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123.45 = 0.111101101110011,x
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This number would be represented internally by storing the mantissa o .1111 o 11 o 111 o o 11 and the exponent 7 separately. For a 32-bit float type, the mantissa is stored in a 23-bit segment and the exponent in an 8-bit segment, leaving 1 bit for the sign of the number. For a 64-bit double type, the mantissa is stored in a 52-bit segment and the exponent in an 1 l-bit segment. The next example can be used on any computer to determine how many bytes it uses for each type. The program uses the s i zeof operator which returns the size in bytes of the type specified.
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EXAMPLE 3.13 Using the s i z eo f Operator
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This program tells you how much space each of the 12 fundamental types uses:
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main () tout tout tout tout tout tout tout tout tout tout tout tout tout { << << << << << << << << << << << <-=c << 'Number of bytes used:\n"; "\t char: ' << sizeof(char) " \t short: ' << sizeof(short '\t int: " << sizeof(int "\t long: " << sizeof(long "\t unsigned char: ' << sizeof(unsigned char "\tunsigned short: ' CC sizeof(unsigned short "\t unsigned int: ' << sizeof(unsigned int "\t unsigned long: " << sizeof(unsigned long "\t signed char: " << sizeof(signed char " \t float: ' << sizeof(float "\t double: ' << sizeof(double "\t long double: ' << sizeof(long double << << << << << << << -x << << CC << endl; endl; endl; endl; endl; endl; endl; endl; endl; endl; endl; endl;
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The output below shows the sizes for a typical UNIX workstation. On this machine, int and long' are equivalent, unsigned int and unsigned long areequivalent,and double and long double are equivalent. In other words, long is no different from regular on this computer.
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Th.e next program can be used to investigate floating-point types on any computer system. It reads t:he values of various constants from the float. h header file. To access it, the program must include the preprocessor directive:
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#include <float.h>
This is like the #include <ios tream. h> directive that we always include in order to use the tin and tout objects.
EXAMPLE 3.14 Reading from the f 1 oat . h File
This program tells you the precision and magnitude range that the f 1 oat type has on your system:
main () { int fbits = 8*sizeof(float); // each byte contains 8 bits tout << "float uses:\t" << fbits << ' bits:\n\t\t' << FLT-MANT-DIG - 1 << ' bits for its mantissa\n\t\t ' << fbits - FLTJANT-DIG << ' bits for its exponent\n\t\t ' << 1 << l bit for its sign\n" << " to obtain: ' << FLT-DIG << ' sig. digits\n" << ' with minimum value: I' << FLT-MIN << end1 << " and maximum value: ' << FLT MAX << endl;
EJoat.
uses:
32 bits: 23 bit23 far its manthsa
8 bits for its exponknt I. bit for its sign ~~o~obtain:"6'sig. digits' " .with minimw vdhe: 1.17549e-38 and mwcimum vale: 3.40282e+3$
Theconstants header file.
FLT MANT DIG , F L T - DIG , FLT
-MIN, and
MA - X are
definedinthe f1oat.h
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 10m3 to about 3 x 103!
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All floating-point arithmetic is done in double precision. So the only time you should use instead of double is when you are storing large quantities of real numbers and are concerned about storage space or access time.
float
3.8 TYPE CONVERSIONS We saw in 2 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 // value 2 is automatically converted to 2.0
tout << x - 2 << endl;
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 (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);
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