55\uff0c\u4f7f\u5f97\u8ba1\u7b97\u673a\u80fd\u591f\u5904\u7406\u66f4\u5e7f\u6cdb\u7684\u6570\u503c\u8303\u56f4\u548c\u66f4\u9ad8\u7684\u7cbe\u5ea6\u3002\u4f8b\u5982\uff0c\u4f7f\u7528\u591a\u7cbe\u5ea6\u6d6e\u70b9\u6570\u6216\u4efb\u610f\u7cbe\u5ea6\u7b97\u672f\u5e93\uff0c\u53ef\u4ee5\u5728\u8ba1\u7b97\u673a\u4e0a\u8868\u793a\u548c\u64cd\u4f5c\u975e\u5e38\u5927\u6216\u975e\u5e38\u5c0f\u7684\u6570\u503c\uff0c\u4ee5\u53ca\u63d0\u4f9b\u6bd4\u6807\u51c6\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\u66f4\u9ad8\u7684\u7cbe\u5ea6\u3002<\/p>\n<\/p>\n<p><p>\u8fd9\u79cd\u65b9\u6cd5\u5e38\u89c1\u4e8e\u9700\u8981\u9ad8\u7cbe\u5ea6\u8ba1\u7b97\u7684\u9886\u57df\uff0c\u5982\u5bc6\u7801\u5b66\u3001\u5929\u4f53\u7269\u7406\u5b66\u548c\u7cbe\u5bc6\u5de5\u7a0b\u3002\u5b83\u901a\u8fc7\u8f6f\u4ef6\u5e93\u5b9e\u73b0\uff0c\u5982GNU MPFR\u3001MP Math\u7b49\uff0c\u8fd9\u4e9b\u5e93\u63d0\u4f9b\u4e86\u5bf9\u4efb\u610f\u7cbe\u5ea6\u7b97\u672f\u7684\u652f\u6301\u3002\u5b83\u4eec\u5141\u8bb8\u7a0b\u5e8f\u5458\u6307\u5b9a\u6240\u9700\u7684\u7cbe\u5ea6\u6c34\u5e73\uff0c\u5e76\u80fd\u591f\u6267\u884c\u52a0\u3001\u51cf\u3001\u4e58\u3001\u9664\u7b49\u57fa\u672c\u7b97\u672f\u8fd0\u7b97\uff0c\u4ee5\u53ca\u5bf9\u6570\u3001\u6307\u6570\u3001\u4e09\u89d2\u51fd\u6570\u7b49\u9ad8\u7ea7\u6570\u5b66\u51fd\u6570\u7684\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<p><h3>\u4e09\u3001\u7b26\u53f7\u8ba1\u7b97<\/h3>\n<\/p>\n<p><p>\u7b26\u53f7\u8ba1\u7b97\u7cfb\u7edf\u53ef\u4ee5\u7cbe\u786e\u8868\u793a\u548c\u64cd\u4f5c\u65e0\u7406\u6570\u3002\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u662f\u901a\u8fc7\u6570\u503c\u8fd1\u4f3c\u6765\u5904\u7406\u65e0\u7406\u6570\uff0c\u800c\u662f\u901a\u8fc7\u7b26\u53f7\u8868\u8fbe\u5f0f\u6765\u76f4\u63a5\u8868\u793a\u3002\u4f8b\u5982\uff0c\u221a2\u53ef\u4ee5\u76f4\u63a5\u5b58\u50a8\u4e3a<code>sqrt(2)<\/code>\u7684\u5f62\u5f0f\uff0c\u03c0\u53ef\u4ee5\u76f4\u63a5\u5b58\u50a8\u4e3a<code>pi<\/code>\u7684\u5f62\u5f0f\u3002<\/p>\n<\/p>\n<p><p>\u7b26\u53f7\u8ba1\u7b97\u80fd\u591f\u63d0\u4f9b\u7cbe\u786e\u7684\u7ed3\u679c\uff0c\u56e0\u4e3a\u5b83\u4e0d\u4f9d\u8d56\u4e8e\u6570\u503c\u8fd1\u4f3c\u3002\u8fd9\u5728\u9700\u8981\u7cbe\u786e\u8ba1\u7b97\u7684\u6570\u5b66\u3001\u7269\u7406\u95ee\u9898\u89e3\u51b3\u65b9\u6848\u65f6\u975e\u5e38\u91cd\u8981\u3002\u7b26\u53f7\u8ba1\u7b97\u7cfb\u7edf\uff0c\u5982Mathematica\u3001Maple\u548cSymPy\uff0c\u652f\u6301\u5bf9\u7b26\u53f7\u8868\u8fbe\u5f0f\u7684\u64cd\u4f5c\uff0c\u5305\u62ec\u5c55\u5f00\u3001\u7b80\u5316\u3001\u56e0\u5f0f\u5206\u89e3\u548c\u79ef\u5206\u7b49\u3002<\/p>\n<\/p>\n<p><h3>\u56db\u3001\u533a\u95f4\u4f30\u8ba1<\/h3>\n<\/p>\n<p><p>\u533a\u95f4\u4f30\u8ba1\u662f\u4e00\u79cd\u901a\u8fc7\u7ed9\u51fa\u4e00\u4e2a\u5305\u542b\u65e0\u7406\u6570\u7684\u6570\u503c\u533a\u95f4\u6765\u8868\u793a\u65e0\u7406\u6570\u7684\u65b9\u6cd5\u3002\u8fd9\u79cd\u8868\u793a\u65b9\u6cd5\u4e0d\u76f4\u63a5\u7ed9\u51fa\u4e00\u4e2a\u8fd1\u4f3c\u503c\uff0c\u800c\u662f\u7ed9\u51fa\u4e00\u4e2a\u5305\u542b\u8be5\u65e0\u7406\u6570\u7684\u533a\u95f4\uff0c\u4ece\u800c\u4fdd\u8bc1\u4e86\u65e0\u7406\u6570\u7684\u7cbe\u786e\u5ea6\u3002<\/p>\n<\/p>\n<p><p>\u8fd9\u79cd\u65b9\u6cd5\u5e38\u7528\u4e8e\u6570\u503c\u5206\u6790\u548c\u79d1\u5b66\u8ba1\u7b97\u4e2d\uff0c\u5c24\u5176\u662f\u5728\u8bef\u5dee\u63a7\u5236\u975e\u5e38\u91cd\u8981\u7684\u573a\u5408\u3002\u901a\u8fc7\u4f7f\u7528\u533a\u95f4\u7b97\u672f\u5e93\uff0c\u5982INTLAB\u6216Boost Interval Arithmetic Library\uff0c\u7a0b\u5e8f\u53ef\u4ee5\u64cd\u4f5c\u533a\u95f4\uff0c\u5e76\u4e14\u80fd\u591f\u4fdd\u8bc1\u8ba1\u7b97\u7ed3\u679c\u7684\u6b63\u786e\u6027\u548c\u7cbe\u5ea6\u3002<\/p>\n<\/p>\n<p><h3>\u603b\u7ed3<\/h3>\n<\/p>\n<p><p>\u5728\u8ba1\u7b97\u673a\u7a0b\u5e8f\u4e2d\u8868\u793a\u65e0\u7406\u6570\u662f\u4e00\u4e2a\u6311\u6218\uff0c\u56e0\u4e3a\u8ba1\u7b97\u673a\u7684\u6570\u503c\u8868\u793a\u662f\u6709\u9650\u7684\u3002\u4f46\u662f\uff0c\u901a\u8fc7<strong>\u6570\u503c\u8fd1\u4f3c\u3001\u6570\u503c\u7c7b\u578b\u6269\u5c55\u3001\u7b26\u53f7\u8ba1\u7b97<\/strong>\u548c<strong>\u533a\u95f4\u4f30\u8ba1<\/strong>\u7b49\u65b9\u6cd5\uff0c\u80fd\u591f\u5728\u5b9e\u8df5\u4e2d\u6709\u6548\u5730\u8868\u793a\u548c\u5904\u7406\u65e0\u7406\u6570\u3002\u6bcf\u79cd\u65b9\u6cd5\u90fd\u6709\u5176\u9002\u7528\u7684\u573a\u666f\u548c\u4f18\u7f3a\u70b9\uff0c\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u9700\u8981\u6839\u636e\u5177\u4f53\u7684\u5e94\u7528\u9700\u6c42\u548c\u7cbe\u5ea6\u8981\u6c42\u6765\u5224\u65ad\u3002\u5728\u5b9e\u7528\u4e2d\uff0c\u8fd9\u4e9b\u65b9\u6cd5\u5f80\u5f80\u88ab\u7efc\u5408\u8fd0\u7528\uff0c\u4ee5\u8fbe\u5230\u65e2\u5b9e\u7528\u53c8\u7cbe\u786e\u7684\u8ba1\u7b97\u7ed3\u679c\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p><strong>1. \u5982\u4f55\u4f7f\u7528\u8ba1\u7b97\u673a\u7a0b\u5e8f\u8868\u793a\u65e0\u7406\u6570\uff1f<\/strong><br \/>\n\u8ba1\u7b97\u673a\u7a0b\u5e8f\u53ef\u4ee5\u4f7f\u7528\u4e0d\u540c\u7684\u65b9\u6cd5\u6765\u8868\u793a\u65e0\u7406\u6570\u3002\u4e00\u79cd\u5e38\u7528\u7684\u65b9\u6cd5\u662f\u4f7f\u7528\u6d6e\u70b9\u6570\u6570\u636e\u7c7b\u578b\uff0c\u5982\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\uff08double\uff09\u6216\u6269\u5c55\u7cbe\u5ea6\u6d6e\u70b9\u6570\uff08long double\uff09\uff0c\u4ee5\u5b9e\u73b0\u9ad8\u7cbe\u5ea6\u7684\u8ba1\u7b97\u3002\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528\u65e0\u9650\u5c0f\u6570\u6216\u8fde\u5206\u6570\u7684\u5f62\u5f0f\u8868\u793a\u65e0\u7406\u6570\uff0c\u8fd9\u6837\u53ef\u4ee5\u4fdd\u7559\u5c3d\u53ef\u80fd\u591a\u7684\u7cbe\u5ea6\u3002\u5728\u7f16\u5199\u7a0b\u5e8f\u65f6\uff0c\u8fd8\u53ef\u4ee5\u4f7f\u7528\u73b0\u6709\u7684\u6570\u5b66\u5e93\u6216\u81ea\u5b9a\u4e49\u7684\u7b97\u6cd5\u6765\u8fdb\u884c\u7cbe\u786e\u8ba1\u7b97\u548c\u5904\u7406\u3002<\/p>\n<p><strong>2. \u6709\u4ec0\u4e48\u8ba1\u7b97\u673a\u7a0b\u5e8f\u53ef\u4ee5\u7528\u6765\u5904\u7406\u65e0\u7406\u6570\uff1f<\/strong><br \/>\n\u8ba1\u7b97\u673a\u7a0b\u5e8f\u53ef\u4ee5\u4f7f\u7528\u4e0d\u540c\u7684\u6570\u5b66\u5e93\u6216\u8f6f\u4ef6\u6765\u5904\u7406\u65e0\u7406\u6570\u3002\u4e00\u4e9b\u5e38\u89c1\u7684\u6570\u5b66\u5e93\u5982Python\u4e2d\u7684NumPy\u548cSciPy\uff0c\u4ee5\u53caJava\u4e2d\u7684Apache Commons Math\u5e93\uff0c\u90fd\u63d0\u4f9b\u4e86\u5904\u7406\u65e0\u7406\u6570\u7684\u529f\u80fd\u3002\u8fd9\u4e9b\u5e93\u53ef\u4ee5\u8fdb\u884c\u65e0\u7406\u6570\u7684\u8ba1\u7b97\u3001\u8f6c\u6362\u3001\u6bd4\u8f83\u7b49\u64cd\u4f5c\uff0c\u5e76\u63d0\u4f9b\u4e86\u4e00\u4e9b\u7279\u5b9a\u7684\u51fd\u6570\u548c\u7b97\u6cd5\u6765\u5904\u7406\u65e0\u7406\u6570\u3002<\/p>\n<p><strong>3. \u5982\u4f55\u5728\u8ba1\u7b97\u673a\u7a0b\u5e8f\u4e2d\u8fdb\u884c\u65e0\u7406\u6570\u7684\u8fd0\u7b97\u548c\u6bd4\u8f83\uff1f<\/strong><br 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