STM AN4044

Floating-point calculations require a lot of resources, as for any operation between two numbers. For example, we need to:

• Align the two numbers (have them with the same exponent)
• Perform the operation
• Round out the result
• Code the result

On an FPU-less processor, all these operations are done by software through the C compiler library (or Forth Words) and are not visible to the programmer; but the performances are very low. On a processor having an FPU, all of the operations are entirely done by hardware in a single cycle, for most of the instructions. The C (or Forth) compiler does not use its own floating-point library but directly generates FPU native instructions.

When implementing a mathematical algorithm on a microprocessor having an FPU, the programmer does not have to choose between performance and development time. The FPU brings reliability allowing to use directly any generated code through a high level tool, such as MATLAB or Scilab, with the highest level of performance.

Normalized Numbers Range

IEEE.754 Single and Double Precision Floating-Point Coding

Some Links

• https://forth-standard.org/standard/float
• https://de.wikipedia.org/wiki/IEEE_754