Modern-CPP-Programming/htmls/04.Basic_Concepts_II.html

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/*!
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* https://github.com/pdf2htmlEX/pdf2htmlEX/blob/master/share/LICENSE
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2024-03-31 01:05:40 +01:00
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2024-03-31 01:05:40 +01:00
<ul><li><a class="l" href="#pf5" data-dest-detail='[5,"XYZ",28.346,255.118,null]'>Integral Data Types</a><ul><li><a class="l" href="#pfa" data-dest-detail='[10,"XYZ",28.346,212.159,null]'>Fixed Width Integers</a></li><li><a class="l" href="#pfd" data-dest-detail='[13,"XYZ",28.346,228.21,null]'>size_t and ptrdiff_t</a></li><li><a class="l" href="#pfe" data-dest-detail='[14,"XYZ",28.346,204.571,null]'>Signed/Unsigned Integer Characteristics</a></li><li><a class="l" href="#pf14" data-dest-detail='[20,"XYZ",28.346,228.21,null]'>Promotion, Truncation</a></li><li><a class="l" href="#pf18" data-dest-detail='[24,"XYZ",28.346,228.21,null]'>Undefined Behavior</a></li></ul></li><li><a class="l" href="#pf20" data-dest-detail='[32,"XYZ",28.346,255.118,null]'>Floating-point Types and Arithmetic</a><ul><li><a class="l" href="#pf21" data-dest-detail='[33,"XYZ",28.346,228.21,null]'>IEEE Floating-point Standard and Other Representations</a></li><li><a class="l" href="#pf2a" data-dest-detail='[42,"XYZ",28.346,217.069,null]'>Normal/Denormal Values</a></li><li><a class="l" href="#pf2c" data-dest-detail='[44,"XYZ",28.346,228.21,null]'>Infinity ()</a></li><li><a class="l" href="#pf2e" data-dest-detail='[46,"XYZ",28.346,228.21,null]'>Not a Number (NaN)</a></li><li><a class="l" href="#pf30" data-dest-detail='[48,"XYZ",28.346,186.503,null]'>Machine Epsilon</a></li><li><a class="l" href="#pf31" data-dest-detail='[49,"XYZ",28.346,228.21,null]'>Units at the Last Place (ULP)</a></li><li><a class="l" href="#pf33" data-dest-detail='[51,"XYZ",28.346,228.21,null]'>Cheatsheet</a></li><li><a class="l" href="#pf36" data-dest-detail='[54,"XYZ",28.346,228.21,null]'>Limits and Useful Functions</a></li></ul></li><li><a class="l" href="#pf38" data-dest-detail='[56,"XYZ",28.346,255.118,null]'>tmp</a><ul><li><a class="l" href="#pf38" data-dest-detail='[56,"XYZ",28.346,203.183,null]'>Arithmetic Properties</a></li><li><a class="l" href="#pf3b" data-dest-detail='[59,"XYZ",28.346,228.21,null]'>Special Values Behavior</a></li><li><a class="l" href="#pf3c" data-dest-detail='[60,"XYZ",28.346,228.21,null]'>Floating-Point Undefined Behavior</a></li><li><a class="l" href="#pf3d" data-dest-detail='[61,"XYZ",28.346,228.21,null]'>Detect Floating-point Errors </a></li></ul></li><li><a class="l" href="#pf3f" data-dest-detail='[63,"XYZ",28.346,255.118,null]'>Floating-point Issues</a><ul><li><a class="l" href="#pf45" data-dest-detail='[69,"XYZ",28.346,214.682,null]'>Catastrophic Cancellation</a></li><li><a class="l" href="#pf4a" data-dest-detail='[74,"XYZ",28.346,228.21,null]'>Floating-point Comparison</a></li></ul></li></ul></div>
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2024-03-31 01:05:40 +01:00
<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="data:image/png;base64,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"/><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Mo<span class="_ _0"></span>dern<span class="_ _1"> </span>C++</div><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">Programming</div><div class="t m0 x2 h3 y3 ff2 fs1 fc0 sc0 ls0 ws0">3.<span class="_ _2"> </span>Basic<span class="_ _3"> </span>Concepts<span class="_ _3"> </span>I<span class="_ _0"></span>I</div><div class="t m0 x3 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">Integral<span class="_ _4"> </span>and<span class="_ _4"> </span>Flo<span class="_ _5"></span>a<span class="_ _6"></span>ting-point<span class="_ _4"> </span>Types</div><div class="t m0 x1 h5 y5 ff3 fs3 fc0 sc0 ls0 ws0">F<span class="_ _5"></span>ederico<span class="_ _7"> </span>Busato</div><div class="t m0 x4 h6 y6 ff4 fs4 fc0 sc0 ls0 ws0">2024-03-29</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA4wAAAH/CAIAAACTgcSzAAAACXBIWXMAABYlAAAWJQFJUiTwAAAJEklEQVR42u3cMWoVURSA4RmdkzKd6cVqaguRMMUUBnE3rsJNuJcpxsIdTJMdWNkYOJWdoDIkjyfe85jv68JNAvfkFj8n8PpXb247AAAo4/7rl2emAABANSIVAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAEQqAAAiFQAARCoAACIVAABEKgAAIhUAAEQqAAAiFQAARCoAAIhUAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAQKQCACBSAQBApAIAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAIBf+sw0BQAA6ogIm1QAAMoRqQAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQBApAIAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAABEKgAAIhUAAEQqAAAiFQAARCoAACIVAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAAEQqAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAIFIBAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAACIVAACRCgAATzBc+gXGaT7nx7d18QgAAKqxSQUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgAAIhUAAJEKAADn6TPTFAAAqCMibFIBAChHpAIAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAIFIBAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAIBIBQCAtobD3nyc5r2jbV28DACAhmxSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQAQqQAA0FqfmaYAAEAdEWGTCgBAOSIVAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAEQqAAAiFQAARCoAACIVAABEKgAAIhUAAEQqAAAiFQAARCoAAIhUAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAAAQqQAAiFQAADjJcNibj9O8d7Sti5cBANCQTSoAACIVAABEKgAAIhUAAEQqAAAiFQAARCoAAIczGMFl+fvjXX2qa1s/Hh5e333wRwGAf6vPTFMAAKCOiPDvfgAAyhGpAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAIFIBAECkAgCASAUAQKQCAMBJhsPefJzmvaNtXbwMAICGbFIBABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBABCpAADQWp+ZpgAAQB0RYZMKAEA5IhUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQAARCoAACIVAABEKgAAIhUAAEQqAAAiFQAARCoAACIVAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAABCpAACIVAAAEKkAAFy24bA3H6d572hbFy8DAKAhm1QAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAAEQqAAC01memKQAAUEdE2KQCAFCOSAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAEQqAAAiFQAATjIc9ubjNO8dbeviZQAANGSTCgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgCASAUAgNb6zDQFAADqiAibVAAAyhGpAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAIFIBAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAEQqAAAiFQAARCoAACIVAABEKgAAIhUAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAQKQCACBSAQBApAIAIFIBAECkAgAgUgEAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQAARCoAACIVAABEKgAAIhUAAEQqAAAiFQAARCoAAIhUAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAAPjT8P3Ty0e/6du7zyYFAMD/Mb593328vuq6rutedP1Zv8tKtoWr3766MRAATvTcCCjqJzmrO7h4dD3wAAAAAElFTkSuQmCC"/><div class="t m0 x5 h7 y7 ff1 fs3 fc1 sc0 ls0 ws0">T<span class="_ _6"></span>able<span class="_ _8"> </span>of<span class="_ _8"> </span>Contents</div><div class="t m0 x6 h8 y8 ff1 fs4 fc2 sc0 ls0 ws0">1<span class="_ _9"> </span><span class="fs2 fc0">Integral<span class="_ _4"> </span>Data<span class="_ _a"> </span>T<span class="_ _b"></span>yp<span class="_ _c"></span>es</span></div><div class="t m0 x7 h6 y9 ff4 fs4 fc0 sc0 ls0 ws0">Fixed<span class="_ _d"> </span>Width<span class="_ _d"> </span>Integers</div><div class="t m0 x7 h6 ya ff5 fs4 fc0 sc0 ls0 ws0">size<span class="_ _7"> </span>t<span class="_ _d"> </span><span class="ff4">and<span class="_ _d"> </span></span>ptrdiff<span class="_ _e"> </span>t</div><div class="t m0 x7 h6 yb ff4 fs
<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA4wAAAH/CAIAAACTgcSzAAAACXBIWXMAABYlAAAWJQFJUiTwAAAJNElEQVR42u3YMY7UQBBAUTe4NiSDfEXkEyCEHDhA4jqcYi+xd3FgAm7ghBsQkVa0GRKBg9Gs1GX8XjZqjaUudfBV7eOnLwMAAJTx6+ePN6YAAEA1IhUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQAARCoAACIVAABEKgAAIhUAAEQqAAAiFQAARCoAACIVAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQBApAIAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAIFIBAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAgL9aZpoCAAB1RIRNKgAA5YhUAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQBApAIAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAIFIBAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAAJEKAIBIBQAAkQoAwJmNZ7/ANC/3/H3fVo8AAKAam1QAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAAEQqAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAIFIBADiZlpmmAABAHRFhkwoAQDkiFQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAABEKgAAIhUAAEQqAAAiFQAARCoAACIVAABEKgAAIhUAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAAEQqAAD0NV725tO8HB3t2+plAAB0ZJMKAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAIBIBQCA3lpmmgIAAHVEhE0qAADliFQAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAAEQqAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBAECkAgAgUgEA4CbjZW8+zcvR0b6tXgYAQEc2qQAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAiFQAAOitZaYpAABQR0TYpAIAUI5IBQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQAARCoAACIVAABEKgAA5zZe9ubTvBwd7dvqZQAAdGSTCgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgCASAUAgN5aZpoCAAB1RIRNKgAA5YhUAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQBApAIAIFIBAOAm42VvPs3L0dG+rV4GAEBHNqkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAAIhUAADorWWmKQAAUEdE2KQCAFCOSAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAEQqAAAiFQAARCoAAOc2Xvbm07wcHe3b6mUAAHRkkwoAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAgEgFAIDeWmaaAgAAdUSETSoAAOWIVAAARCoAAIhUAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAQKQCACBSAQDgJuNlbz7Ny9HRvq1eBgBARzapAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAA6K1lpikAAFBHRNikAgBQjkgFAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAABEKgAAIhUAAEQqAADnNl725tO8HB3t2+plAAB0ZJMKAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAMDltMw0BQAA6ogIm1QAAMoRqQAAiFQAABCpAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQBApAIAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAgEgFAECkAgCASAUA4NzGy958mpejo31bvQwAgI5sUgEAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAANBby0xTAACgjoiwSQUAoByRCgCASAUAAJEKAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAAAiFQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQAAkQoAACIVAABEKgAAIhUAAEQqAAAiFQAARCoAACIVAABEKgAAiFQAAEQqAACIVAAARCoAAIhUAABEKgAAiFQAAEQqAACIVAAAEKkAAIhUAAAQqQAAiFQAABCpAACIVAAAEKkAACBSAQAQqQAAIFIBABCpAAAgUgEAEKkAACBSAQAQqQAAIFIBAECkAgAgUgEAQKQCACBSAQBApAIAIFIBAECkAgCASAUAQKQCAIBIBQBApAIAgEgFAECkAgCASAUAQKQCAIBIBQAAkQoAgEgFAACRCgCASAUAAJEKAIBIBQAAkQoAACIVAACRCgAAIhUAAJEKAAAiFQCA/9X45+nxVT70++uzaQIAcL/p87fh+7uHYRiG4f3Q7vqWlWwPD//8+mAgANzorRFQ1AvTVkSwP1FgcAAAAABJRU5ErkJggg=="/><div class="t m0 x5 h7 y7 ff1 fs3 fc1 sc0 ls0 ws0">T<span class="_ _b"></span>able<span class="_ _f"> </span>of<span class="_ _8"> </span>Contents</div><div class="t m0 x6 h8 yf ff1 fs4 fc2 sc0 ls0 ws0">2<span class="_ _9"> </span><span class="fs2 fc0">Floating-p<span class="_ _c"></span>oint<span class="_ _a"> </span>T<span class="_ _b"></span>yp<span class="_ _c"></span>es<span class="_ _4"> </span>and<span class="_ _a"> </span>Arithmetic</span></div><div class="t m0 x7 h6 y10 ff4 fs4 fc0 sc0 ls0 ws0">IEEE<span class="_ _d"> </span>Floating-p<span class="_ _c"></span>oint<span class="_ _d"> </span>Standa<span class="_ _5"></span>rd<span class="_ _d"> </span>and<span class="_ _d"> </span>Other<span
<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="data:image/png;base64,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"/><div class="t m0 x5 h7 y7 ff1 fs3 fc1 sc0 ls0 ws0">T<span class="_ _b"></span>able<span class="_ _f"> </span>of<span class="_ _8"> </span>Contents</div><div class="t m0 x7 h6 y18 ff4 fs4 fc0 sc0 ls0 ws0">Arithmetic<span class="_ _d"> </span>Prop<span class="_ _c"></span>erties</div><div class="t m0 x7 h6 y19 ff4 fs4 fc0 sc0 ls0 ws0">Sp<span class="_ _c"></span>ecial<span class="_ _d"> </span>V<span class="_ _5"></span>alues<span class="_ _d"> </span>Behavio<span class="_ _5"></span>r</div><div class="t m0 x7 h6 y1a ff4 fs4 fc0 sc0 ls0 ws0">Floating-P<span class="_ _5"></span>oint<span class="_ _d"> </span>Undefined<span class="_ _d"> </span>Behavior</div><div class="t m0 x7 h6 y1b ff4 fs4 fc0 sc0 ls0 ws0">Detect<span class="_ _d"> </span>Floating-p<
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