Fixed-Point Math

For fast performance TypeServer is tightly optimized using fix-point arithmetic based on integer math. The TypeServer source code allows you to choose between two fixed-point formats referred to as "F26DOT6" (32-bits, F26.6) and "F12DOT4" (16-bits, F12.4).

The F26DOT6 data type consists of a 26-bit signed mantissa and a positive unsigned 6-bit fraction (32-bits total). This data type is typically used to define fraction pixel positions for 32- and 64-bit processors.

The F12DOT4 data type consists of a 12-bit signed mantissa and a positive unsigned 4-bit fraction (16-bits total). This data type is typically used to define fraction pixel positions for 16- and 8-bit processors.

The F26DOT6 and F12DOT4 data types provide fractional accuracy to 1/64th or 1/16th if a unit, respectively. For example, a pixel position in F26DOT6 format provides fractional accuracy to 1/64th of a pixel.

"FIXDOT" is a special conditional data type equated either to F26DOT6 or F12DOT4 depending if the identifier "FIXDOT26" is defined. Normally FIXDOT26 is defined 32-bit systems, and is left undefined for 16-bit systems (again, this is a TypeServer source code option that is easily changed).

typedef signed long F26DOT6; /* F26.6 signed fixed-point, 32-bit */ typedef struct F26POINT_ /* F26.6 coordinate-point structure */ { F26DOT6 x; F26DOT6 y; } F26POINT; typedef signed short F12DOT4; /* F12.4 signed fixed-point, 16-bit */ typedef struct F12POINT_ /* F12.4 coordinate-point structure */ { F12DOT4 x; F12DOT4 y; } F12POINT; /* FIXDOT conditional data type based on if "FIXDOT26" is defined */ #ifdef FIXDOT26 /* (typically for 32-bit systems) - - - - - - - */ #define FIXDOT F26DOT6 /* FIXDOT is signed fixed-point F26DOT6*/ #define FIXPOINT F26POINT /* F26.6 coordinate-point structure */ #define IntToFix(intValue) (FIXDOT)( (intValue) << 6 ) #else /*FIXDOT12 * (typically for 16-bit systems) - - - */ #define FIXDOT F12DOT4 /* FIXDOT is signed fixed-point F12DOT4*/ #define FIXPOINT F12POINT /* F12.4 coordinate-point structure */ #define IntToFix(intValue) (FIXDOT)( (intValue) << 4 ) #endif /*FIXDOTxx * - - - - - - - - - - - - - - - - - - - - - - - */

For additional information on fixed-point types and math functions, please see Appendix A of the Metagraphics Programming Guidelines Manual (.pdf, 235Kb).