Floating Point versus Fixed point Tradeoffs in FPGA Implementations of QR Decomposition Algorithm

Floating-point to Fixed-point Conversion

Converting floating - point applications to fixed - point

Without knowledge of the issues, the right tools, and a well-thought out development methodology, floating-point applications can in fact suffer the same problems as fixed-point equivalents. The reduced precision and range of fixed-point numbers means that fixed-point applications encounter stability problems more easily than floating-point applications, but both types of applications encounter...

Automatic Conversion of Floating Point MATLAB Programs into Fixed Point FPGA Based Hardware Design

Most practical FPGA designs are limited to finite precision signal processing using fixed-point arithmetic because of the cost and complexity of floating point hardware. While mapping DSP applications onto FPGAs, a DSP algorithm designer, who often develops his applications in MATLAB, must determine the dynamic range and desired precision of input, intermediate and output signals in a design im...

Certifying floating-point implementations using Gappa

High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well bounded. Such work may require several lines of proof for each line of code, and will usually be broken by the smallest change to the code (e.g. for maintenance or...

Floating- to fixed-point MATLAB algorithm conversion for FPGAs

Although MATLAB is a powerful algorithm development tool, many of its benefits are reduced during the fixed-point conversion process. For example, new mathematical errors are introduced into the algorithm because of the reduced precision of the fixed-point arithmetic. You must rewrite code to replace high-level functions and operators with low-level models that reflect the actual hardware macro...