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## Global Constants and Variables

The global constants and variables described in this chapter are found in pspglb.web. Others, of types defined in 3DLDF, are described in subsequent chapters.

 bool ldf_real_float Constants bool ldf_real_double
 Set to 0 or 1 to match the values of the preprocessor macros LDF_REAL_FLOAT and LDF_REAL_DOUBLE. The latter are used for conditional compilation and determine whether real is "typedeffed" to float or double, i.e., whether real is made to be a synonym of float or double using typedef. ldf_real_float and ldf_real_double can be used to control conditional expressions in non-conditionally compiled code.

 real PI Constant
 The value of PI is calculated as 4.0 * arctan(1.0). I believe that a preprocessor macro "PI" was available when I compiled 3DLDF using the DEC C++ compiler, and that it wasn't, when I used GNU CC under Linux, but I'm no longer sure.

 valarray null_coordinates Variable
 Contains four elements, all 0. Used for resetting the sets of coordinates belonging to Points, but only when the DEC C++ compiler is used. This doesn't work when GCC is used.

 real INVALID_REAL Constant
 Actually, INVALID_REAL is the largest possible real value (i.e., float or double) on a given machine. So, from the point of view of the compiler, it's not invalid at all. However, 3DLDF uses it to indicate failure of some kind. For example, the return value of a function returning real can be compared with INVALID_REAL to check whether the function succeeded or failed. An alternative approach would be to use the exception handling facilities of C++ . I do use these, but only in a couple of places, so far.

 real_pair INVALID_REAL_PAIR Constant
 first and second are both INVALID_REAL.

 real INVALID_REAL_SHORT Constant
 first is INVALID_REAL and second is 0.

 real MAX_REAL Variable
 The largest real value permitted in the the elements of Transforms and the coordinates of Points. It is the second largest real value (i.e., float or double) on a given machine (INVALID_REAL is the largest). MAX_REAL is a variable, but it should be used like a constant. In other words, users should never reset its value. It can't be declared const because its value must be calculated using function calls, which can't be done before the entry point of the program, i.e., main(). Therefore, the value of MAX_REAL is calculated at the beginning of main().

 real MAX_REAL_SQRT Variable
 The square root of MAX_REAL. MAX_REAL_SQRT is a variable, but it should be used like a constant. In other words, users should never reset its value. It can't be declared const because its value is calculated using the sqrt() function, which can't be done before the entry point of the program, i.e., main(). Therefore, the value of MAX_REAL_SQRT is set after MAX_REAL is calculated, at the beginning of main(). MAX_REAL_SQRT is used in Point::magnitude() (see Vector Operations). The magnitude of a Point is found by using the formula \sqrtx^2 + y^2 + z^2. x, y, and z are all tested against MAX_REAL_SQRT to ensure that x^2, y^2, and z^2 will all be less than or equal to MAX_REAL before trying to calculate them. Metafont implements an operation called Pythagorean addition, notated as "++"which can be used to calculate distances without first squaring and then taking square roots:1 a++b == \sqrt(a^2 + b^2) and a++b++c == \sqrt(a^2 + b^2 + c^2). This makes it possible to calculate distances for greater values of a, b, and c, that would otherwise cause floating point errors. Metafont also implements the inverse operation Pythagorean subtraction, notated as "+-+": a+-+b == \sqrt(a^2 - b^2). Unfortunately, 3DLDF implements neither Pythagorean addition nor subtraction as yet, but it's on my list of "things to do".

#### Footnotes

1. Knuth, Donald E. The Metafontbook, p. 66.