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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_530</title> <link rel="stylesheet" href="reset.css" type="text/css" media="all"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> </head> <body> <table summary="top nav" border="0" width="100%"> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_529.html">< previous page</a></td> <td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_530</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_531.html">next page ></a></td> </tr> <tr> <td align="left" colspan="3" style="background: #ffffff; padding: 20px;"> <table border="0" width="100%" cellpadding="0"><tr><td align="center"> <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td> <td align="right"></td> </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 530</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Also because of representational errors, we should never compare floating point numbers for exact equality. Rarely are two floating point numbers exactly equal, and thus they should be compared only for near equality. If the difference between the two numbers is less than some acceptable small value, we can consider them equal for the purposes of the given problem.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><i>Implementation of Floating Point Numbers in the Computer</i></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Let's formally define some of the terms we used informally in the previous section.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="96" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="96" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td></tr><tr><td colspan="3" height="2"><table cellpadding="0" cellspacing="0" border="0"><tr><td></td></tr></table></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2">Significant Digits Those digits from the first nonzero digit on the left to the last nonzero digit on the right (plus any zero digits that are exact).</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="96" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="96" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2">Precision The maximum number of significant digits.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="96" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="96" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2">Representational Error Arithmetic error that occurs when the precision of the true result of an arithmetic operation is greater than the precision of the machine.</font></td><td></td></tr><tr><td colspan="3" height="2"><table cellpadding="0" cellspacing="0" border="0"><tr><td></td></tr></table></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">All computers limit the precision of a floating point number, although most machines use binary rather than decimal arithmetic. In our representation, we used only 5 digits to simplify the examples, and some computers really are limited to only 4 or 5 digits of precision. A more typical system might provide 6 significant digits for </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">float</font><font face="Times New Roman, Times, Serif" size="3"> values, 15 digits for </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">double</font><font face="Times New Roman, Times, Serif" size="3"> values, and 19 for the </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">long聽double</font><font face="Times New Roman, Times, Serif" size="3"> type. We have shown only a single-digit exponent, but most systems allow 2 digits for the </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">float</font><font face="Times New Roman, Times, Serif" size="3"> type and up to 4-digit exponents for type </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">long聽double</font><font face="Times New Roman, Times, Serif" size="3">.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">When you declare a floating point variable, part of the memory location is assumed to contain the exponent, and the number itself (called the <i>mantissa</i>) is assumed to be in the balance of the location. The system is called floating point representation because the number of significant digits is fixed, and the decimal point conceptually floats (is moved to different positions as necessary). In our coding scheme, every number is stored as four digits, with the leftmost being nonzero, and the exponent adjusted accordingly. The number 1,000,000 was stored as</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="f32ae64b8194b3ed1eb8694d7ebf49a6.gif" border="0" alt="0530-01.gif" width="138" height="29" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">and 0.1032 was stored as</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="a9c537486694b3c53dea4fe25cd995e7.gif" border="0" alt="0530-02.gif" width="141" height="33" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><p><font size="0"></font></p>聽 </td> </tr> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_529.html">< previous page</a></td> <td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_530</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_531.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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