{"id":304021,"date":"2024-05-20T19:13:00","date_gmt":"2024-05-20T11:13:00","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/304021.html"},"modified":"2024-05-20T19:13:18","modified_gmt":"2024-05-20T11:13:18","slug":"ieee754%e5%8d%95%e7%b2%be%e5%ba%a6%e9%98%b6%e7%a0%81%e7%9c%9f%e5%80%bc%e4%b8%ba%e4%bb%80%e4%b9%88%e6%98%af-126-127","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/304021.html","title":{"rendered":"IEEE754\u5355\u7cbe\u5ea6\u9636\u7801\u771f\u503c\u4e3a\u4ec0\u4e48\u662f-126-127"},"content":{"rendered":"

\"IEEE754\u5355\u7cbe\u5ea6\u9636\u7801\u771f\u503c\u4e3a\u4ec0\u4e48\u662f-126-127\"<\/p>\n

IEEE754\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u7684\u9636\u7801\u5b9e\u9645\u53ef\u8868\u793a\u7684\u771f\u503c\u8303\u56f4\u4e3a-126\u81f3127\u3002\u8fd9\u662f\u56e0\u4e3a\u3001\u5728IEEE754\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u683c\u5f0f\u4e2d\u3001\u9636\u7801\u90e8\u5206\u5206\u914d\u4e868\u4f4d\u6765\u5b58\u50a8\u3001\u4f46\u8fd9\u4e0d\u662f\u7b80\u5355\u5730\u76f4\u63a5\u5b58\u50a8\u5b9e\u9645\u9636\u7801\u503c\u3002\u800c\u662f\u91c7\u7528\u4e00\u79cd\u88ab\u79f0\u4e3a\u201c\u504f\u79fb\u4e8c\u8fdb\u5236\u201d\u6216\u201cExcess-K\u201d\u8bb0\u6cd5\u7684\u5b58\u50a8\u65b9\u5f0f\u3001\u5176\u4e2dK\u4e3a\u504f\u79fb\u91cf\u3001\u5728\u5355\u7cbe\u5ea6\u683c\u5f0f\u4e2d\u4e3a127\u3002\u8be6\u7ec6\u6765\u8bf4\u3001IEEE754\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u4f7f\u7528\u4e861\u4f4d\u7b26\u53f7\u4f4d\u30018\u4f4d\u9636\u7801\u3001\u548c23\u4f4d\u5c0f\u6570\uff08\u5c3e\u6570\uff09\u6765\u8868\u793a\u4e00\u4e2a\u6d6e\u70b9\u6570\u3002<\/p>\n<\/p>\n

\u5728\u201c\u504f\u79fb\u4e8c\u8fdb\u5236\u201d\u5b58\u50a8\u4e2d\u3001\u5b9e\u9645\u7684\u9636\u7801\u503c\u9700\u8981\u52a0\u4e0a\u4e00\u4e2a\u56fa\u5b9a\u7684\u504f\u79fb\u91cf\uff08127\uff09\u6765\u5f97\u5230\u5b58\u50a8\u7684\u9636\u7801\u503c\u3002\u56e0\u6b64\u3001\u9636\u7801\u5b57\u6bb5\u4e2d\u51680\u8868\u793a\u7684\u662f-127\uff08\u8868\u793a\u6700\u5c0f\u7684\u975e\u89c4\u8303\u5316\u6570\uff09\uff0c\u800c\u4e0d\u662f-127\u672c\u8eab\uff0c\u9700\u8981\u7279\u6b8a\u5bf9\u5f85\u3002\u540c\u6837\u7684\u3001\u5f53\u9636\u7801\u5b57\u6bb5\u51681\u65f6\u3001\u5b83\u88ab\u7528\u4e8e\u8868\u793a\u65e0\u7a77\u5927\u6216NaN\uff08\u4e0d\u662f\u4e00\u4e2a\u6570\uff09\uff0c\u800c\u4e0d\u662f\u5177\u4f53\u7684\u9636\u7801\u503c\u3002\u56e0\u6b64\u3001\u53ef\u8868\u793a\u7684\u6700\u5c0f\u9636\u7801\u771f\u503c\u4e3a-126\uff08\u7f16\u7801\u4e3a00000001\uff09\uff0c\u800c\u6700\u5927\u9636\u7801\u771f\u503c\u4e3a127\uff08\u7f16\u7801\u4e3a11111110\uff09\u3002<\/p>\n<\/p>\n

\u4e00\u3001IEEE754 SINGLE PRECISION OVERVIEW<\/strong><\/h3>\n<\/p>\n

IEEE754\u6807\u51c6\u5b9a\u4e49\u4e86\u6d6e\u70b9\u6570\u7684\u5b58\u50a8\u548c\u8ba1\u7b97\u89c4\u5219\uff0c\u786e\u4fdd\u4e86\u4e0d\u540c\u8ba1\u7b97\u673a\u7cfb\u7edf\u95f4\u6d6e\u70b9\u6570\u7684\u517c\u5bb9\u6027\u3002\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u5360\u75284\u5b57\u8282\uff0832\u4f4d\uff09\uff0c\u5176\u4e2d1\u4f4d\u7528\u4e8e\u8868\u793a\u7b26\u53f7\uff08S\uff09\u30018\u4f4d\u7528\u4e8e\u8868\u793a\u9636\u7801\uff08E\uff09\uff0c\u5269\u4e0b\u768423\u4f4d\u7528\u4e8e\u8868\u793a\u5c0f\u6570\u90e8\u5206\uff08\u4e5f\u79f0\u4e3a\u5c3e\u6570M\uff09\u3002<\/p>\n<\/p>\n

\u4e8c\u3001\u9636\u7801\u7684\u5b58\u50a8\u65b9\u5f0f<\/strong><\/h3>\n<\/p>\n

\u9636\u7801\u7684\u5b58\u50a8\u4f7f\u7528\u4e86\u4e00\u79cd\u53eb\u505aExcess-K\u6216\u504f\u79fb\u4e8c\u8fdb\u5236\u7684\u683c\u5f0f\u3002\u8fd9\u79cd\u683c\u5f0f\u4e2d\uff0c\u5b9e\u9645\u7684\u9636\u7801\u503c\u4f1a\u52a0\u4e0a\u4e00\u4e2a\u504f\u79fb\u91cf\u540e\u5b58\u50a8\u3002\u5bf9\u4e8e\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\uff0cK\u4e3a127\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5982\u679c\u6211\u4eec\u8981\u5b58\u50a8\u9636\u7801\u503c0\uff0c\u9636\u7801\u5b57\u6bb5\u4e2d\u5c06\u5b58\u50a8127\uff08\u537301111111\uff09\u3002<\/p>\n<\/p>\n

\u4e09\u3001\u4e3a\u4ec0\u4e48\u4f7f\u7528\u504f\u79fb\u91cf<\/strong><\/h3>\n<\/p>\n

\u4f7f\u7528\u504f\u79fb\u91cf\u53ef\u4ee5\u4f7f\u5f97\u6d6e\u70b9\u6570\u7684\u6bd4\u8f83\u548c\u6392\u5e8f\u53d8\u5f97\u66f4\u52a0\u7b80\u5355\u9ad8\u6548\u3002\u7531\u4e8e\u9636\u7801\u91c7\u7528\u4e86\u504f\u79fb\u91cf\u65b9\u6cd5\uff0c\u6240\u6709\u53ef\u80fd\u7684\u9636\u7801\u503c\uff08\u5305\u62ec\u8d1f\u6570\uff09\u90fd\u53ef\u4ee5\u7528\u4e00\u4e2a\u65e0\u7b26\u53f7\u6574\u6570\u6765\u8868\u793a\uff0c\u4f7f\u5f97\u8ba1\u7b97\u673a\u80fd\u591f\u76f4\u63a5\u4f7f\u7528\u6574\u6570\u8fd0\u7b97\u6765\u6bd4\u8f83\u6d6e\u70b9\u6570\u7684\u5927\u5c0f\u3002\u8fd9\u79cd\u5b58\u50a8\u65b9\u6cd5\u4e5f\u4fbf\u4e8e\u8868\u793a\u7279\u6b8a\u503c\uff0c\u59820\u3001\u65e0\u7a77\u5927\u548cNaN\u3002<\/p>\n<\/p>\n

\u56db\u3001\u89c4\u8303\u5316\u6570\u4e0e\u975e\u89c4\u8303\u5316\u6570<\/strong><\/h3>\n<\/p>\n

\u5728IEEE754\u6807\u51c6\u4e2d\uff0c\u6d6e\u70b9\u6570\u53ef\u4ee5\u5206\u4e3a\u89c4\u8303\u5316\u6570\u548c\u975e\u89c4\u8303\u5316\u6570\u3002\u89c4\u8303\u5316\u6570\u6709\u4e00\u4e2a\u9690\u542b\u7684\u524d\u5bfc1\uff08\u5373\u5c0f\u6570\u90e8\u5206\u524d\u9762\u9690\u542b\u4e00\u4e2a1\uff09\uff0c\u800c\u975e\u89c4\u8303\u5316\u6570\u4e0d\u9075\u5faa\u8fd9\u4e2a\u89c4\u5219\uff0c\u7528\u4e8e\u8868\u793a\u63a5\u8fd1\u4e8e0\u7684\u975e\u5e38\u5c0f\u7684\u6570\u3002\u5f53\u9636\u7801\u5b57\u6bb5\u51680\u65f6\uff0c\u8868\u793a\u7684\u662f\u975e\u89c4\u8303\u5316\u6570\uff0c\u8fd9\u4f7f\u5f97\u6211\u4eec\u53ef\u4ee5\u8868\u793a\u66f4\u63a5\u8fd1\u4e8e0\u7684\u6570\u503c\uff0c\u589e\u52a0\u4e86\u6d6e\u70b9\u6570\u7684\u8868\u793a\u8303\u56f4\u3002<\/p>\n<\/p>\n

\u4e94\u3001\u7279\u6b8a\u503c\u7684\u8868\u793a<\/strong><\/h3>\n<\/p>\n

IEEE754\u6807\u51c6\u8fd8\u5b9a\u4e49\u4e86\u6d6e\u70b9\u6570\u7684\u51e0\u79cd\u7279\u6b8a\u503c\uff1a+0\u548c-0\u3001\u6b63\u8d1f\u65e0\u7a77\u5927\u3001NaN\uff08Not a Number\uff09\u3002\u8fd9\u4e9b\u7279\u6b8a\u503c\u5728\u9636\u7801\u548c\u5c3e\u6570\u5b57\u6bb5\u4e2d\u6709\u7279\u6b8a\u7684\u8868\u793a\u65b9\u6cd5\uff0c\u4f8b\u5982\uff0c\u9636\u7801\u51681\u800c\u5c3e\u6570\u975e0\u7684\u60c5\u51b5\u8868\u793aNaN\uff0c\u9636\u7801\u51681\u800c\u5c3e\u6570\u4e3a0\u8868\u793a\u65e0\u7a77\u5927\u3002\u8fd9\u4e9b\u7279\u6b8a\u503c\u5728\u79d1\u5b66\u8ba1\u7b97\u4e2d\u975e\u5e38\u91cd\u8981\uff0c\u7528\u4e8e\u8868\u793a\u8ba1\u7b97\u7684\u5f02\u5e38\u60c5\u51b5\u3002<\/p>\n<\/p>\n

\u516d\u3001\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u5f71\u54cd<\/strong><\/h3>\n<\/p>\n

\u4e86\u89e3IEEE754\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u7684\u9636\u7801\u771f\u503c\u8303\u56f4\u5bf9\u4e8e\u8ba1\u7b97\u673a\u7f16\u7a0b\u548c\u79d1\u5b66\u8ba1\u7b97\u6765\u8bf4\u81f3\u5173\u91cd\u8981\u3002\u5b83\u5f71\u54cd\u7740\u7b97\u6cd5\u7684\u8bbe\u8ba1\uff0c\u7279\u522b\u662f\u90a3\u4e9b\u9700\u8981\u7cbe\u786e\u63a7\u5236\u6570\u503c\u7cbe\u5ea6\u548c\u8303\u56f4\u7684\u7b97\u6cd5\u3002\u4f8b\u5982\uff0c\u5728\u56fe\u5f62\u5b66\u3001\u673a\u5668\u5b66\u4e60<\/a>\u7b49\u9886\u57df\uff0c\u6d6e\u70b9\u6570\u7684\u7cbe\u786e\u8868\u793a\u548c\u8fd0\u7b97\u5bf9\u7ed3\u679c\u7684\u8d28\u91cf\u6709\u7740\u76f4\u63a5\u7684\u5f71\u54cd\u3002\u6b64\u5916\uff0c\u5bf9\u7279\u6b8a\u503c\u7684\u6b63\u786e\u5904\u7406\u4e5f\u662f\u7f16\u5199\u5065\u58ee\u3001\u53ef\u9760\u8f6f\u4ef6\u7684\u5173\u952e\u90e8\u5206\u3002<\/p>\n<\/p>\n

\u901a\u8fc7\u6df1\u5165\u7406\u89e3IEEE754\u6807\u51c6\u53ca\u5176\u5728\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u4e2d\u7684\u5177\u4f53\u5b9e\u73b0\uff0c\u5f00\u53d1\u8005\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u6d6e\u70b9\u6570\u7684\u8fd0\u7b97\u89c4\u5219\u548c\u9650\u5236\uff0c\u4ece\u800c\u5199\u51fa\u66f4\u9ad8\u6548\u3001\u66f4\u51c6\u786e\u7684\u8f6f\u4ef6\u3002<\/p>\n<\/p>\n

\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n

1. \u4e3a\u4ec0\u4e48IEEE754\u5355\u7cbe\u5ea6\u9636\u7801\u771f\u503c\u8303\u56f4\u662f-126\u5230127?<\/strong><\/p>\n

IEEE754\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u662f\u753132\u4f4d\u4e8c\u8fdb\u5236\u6570\u8868\u793a\u7684\uff0c\u5176\u4e2d\u5305\u62ec\u4e00\u4f4d\u7b26\u53f7\u4f4d\u30018\u4f4d\u9636\u7801\u548c23\u4f4d\u5c3e\u6570\u3002\u9636\u7801\u7528\u6765\u786e\u5b9a\u6d6e\u70b9\u6570\u7684\u6307\u6570\u90e8\u5206\uff0c\u800c\u771f\u503c\u8303\u56f4\u5219\u53d6\u51b3\u4e8e\u9636\u7801\u7684\u53d6\u503c\u8303\u56f4\u3002<\/p>\n

\u5bf9\u4e8e\u5355\u7cbe\u5ea6\u9636\u7801\u800c\u8a00\uff0c8\u4f4d\u7684\u53d6\u503c\u8303\u56f4\u662f\u4ece0\u5230255\u3002\u7136\u800c\uff0c\u4e3a\u4e86\u5c06\u9636\u7801\u7684\u6709\u6548\u8303\u56f4\u5bf9\u79f0\u5730\u5206\u5e03\u5728\u6b63\u6570\u548c\u8d1f\u6570\u4e4b\u95f4\uff0cIEEE754\u6807\u51c6\u89c4\u5b9a\uff0c\u5b9e\u9645\u7684\u9636\u7801\u771f\u503c\u8303\u56f4\u662f\u4ece-126\u5230127\u3002<\/p>\n

\u8fd9\u610f\u5473\u7740\u9636\u7801\u7684\u4e8c\u8fdb\u5236\u8868\u793a\u53ef\u4ee5\u8868\u793a\u4ece2^(-126)\u52302^127\u7684\u6307\u6570\u8303\u56f4\u3002\u901a\u8fc7\u5c06\u771f\u503c\u8303\u56f4\u5bf9\u79f0\u5730\u5206\u5e03\u5728\u6b63\u8d1f\u4e24\u4fa7\uff0c\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u53ef\u4ee5\u8868\u793a\u975e\u5e38\u5927\u7684\u6b63\u6570\u548c\u975e\u5e38\u5c0f\u7684\u8d1f\u6570\uff0c\u4ece\u800c\u6ee1\u8db3\u4e86\u5e7f\u6cdb\u7684\u6570\u503c\u8ba1\u7b97\u9700\u6c42\u3002<\/p>\n

2. \u9636\u7801\u771f\u503c\u4e3a\u4ec0\u4e48\u4e0d\u5305\u62ec-128\u548c128?<\/strong><\/p>\n

\u867d\u71368\u4f4d\u4e8c\u8fdb\u5236\u6570\u53ef\u4ee5\u8868\u793a\u4ece0\u5230255\u7684\u53d6\u503c\u8303\u56f4\uff0c\u4f46\u662fIEEE754\u6807\u51c6\u4e2d\u7684\u9636\u7801\u771f\u503c\u8303\u56f4\u88ab\u9650\u5236\u5728-126\u5230127\u4e4b\u95f4\u3002\u5176\u4e2d\u7684\u539f\u56e0\u6709\u4ee5\u4e0b\u51e0\u70b9\uff1a<\/p>\n

\u9996\u5148\uff0cIEEE754\u6807\u51c6\u5c068\u4f4d\u9636\u7801\u4e2d\u7684\u51680\u548c\u51681\u7684\u7ec4\u5408\u4f5c\u4e3a\u7279\u6b8a\u60c5\u51b5\u7684\u6307\u793a\u7b26\u3002\u51680\u7684\u9636\u7801\u8868\u793a\u975e\u89c4\u683c\u5316\u6570\uff08subnormal number\uff09\uff0c\u800c\u51681\u7684\u9636\u7801\u8868\u793a\u7279\u6b8a\u6570\u503c\uff0c\u5982\u65e0\u7a77\u5927\u548cNaN\uff08Not-a-Number\uff09\u3002<\/p>\n

\u5176\u6b21\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u9636\u7801\u7684\u6709\u6548\u8303\u56f4\u5bf9\u79f0\u5206\u5e03\u5728\u6b63\u8d1f\u4e24\u4fa7\uff0c\u540c\u65f6\u4f7f\u5f97\u6570\u503c\u8303\u56f4\u66f4\u52a0\u5747\u8861\u3002\u901a\u8fc7\u5c06\u9636\u7801\u771f\u503c\u4ece-128\u548c128\u5254\u9664\uff0c\u4e3a\u7279\u6b8a\u60c5\u51b5\u9884\u7559\u4e86\u66f4\u591a\u7684\u4e8c\u8fdb\u5236\u7ec4\u5408\u3002<\/p>\n

\u6700\u540e\uff0c-128\u548c128\u8fd9\u4e24\u4e2a\u9636\u7801\u771f\u503c\u5e76\u6ca1\u6709\u5b9e\u9645\u7684\u6709\u6548\u7528\u9014\u3002\u7531\u4e8e\u89c4\u683c\u5316\u6570\u7684\u8868\u793a\u9700\u8981\u4fdd\u7559\u4e00\u4f4d\u9690\u85cf\u4f4d\uff0c\u56e0\u6b64\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u8fd9\u4e24\u4e2a\u9636\u7801\u771f\u503c\u65e0\u6cd5\u8868\u793a\u5177\u4f53\u7684\u6d6e\u70b9\u6570\u3002<\/p>\n

3. \u9636\u7801\u771f\u503c\u7684\u8303\u56f4\u5bf9\u8ba1\u7b97\u673a\u8868\u793a\u6709\u4f55\u5f71\u54cd?<\/strong><\/p>\n

\u9636\u7801\u771f\u503c\u7684\u8303\u56f4\u5728IEEE754\u5355\u7cbe\u5ea6\u6d6e\u70b9\u8868\u793a\u4e2d\u8d77\u5230\u4e86\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u5bf9\u8ba1\u7b97\u673a\u7684\u6570\u503c\u8868\u793a\u548c\u8ba1\u7b97\u80fd\u529b\u4ea7\u751f\u4e86\u5f71\u54cd\u3002<\/p>\n

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