If all the arguments are the same type of number (rational, floating point, or complex), the result will be the same type except in the case where the result of an operation on complex numbers with rational components yields a number with a zero imaginary part, in which case the result will be a rational. However, floating-point and complex numbers are contagious--if all the arguments are reals but one or more are floating-point numbers, the other arguments are converted to the nearest floating-point value in a “largest” floating-point representation of the actual floating-point arguments. Floating-point numbers in a “smaller” representation are also converted to the larger representation. Similarly, if any of the arguments are complex, any real arguments are converted to the complex equivalents.

Two related functions are **MOD** and **REM**, which return the modulus and remainder of a truncating division on real numbers. These two functions are related to the **FLOOR** and **TRUNCATE** functions as follows:

The functions **1+** and provide a shorthand way to express adding and subtracting one from a number. Note that these are different from the macros **INCF** and **DECF**. **1+** and **1-** are just functions that return a new value, but **INCF** and **DECF** modify a place. The following equivalences show the relation between **INCF**/**DECF**, **1+**/**1-**, and /**-**: