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The complex number class provided by the standard library is an excellent model of an object-based class abstraction Through its use of operator overloading, objects of the complex class type can be used nearly as easily as the simpler built-in arithmetic types As we'll see in this section, not only are the usual arithmetic operators such as addition, subtraction, multiplication, and division supported, but also complex number objects can generally be intermixed with the built-in arithmetic types For the programmer, the complex numbers are a part of the basic language even if their implementation is within the standard library (Note that this section treats only the use of the complex number class; for an introduction to the mathematics of complex numbers, see [PERSON68] or any elementary book on mathematics) One can write, for example:

#include <complex> complex< double > a; complex< double > b; // assign to a and b complex< double > c = a * b + a / b;

complex< double > complex_obj = a + 314159;

Similarly, a complex number can be initialized with or assigned a value of an arithmetic data type, such as

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double dval = 314159; complex_obj = dval;

int ival = 3; complex_obj = ival;

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By identifying the five-month cycle low count and looking at the historical price record, I was able to make a keen observation and share it with my fellow investors A good plan based on good analysis does pay off! This book was not intended to go much into cycle studies However, the amazing repetitiveness of another timing cycle is worth mentioning The equities market seems to respond to what I identified as an 11-week cycle low back in late 2001 The relevance of the 11-week cycle is that it is approximately 55 trading days the number 55 is a Fibonacci series number, and it is approximately half or 50 percent of the five-month cycle The 50 percent Fibonacci ratio number also interacts as a reference with the 11-week cycle So there is a connection with the Fibonacci series and ratio numbers.

The reverse, however, is not automatically supported that is, an arithmetic data type cannot be directly initialized or assigned with a complex number class object For example, the following results in a compile-time error:

// error: no implicit conversion of a complex number // to a built-in arithmetic data type double dval = complex_obj;

Circuit Level Integration Very High Performance (VHPIC) Very Large Scale (VLSI) Large Scale (LSI) Medium Scale (MSI) Small Scale (SSI)

To do this, we must explicitly indicate which component of the complex object we wish to assign The complex number class supports a pair of operations for reading either the real or the imaginary part For example, we can either use the member access syntax

double re = complex_objreal(); double im = complex_objimag();

or the equivalent nonmember syntax:

// equivalent to the member syntax, above double re = real( complex_obj ); double im = imag( complex_obj );

The complex number class supports four compound assignment operators: those of addition (+=), subtraction (-=), multiplication (*=), and division (/=) Thus, we can write, for example:

complex_obj += second_complex_obj;

Both the input and the output of a complex number are supported The output of a complex number is an ordered pair separated by a comma and surrounded by parentheses The first value is the real part, and the second value is the imaginary part For example,

complex< double > complex0( 314159, -2171 );

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Futures magazine printed an article I wrote in the December 2002 issue predicting that the week ending December 29 would be the date to expect.

complex< double > complex1( complex0real() ); cout complex0 " " complex1 endl;

yields the following:

104 103 102 10

( 314159, -2171 ) ( 314159, 00 )

Any of the following forms of numeric representation can be read as a complex number:

// valid input forms of a complex number // 314159 ==> complex( 314159 ); // ( 314159 ) ==> complex( 314159 ); // ( 314, -10 ) ==> complex( 314, -10 ); // could be read in as // cin >> a >> b >> c // where a, b, c are complex numbers 314159 ( 314159 ) ( 314, -10 )

Additional operations supported by the complex number class include sqrt(), abs(), polar(), sin(), cos(), tan(), exp(), log(), log10(), and pow() Exercise 49 In the Rogue Wave implementation of the standard library available to us at the time of this writing, the four compound assignment operators support only a right-hand operand of type complex For example, an attempt to write

complex_obj += 1;

results in a compile-time error, although Standard C++ specifies that the assignment is legal (It is not uncommon to find implementations at this point still lagging behind the Standard) We can fix this lapse by providing our own instance of the compound operators For example, here is a nontemplate instance of compound addition assignment operator for complex<double>:

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