ssrs upc-a #include <cfloat> in Software

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#include <cfloat>
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This is like the #include <iostream> directive that we always include in order to use the cin and cout objects. EXAMPLE 2.9 Reading from the <cfloat> Header File
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This program tells you the precision and magnitude range that the float type has on your system: #include <cfloat> // defines the FLT constants #include <iostream> // defines the FLT constants using namespace std; int main() { // prints the storage sizes of the fundamental types: int fbits = 8*sizeof(float); // each byte contains 8 bits cout << "float uses " << fbits << " bits:\n\t" << FLT_MANT_DIG - 1 << " bits for its mantissa,\n\t " << fbits - FLT_MANT_DIG << " bits for its exponent,\n\t " << 1 << " bit for its sign\n" << " to obtain: " << FLT_DIG << " sig. digits\n"
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<< " with minimum value: " << FLT_MIN << endl << " and maximum value: " << FLT_MAX << endl; 32 bits: bits for its mantissa, bits for its exponent, bit for its sign to obtain: 6 sig. digits with minimum value: 1.17549e-38 and maximum value: 3.40282e+38 The constants FLT_MANT_DIG, FLT_DIG, FLT_MIN, and FLT_MAX are defined in the <cfloat> header file. This output is from a UNIX workstation. It shows that the 32 bits it uses to store a float are partitioned into 3 parts: 23 bits for the mantissa, 8 bits for the exponent, and 1 bit for the sign. The 23-bit mantissa produces a floating-point value with 6 significant digits, and the 8-bit exponent yields a range in magnitude from about 10 37 to about 3 1038. i.e.,
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0.0000000000000000000000000000000000001 < |x| < 300,000,000,000,000,000,000,000,000,000,000,000,000
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} float uses 23 8 1
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for any variable x declared to have type float.
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All floating-point arithmetic is done in double precision. So the only time you should use float instead of double is when you are storing large quantities of real numbers and are concerned about storage space or access time. 2.10 TYPE CONVERSIONS We saw in 1 how one integer type can be converted automatically to another. C++ also converts integral types into floating point types when they are expected. For example,
int n = 22; float x = 3.14159; x += n; // the value 22 is automatically converted to 22.0 cout << x - 2 << endl; // value 2 is automatically converted to 2.0
Converting from integer to float like this is what one would expect and is usually taken for granted. But converting from a floating point type to an integral type is not automatic. In general, if T is one type and v is a value of another type, then the expression
T(v)
converts v to type T. This is called type casting. For example, if expr is a floating-point expression and n is a variable of type int, then
n = int(expr);
converts the value of expr to type int and assigns it to n. The effect is to remove the real number s fractional part, leaving only its whole number part to be assigned to n. For example, 2.71828 would be converted to 2. Note that this is truncating, not rounding. EXAMPLE 2.10 Simple Type Casting
This program casts a double value into int value: int main() { // casts a double value as an int: double v = 1234.56789; int n = int(v);
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[CHAP. 2
cout << "v = " << v << ", n = " << n << endl; } v = 1234.57, n = 1234 The double value 1234.56789 is converted to the int value 1234.
When one type is to be converted to a higher type, the type case operator is not needed. This is called type promotion. Here s a simple example of promotion from char all the way up to double: EXAMPLE 2.11 Promotion of Types
This program promotes a char to a short to an int to a float to a double: int main() { // prints promoted vales of 65 from char to double: char c='A'; cout << " char c = " << c << endl; short k=c; cout << " short k = " << k << endl; int m=k; cout << " int m = " << m << endl; long n=m; cout << " long n = " << n << endl; float x=m; cout << " float x = " << x << endl; double y=x; cout << "double y = " << y << endl; } char c = A short k = 65 int m = 65 long n = 65 float x = 65 double y = 65 The integer value of the character 'A' is its ASCII code 65. This value is converted as a char in c, a short in k, an int in m, and a long in n. The value is then converted to the floating point value 65.0 and stored as a float in x and as a double in y. Notice that cout prints the integer c as a character, and that it prints the real numbers x and y as integers because their fractional parts are 0.
Because it is so easy to convert between integer types and real types in C++, it is easy to forget the distinction between them. In general, integers are used for counting discrete things, while reals are used for measuring on a continuous scale. This means that integer values are exact, while real values are approximate. Note that type casting and promotion convert the type of the value of a variable or expression, but it does not change the type of the variable itself. In the C programming language, the syntax for casting v as type T is (T) v. C++ inherits this form also, so we could have done n = int(v) as n = (int) v. 2.11 NUMERIC OVERFLOW On most computers the long int type allows 4,294,967,296 different values. That s a lot of values, but it s still finite. Computers are finite, so the range of any type must also be finite. But in mathematics there are infinitely many integers. Consequently, computers are manifestly prone to error when their numeric values become too large. That kind of error is called numeric overflow.
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