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探秘 JavaScript 世界的神秘数字 1.7976931348623157e+308
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","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"01111111011","attrs":{}}],"attrs":{}},{"type":"text","text":"：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/f6/f64fda7b0ad734c7939d03315e7a487a.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"再来看尾数部分：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/80/80c92c6b9d8d9cc8248d819427405a99.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"1 开始，0111 循环，到了第 52 位为 1，但是需要额外注意，第 53 位仍然是 1，舍去需要进 1，尾数部分变为了（为了方便阅读，使用了 ES2021 的","attrs":{}},{"type":"link","attrs":{"href":"https://github.com/tc39/proposal-numeric-separator","title":"","type":null},"content":[{"type":"text","text":"数值分隔符","attrs":{}}]},{"type":"text","text":"） 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：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/fd/fde4e1e2580f779a2a729f46a37f83cc.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"共 10 位，头部补 0 得到 11 位指数 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0.1 指数位调整到 1020，因此尾数位需要右移，注意规约数小数点前的 1 也要右移，变为尾数部分变为 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\n+ 0b11_0011_0011_0011_0011_0011_0011_0011_0011_0011_0011_0011_0011_01\n).toString(2)\n","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"得到结果 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"10110011001100110011001100110011001100110011001100111","attrs":{}}],"attrs":{}},{"type":"text","text":" ，共 53 位。这块需要特别注意，规约数小数点左侧默认为 1，现在加法之后多出一位，小数点左侧 +1，变为了 ","attrs":{}},{"type":"katexinline","attrs":{"mathString":"(10)_2"}},{"type":"text","text":"，可以理解为 ","attrs":{}},{"type":"katexinline","attrs":{"mathString":"(10.0110011001100110011001100110011001100110011001100111)_2"}},{"type":"text","text":" 这个数字。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"小数点需要左移动，指数 +1，变为 1021，尾数需要舍去 1 位，由于尾数为 1，需要进 1，代入公式：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"katexblock","attrs":{"mathString":"1.0011001100110011001100110011001100110011001100110100 * 2^{1021 - 1023}\n\n\\\\= 10011001100110011001100110011001100110011001100110100* 2^{-2 - 52}\n\n\\\\= 10011001100110011001100110011001100110011001100110100* 2^{-54}"}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"用 JavaScript 验证：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":"javascript"},"content":[{"type":"text","text":"0b10011001100110011001100110011001100110011001100110100 * (2**-54) // 0.30000000000000004\n0b10011001100110011001100110011001100110011001100110100 * (2**-54) === 0.1 + 0.2 // true\n","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/82/82ebda0bf15204795e238d653dd89963.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"没问题，验证结束。","attrs":{}}]},{"type":"heading","attrs":{"align":null,"level":2},"content":[{"type":"text","marks":[{"type":"color","attrs":{"color":"#3db243","name":"user"}}],"text":"参考资料","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"bulletedlist","content":[{"type":"listitem","attrs":{"listStyle":null},"content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"link","attrs":{"href":"https://zh.wikipedia.org/wiki/IEEE_754","title":"","type":null},"content":[{"type":"text","text":"IEEE 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