{"id":138,"date":"2013-03-05T23:50:34","date_gmt":"2013-03-05T15:50:34","guid":{"rendered":"http:\/\/blog.feizhaojun.com\/?p=138"},"modified":"2013-03-05T23:50:53","modified_gmt":"2013-03-05T15:50:53","slug":"%e8%ae%a1%e7%ae%97%e6%9c%ba%e6%b5%ae%e7%82%b9%e6%95%b0%e8%bf%90%e7%ae%97%e5%ad%98%e5%9c%a8%e8%af%af%e5%b7%ae%e7%9a%84%e5%8e%9f%e5%9b%a0","status":"publish","type":"post","link":"https:\/\/feizhaojun.com\/?p=138","title":{"rendered":"\u8ba1\u7b97\u673a\u6d6e\u70b9\u6570\u8fd0\u7b97\u5b58\u5728\u8bef\u5dee\u7684\u539f\u56e0"},"content":{"rendered":"

\u8ba1\u7b97\u673a\u4e2d\u7684\u4e8c\u8fdb\u5236\u7684\u5c0f\u6570\u540c\u5341\u8fdb\u5236\u4e00\u6837\uff0c\u6bd4\u5982\u5341\u8fdb\u5236\u91cc\u976210.125\u53ef\u4ee5\u5199\u62101.125*10e1\uff0810e1=10^{1}\uff1a\u537310\u76841\u6b21\u65b9\uff09\uff0c\u4e8c\u8fdb\u5236\u91cc\u97621010.001\u53ef\u4ee5\u5199\u62101.010001*2e3\uff0c\u90fd\u53ef\u4ee5\u5199\u6210\u8c01\u4e58\u4ee5\u8fdb\u5236\u7684\u6307\u6570\u6b21\uff0c\u6240\u4ee5\uff0c\u5728IEEE\u89c4\u5219\u4e2d\u89c4\u5b9a\u6d6e\u70b9\u6570\u7684\u6784\u6210\u662f\u7b26\u53f7\u4f4dS+\u6307\u6570\u4f4dE+\u5c3e\u6570M\uff0c\u8fd9\u4e2a\u4f4d\u6570\u7684\u7ec4\u5408\u6784\u6210\u6d6e\u70b9\u6570<\/strong>\u3002<\/p>\n

JAVA\u9075\u5b88IEEE754\u89c4\u5219\uff1a<\/p>\n

float\u53604\u4e2a\u5b57\u8282\uff0c32\u4f4d\uff0c\u8868\u793a\u4e3aSEEEEEEEEMMMMMMMMMMMMMMMMMM\uff0c1\u4f4d\u7b26\u53f7\u4f4d\uff0c8\u4f4d\u6307\u6570\u4f4d\uff0c23\u4f4d\u5c3e\u6570\u4f4d\u3002\u5f53\u7136\u5982\u679c\u6307\u6570\u503c\u57281-254\u4e4b\u95f4\u65f6\uff0c\u4e3a1.M,\u5426\u5219\u5c31\u662f0.M,\u6307\u6570\u53c8\u53eb\u9636\u7801\uff0c\u9636\u7801\u91c7\u7528\u79fb\u7801\u8868\u793a\uff0c\u53d6\u503cE-127.\u6240\u4ee5\u516c\u5f0f\u53ef\u603b\u7ed3\u4e3a\uff1a\u5c0f\u4e8e0\u7684\u5c0f\u6570:(-1)\u7684S\u6b21*2\u7684(1-127)\u6b21*(0.M)\uff0c\u5927\u4e8e0\u7684\u5c0f\u6570:(-1)\u7684S\u6b21*2\u7684(E-127)*(1.M).<\/p>\n

5.0\u7684\u5728JAVA\u4e2d\u7684\u8ba1\u7b97\u673a\u4e8c\u8fdb\u5236\u6d41\u8868\u793a\u4e3a\uff1a<\/p>\n

S=0,
\n5.0=101=1.01*2\u76842\u6b21
\nE-127=2\u00a0 E=129=10000001
\nM=1.01<\/p>\n

\u7ec4\u5408\u5728\u4e00\u8d77\u5c31\u662f 0 10000001 01000000000000000000000<\/p>\n

\u518d\u8f6c\u6210\u5341\u8fdb\u5236\uff1a(-1)\u76840\u6b21 * 2\u7684(129-127)\u6b21*(1.01)=101=5.0<\/p>\n

\u8f93\u51fafloat\u7684\u4e8c\u8fdb\u5236\u6d41\uff0cJava\u4e2d\u7684\u65b9\u6cd5Float.floatToIntBits()<\/p>\n

-5.0\u7684\u8868\u793a\uff1a<\/p>\n

Java\u4e8c\u8fdb\u5236\u6d41\uff1a1 10000001 01000000000000000000000,\u5176\u4ed6\u7701\u7565\u3002<\/p>\n

0.1\u7684\u8868\u793a\uff1a<\/p>\n

0.1\u7ea6\u7b49\u4e8e0.0001100110011001100110011001=1.100110011001100110011001*2\u7684-4\u6b21<\/p>\n

S=0<\/p>\n

E-127=-4 E=123=01111011<\/p>\n

M=10011001100110011001100<\/p>\n

\u7ec4\u5408\u5728\u4e00\u8d77\u5728JAVA\u4e2d\u4e8c\u8fdb\u5236\u6d41\u5c31\u662f0 01111011 100110011001100110011001100<\/p>\n

\u5728\u8f6c\u6362\u621010\u8fdb\u5236\u4e3a0.100000001490116119384765625<\/p>\n

\u8bef\u5dee\u4e3a0.000000001490116119384765625 \u5982\u679c26\u4e2afloat\u76840.1\u76f8\u52a0\uff0c\u7ed3\u679c\u4e3a2.5999997 \u5982\u679c\u5b9a\u4e4926\u4e2adouble\u76840.1\u76f8\u52a0\uff0c\u7ed3\u679c\u4e3a2.600000000000001\u3002<\/p>\n

\u6240\u4ee5\u53ef\u4ee5\u5f97\u51fa\uff1a<\/p>\n

1.\u6d6e\u70b9\u6570\u5f3a\u5236\u8f6c\u6362\u6210\u6574\u6570\u65f6\uff0c\u820d\u5165\u8bef\u5dee\u4e25\u91cd\u52a0\u91cd\uff0c\u5f3a\u5236\u8f6c\u6362\u65f6\u4f1a\u820d\u5f03\u975e\u6574\u6570\u90e8\u5206\u3002<\/p>\n

double d=29*0.01;\/\/d=0.29
\nd=((int)d*100);\/\/d=28<\/p>\n

2.\u79d1\u5b66\u8ba1\u6570\u8868\u793a\u6cd5\u4e2d\u4e8c\u8fdb\u5236\u4f4d\u6570\u8d8a\u591a\uff0c\u7cbe\u5ea6\u5c31\u8d8a\u9ad8\u300264\u4f4ddouble\u5c31\u6bd432\u4f4d\u7684float\u7cbe\u5ea6\u9ad8\u3002\u5bf9\u7cbe\u5ea6\u8981\u6c42\u975e\u5e38\u9ad8\u7684\u573a\u5408\u53ef\u4ee5\u7528BigDecimal\u7c7b\uff0c\u80fd\u8868\u793a\u4efb\u610f\u7cbe\u5ea6\u7684\u6570\u3002<\/p>\n

3.\u6307\u6570E\u4e3a255\u65f6\u8868\u793a\u7279\u6b8a\u6570\u5b57\u3002<\/p>\n

--------------------\u8fd9\u91cc\u662f\u4f20\u8bf4\u4e2d\u7684\u5206\u5272\u7ebf--------------------<\/p>\n

\u5f15\u7528\u53e6\u5916\u4e00\u7bc7\u6587\u7ae0\u6765\u8bf4\u660e\uff0c\u4ee5\u5e2e\u52a9\u7406\u89e3\uff1a<\/p>\n

\u6d6e\u70b9\u6570\u662f\u7528\u6765\u8868\u793a\u5b9e\u6570\u7684\u4e00\u79cd\u65b9\u6cd5\uff0c\u5b83\u7528M(\u5c3e\u6570) * B(\u57fa\u6570)\u7684E(\u6307\u6570\uff09\u6b21\u65b9\u6765\u8868\u793a\u5b9e\u6570\uff0c\u76f8\u5bf9\u4e8e\u5b9a\u70b9\u6570\u6765\u8bf4\uff0c\u5728\u957f\u5ea6\u4e00\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0c\u5177\u6709\u8868\u793a\u6570\u636e\u8303\u56f4\u5927\u7684\u7279\u70b9\u3002\u4f46\u540c\u65f6\u4e5f\u5b58\u5728\u8bef\u5dee\u95ee\u9898\uff0c\u8fd9\u5c31\u662f\u8457\u540d\u7684\u6d6e\u70b9\u6570\u7cbe\u5ea6\u95ee\u9898\u3002<\/p>\n

\u6d6e\u70b9\u6570\u6709\u591a\u79cd\u5b9e\u73b0\u65b9\u6cd5\uff0c\u8ba1\u7b97\u673a\u4e2d\u6d6e\u70b9\u6570\u7684\u5b9e\u73b0\u5927\u90fd\u9075\u4eceIEEE754\u6807\u51c6\uff0cIEEE754\u89c4\u5b9a\u4e86\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u548c\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\u4e24\u79cd\u89c4\u683c\u3002<\/p>\n

\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u75284\u5b57\u8282\uff0832bit\uff09\u8868\u793a\u6d6e\u70b9\u6570\uff0c\u683c\u5f0f\u662f\uff1a<\/p>\n

1\u4f4d\u7b26\u53f7\u4f4d 8\u4f4d\u8868\u793a\u6307\u6570 23\u4f4d\u8868\u793a\u5c3e\u6570<\/p>\n

\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u65708\u5b57\u8282\uff0864bit\uff09\u8868\u793a\u5b9e\u6570\uff0c\u683c\u5f0f\u662f\uff1a<\/p>\n

1\u4f4d\u7b26\u53f7\u4f4d 11\u4f4d\u8868\u793a\u6307\u6570 52\u4f4d\u8868\u793a\u5c3e\u6570<\/p>\n

\u540c\u65f6\uff0cIEEE754\u6807\u51c6\u8fd8\u5bf9\u5c3e\u6570\u7684\u683c\u5f0f\u505a\u4e86\u89c4\u8303\uff1ad.dddddd...\uff0c\u5c0f\u6570\u70b9\u5de6\u9762\u53ea\u67091\u4f4d\u4e14\u4e0d\u80fd\u4e3a\u96f6\uff0c\u8ba1\u7b97\u673a\u5185\u90e8\u662f\u4e8c\u8fdb\u5236\uff0c\u56e0\u6b64\uff0c\u5c3e\u6570\u5c0f\u6570\u70b9\u5de6\u9762\u90e8\u5206\u603b\u662f1\u3002\u663e\u7136\uff0c\u8fd9\u4e2a1\u53ef\u4ee5\u7701\u53bb\uff0c\u4ee5\u63d0\u9ad8\u5c3e\u6570\u7684\u7cbe\u5ea6\u3002<\/p>\n

\u7531\u4e0a\u53ef\u77e5\uff0c\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u7684\u5c3e\u6570\u662f\u752824bit\u8868\u793a\u7684\uff0c\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\u7684\u5c3e\u6570\u662f\u752853bit\u8868\u793a\u7684\uff0c\u8f6c\u6362\u6210\u5341\u8fdb\u5236\uff1a<\/p>\n

2^24 - 1 = 16777215\uff1b 2^53 - 1 = 9007199254740991<\/p>\n

\u7531\u4e0a\u53ef\u89c1\uff0cIEEE754\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u7684\u6709\u6548\u6570\u5b57\u4e8c\u8fdb\u5236\u662f24\u4f4d\uff0c\u6309\u5341\u8fdb\u5236\u6765\u8bf4\uff0c\u662f8\u4f4d\uff1b\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\u7684\u6709\u6548\u6570\u5b57\u4e8c\u8fdb\u5236\u662f53\u4f4d\uff0c\u6309\u5341\u8fdb\u5236\u6765\u8bf4\uff0c\u662f16\u4f4d\u3002\u663e\u7136\uff0c\u5982\u679c\u4e00\u4e2a\u5b9e\u6570\u7684\u6709\u6548\u6570\u5b57\u8d85\u8fc78\u4f4d\uff0c\u7528\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u6765\u8868\u793a\u7684\u8bdd\uff0c\u5c31\u4f1a\u4ea7\u751f\u8bef\u5dee\uff01\u540c\u6837\uff0c\u5982\u679c\u4e00\u4e2a\u5b9e\u6570\u7684\u6709\u6548\u6570\u5b57\u8d85\u8fc716\u4f4d\uff0c\u7528\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\u6765\u8868\u793a\uff0c\u4e5f\u4f1a\u4ea7\u751f\u8bef\u5dee\uff01\u5bf9\u4e8e1310720000000000000000.66\u8fd9\u4e2a\u6570\uff0c\u6709\u6548\u6570\u5b57\u662f24\u4f4d\uff0c\u7528\u5355\u7cbe\u5ea6\u6216\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\u8868\u793a\u90fd\u4f1a\u4ea7\u751f\u8bef\u5dee\uff0c\u53ea\u662f\u7a0b\u5ea6\u4e0d\u540c\uff1a<\/p>\n

\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\uff1a1310720040000000000000.00\uff1b\u53cc\u7cbe\u5ea6\u6d6e\u70b9\u6570\uff1a 1310720000000000000000.00<\/p>\n

\u53ef\u89c1\uff0c\u53cc\u7cbe\u5ea6\u5dee\u4e86 0.66 \uff0c\u5355\u7cbe\u5ea6\u5dee\u4e86\u8fd14\u4e07\u4ebf\uff01<\/p>\n

\u4ee5\u4e0a\u8bf4\u660e\u4e86\u56e0\u957f\u5ea6\u9650\u5236\u800c\u9020\u6210\u7684\u8bef\u5dee\uff0c\u4f46\u8fd9\u8fd8\u4e0d\u662f\u5168\u90e8\uff0c\u91c7\u7528IEEE754\u6807\u51c6\u7684\u8ba1\u7b97\u673a\u6d6e\u70b9\u6570\uff0c\u5728\u5185\u90e8\u662f\u7528\u4e8c\u8fdb\u5236\u8868\u793a\u7684\uff0c\u4f46\u5728\u5c06\u4e00\u4e2a\u5341\u8fdb\u5236\u6570\u8f6c\u6362\u4e3a\u4e8c\u8fdb\u5236\u6d6e\u70b9\u6570\u65f6\uff0c\u4e5f\u4f1a\u9020\u6210\u8bef\u5dee\uff0c\u539f\u56e0\u662f\u4e0d\u662f\u6240\u6709\u7684\u6570\u90fd\u80fd\u8f6c\u6362\u6210\u6709\u9650\u957f\u5ea6\u7684\u4e8c\u8fdb\u5236\u6570\u3002<\/p>\n

\u5bf9\u4e8e131072.32 \u8fd9\u4e2a\u6570\uff0c\u5176\u6709\u6548\u6570\u5b57\u662f8\u4f4d\uff0c\u6309\u7406\u5e94\u8be5\u80fd\u7528\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u51c6\u786e\u8868\u793a\uff0c\u4e3a\u4ec0\u4e48\u4f1a\u51fa\u73b0\u504f\u5dee\u5462\uff1f<\/p>\n

\u770b\u4e00\u4e0b\u8fd9\u4e2a\u6570\u636e\u4e8c\u8fdb\u5236\u5c3e\u6570\u5c31\u660e\u767d\u4e86 10000000000000000001010001......<\/p>\n

\u663e\u7136\uff0c\u5176\u5c3e\u6570\u8d85\u8fc7\u4e8624bit\uff0c\u6839\u636e\u820d\u5165\u89c4\u5219\uff0c\u5c3e\u6570\u53ea\u53d6 100000000000000000010100\uff0c\u7ed3\u679c\u5c31\u9020\u6210\u6d4b\u8bd5\u4e2d\u9047\u5230\u7684\u201c\u5947\u602a\u201d\u73b0\u8c61\uff0c131072.68\u7528\u5355\u7cbe\u5ea6\u6d6e\u70b9\u6570\u8868\u793a\u53d8\u6210131072.69\uff0c\u539f\u56e0\u4e0e\u6b64\u7c7b\u4f3c\u3002<\/p>\n

\u5b9e\u9645\u4e0a\u6709\u6548\u6570\u5b57\u5c0f\u4e8e8\u4f4d\u7684\u6570\uff0c\u6d6e\u70b9\u6570\u4e5f\u4e0d\u4e00\u5b9a\u80fd\u7cbe\u786e\u8868\u793a\uff0c7.22\u8fd9\u4e2a\u6570\u7684\u5c3e\u6570\u5c31\u65e0\u6cd5\u752824bit\u4e8c\u8fdb\u5236\u8868\u793a\uff0c\u5f53\u7136\u5728\u6570\u636e\u5e93\u4e2d\u6d4b\u8bd5\u4e0d\u4f1a\u6709\u95ee\u9898\uff08\u820d\u5165\u4ee5\u540e\u8fd8\u662f7.22\uff09\uff0c\u4f46\u5982\u679c\u53c2\u4e0e\u4e00\u4e9b\u8ba1\u7b97\uff0c\u8bef\u5dee\u79ef\u7d2f\u540e\uff0c\u5c31\u53ef\u80fd\u4ea7\u751f\u8f83\u5927\u7684\u504f\u5dee\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u8ba1\u7b97\u673a\u4e2d\u7684\u4e8c\u8fdb\u5236\u7684\u5c0f\u6570\u540c\u5341\u8fdb\u5236\u4e00\u6837\uff0c\u6bd4\u5982\u5341\u8fdb\u5236\u91cc\u976210.125\u53ef\u4ee5\u5199\u62101.125*10e1\uff0810e1=10^{1}\uff1a\u53731…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[20],"tags":[],"class_list":["post-138","post","type-post","status-publish","format-standard","hentry","category-20"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/feizhaojun.com\/index.php?rest_route=\/wp\/v2\/posts\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/feizhaojun.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/feizhaojun.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/feizhaojun.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/feizhaojun.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=138"}],"version-history":[{"count":2,"href":"https:\/\/feizhaojun.com\/index.php?rest_route=\/wp\/v2\/posts\/138\/revisions"}],"predecessor-version":[{"id":140,"href":"https:\/\/feizhaojun.com\/index.php?rest_route=\/wp\/v2\/posts\/138\/revisions\/140"}],"wp:attachment":[{"href":"https:\/\/feizhaojun.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/feizhaojun.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/feizhaojun.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}