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Floating-Point vs. Fixed-Point Mathematics 
Each statement in the Open Servo can be executed using either floating-point or integer (fixed-point) 
mathematics.  In a floating-point statement, all variables used are processed through an intermediate 
working format that is 48-bit floating-point, regardless of the storage format of the variable.  Floating-
point statements can utilize any of Turbo PMAC’s I, P, Q, or M-variables, and the compiler’s long F-
variable pointers.  They cannot use the compiler’s short fixed-point L-variable pointers.  All constants 
used in these statements are stored as 48-bit floating-point values. 

In an integer statement, all variables used are processed through an intermediate working format that is 
24-bit signed integer, regardless of the storage format of the variable.  Integer statements can only utilize 
the compiler’s short fixed-point L-variable pointers.  They cannot use the compiler’s long F-variable 
pointers, or Turbo PMAC’s I, P, Q, or M-variables.  All constants used in these statements are stored as 
24-bit signed integers.  All constants used and intermediate values computed must fit in the range of these 
integers: -8,388,608 to +8,388,607.  No mathematical functions (e.g. SIN, COS) may be used in an 
integer statement. 

If a constant appears on a line before any variable (e.g. IF (0=P1) …), the line is assumed to be 
floating-point.  This means that the statement IF (0=L1) is illegal, because it mixes floating-point and 
fixed-point data types. 

Short-word integer operations will execute more than 10 times faster than the same operations done as 
long floating-point operations, but usually will not have the dynamic range to handle the actual control 
calculations.  They can be useful for efficient calculation of associated logic, however. 

 PMAC’s built-in servo algorithms (PID and Extended Servo Algorithm) use long 
[48-bit/56-bit] fixed-point mathematics.  This format is not supported in the Open 
Servo. 

If conversion between integer and floating-point data types is required, Open Servo provides the ITOF 
(integer-to-float) and FTOI (float-to-integer) functions.  The ITOF function (with an integer expression 
as its argument) can be used in a floating-point statement, such as: 

The FTOI function (with a floating-point expression as its argument) can be used in a fixed-point 
statement, such as: 

The FTOI function will round the value of the floating-point expression to the nearest integer. 
It is not permissible to nest FTOI and ITOF functions within an expression. 
Arrays.  Open Servo algorithms support two types of arrays: variable arrays and register arrays.  Both 
provide useful capabilities. 

Variable Arrays:  Variable arrays work with the Turbo PMAC’s standard PMAC I, P, Q, and M-
variables.  The number of the array index is placed inside parentheses, and specifies the variable number 
for the specified type of variable.  The expression that determines this number is a floating-point 
expression, so it can use Turbo PMAC I, P, Q, or M-variables, constants (which will be treated as 
floating-point values) and the compiler’s F-variables, but it cannot use the compiler’s L-variables (unless 
the value has been converted to floating-point with the ITOF function).  The resulting value of this 
floating-point expression is rounded to the nearest integer automatically, to select the variable number to 
be used.  Some examples of statements using these variable arrays are: