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TeamLRN EAN / UCC  13 Recognizer In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. EAN 13 Maker In None Using Barcode printer for Software Control to generate, create EAN13 image in Software applications. CHAP. 2] EAN13 Reader In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. EAN13 Maker In Visual C# Using Barcode generation for VS .NET Control to generate, create EAN13 image in .NET framework applications. FUNDAMENTAL TYPES
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EAN / UCC  13 Generator In Visual Basic .NET Using Barcode creation for VS .NET Control to generate, create EAN13 image in VS .NET applications. Print Code 128 Code Set B In None Using Barcode generator for Software Control to generate, create Code 128B image in Software applications. This program repeatedly multiplies n by 1000 until it overflows. int main() { // prints n until it overflows: int n=1000; cout << "n = " << n << endl; n *= 1000; // multiplies n by 1000 cout << "n = " << n << endl; n *= 1000; // multiplies n by 1000 cout << "n = " << n << endl; n *= 1000; // multiplies n by 1000 cout << "n = " << n << endl; } n = 1000 n = 1000000 n = 1000000000 n = 727379968 This shows that the computer that ran this program cannot multiply 1,000,000,000 by 1000 correctly. European Article Number 13 Generator In None Using Barcode printer for Software Control to generate, create UPC  13 image in Software applications. Create Barcode In None Using Barcode encoder for Software Control to generate, create bar code image in Software applications. EXAMPLE 2.13 Floatingpoint Overflow
GS1 128 Generation In None Using Barcode creation for Software Control to generate, create GS1 128 image in Software applications. GTIN  12 Generation In None Using Barcode drawer for Software Control to generate, create GS1  12 image in Software applications. This program is similar to the one in Example 2.12. It repeatedly squares x until it overflows. int main() { // prints x until it overflows: float x=1000.0; cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; } x = 1000 x = 1e+06 x = 1e+12 x = 1e+24 x = inf This shows that, starting with x = 1000, this computer cannot square x correctly more than three times. The last output is the special symbol inf which stands for infinity. UPC  E0 Printer In None Using Barcode creation for Software Control to generate, create Universal Product Code version E image in Software applications. EAN13 Creation In ObjectiveC Using Barcode creation for iPad Control to generate, create EAN13 image in iPad applications. Note the difference between integer overflow and floatingpoint overflow. The last output in Example 2.12 is the negative integer 727,379,968 instead of the correct value of 1,000,000,000,000 = 1012. The last output in Example 2.13 is the infinity symbol inf instead of the correct value of 1048. Integer overflow wraps around to negative integers. Floatingpoint overflow sinks into the abstract notion of infinity. Bar Code Encoder In None Using Barcode encoder for Font Control to generate, create bar code image in Font applications. Generating USS Code 128 In .NET Framework Using Barcode creator for Reporting Service Control to generate, create Code 128C image in Reporting Service applications. FUNDAMENTAL TYPES
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Bar Code Generation In None Using Barcode drawer for Word Control to generate, create bar code image in Microsoft Word applications. Linear Barcode Encoder In VS .NET Using Barcode maker for ASP.NET Control to generate, create Linear image in ASP.NET applications. 2.12 ROUNDOFF ERROR Roundoff error is another kind of error that often occurs when computers do arithmetic on rational numbers. For example, the number 1/3 might be stored as 0.333333, which is not exactly equal to 1/3. The difference is called roundoff error. In some cases, these errors can cause serious problems. EXAMPLE 2.14 Roundoff Error This program does some simple arithmetic to illustrate roundoff error: int main() { // illustrates roundoff error:: double x = 1000/3.0;cout << "x = " << x << endl; // x = 1000/3 double y = x  333.0;cout << "y = " << y << endl; // y = 1/3 double z = 3*y  1.0;cout << "z = " << z << endl; // z = 3(1/3)  1 if (z == 0) cout << "z == 0.\n"; else cout << "z does not equal 0.\n"; // z != 0 } x = 333.333 y = 0.333333 z = 5.68434e14 z does not equal 0. In exact arithmetic, the variables would have the values x = 333 1/3, y = 1/3, and z = 0. But 1/3 cannot be represented exactly as a floatingpoint value. The inaccuracy is reflected in the residue value for z. Example 2.14 illustrates an inherent problem with using floatingpoint types within conditional tests of equality. The test (z == 0) will fail even if z is very nearly zero, which is likely to happen when z should algebraically be zero. So it is better to avoid tests for equality with floatingpoint types. The next example shows that roundoff error can be difficult to recognize. EXAMPLE 2.15 Hidden Roundoff Error This program implements the quadratic formula to solve quadratic equations. #include <cmath> // defines the sqrt() function #include <iostream> using namespace std; int main() { // implements the quadratic formula float a, b, c; cout << "Enter the coefficients of a quadratic equation:" << endl; cout << "\ta: "; cin >> a; cout << "\tb: "; cin >> b; cout << "\tc: "; cin >> c; cout << "The equation is: " << a << "*x*x + " << b << "*x + " << c << " = 0" << endl;

