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- 15.3.12. Fully-Parallel FFTs with Flexible Ordering (FFT2X, FFT4X, FFT8X, FFT16X, FFT32X, and FFT64X)
- 15.3.13. General Multitwiddle and General Twiddle (GeneralMultiTwiddle, GeneralMultVTwiddle, GeneralTwiddle, GeneralVTwiddle)
11. Floating-Point Data Types
Floating-point designs are useful in:
- Scientific applications
- Numerical algorithms
- High-dynamic range data designs
- Statistical modelling
Fixed-point designs often cannot support data with a high dynamic range unless the design explicitly uses a high precision type. Floating-point designs can represent data over a high dynamic range with limited precision. A compact representation makes efficient use of memory and minimizes data widths. The lowest precision type that DSP Builder supports is float16_m10, otherwise known as half-precision float, which occupies 16 bits of storage. It can represent a range between –216 to +216 (exclusive) and non-zero magnitudes as small as 2-14.
Typically, fixed-point designs may include fixed-point types of various bit widths and precisions. When you create fixed-point designs, keep variations in word growth and word precision within acceptable limits. When you create floating-point designs, you must limit rounding error to ensure an accurate result. A floating-point design typically has only one or two floating-point data types.
DSP Builder provides a comprehensive library of elementary mathematical functions with complete support for all floating-point types. Each core is parameterized by precision, clock frequency, and device family.
- DSP Builder Floating-Point Data Type Features
- DSP Builder Supported Floating-Point Data Types
The supported floating-point types are either IEEE 754 formats (half, single and double precision) or custom IEEE 754-like formats with user-specified exponent and fraction-field widths .
- DSP Builder Round-Off Errors
Every mathematical operation on floating-point data incurs a round-off error.
- Trading Off Logic Utilization and Accuracy in DSP Builder Designs
- Upgrading Pre v14.0 Designs
DSP Builder designs in v14.0 onwards have floating-point data turned on by default, which provides access to all floating-point data types.
- Floating-Point Sine Wave Generator Tutorial
- Newton-Raphson Root Finding Tutorial
This DSP Builder tutorial implements a floating-point iterative algorithm. The tutorial also demonstrates how to exploit pipeline parallelism.
- Forcing Soft Floating-point Data Types with the Advanced Options
The Add, Sub, Mult, Sum of Elements and Scalar Product blocks have default hard floating-point data types (for devices that implement hard floating-point designs and single precision only).
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