Chimera Compute Library (CCL) API Reference

1. Data Access Patterns
2. Discrete Fourier Transforms
3. Elementary Math Functions
4. Image Processing
5. Linear Algebra
6. Processor Elementwise (PE) Operations
7. Neural Network Blocks
8. N-Dimensional Arrays
9. Python Host API Guide
10. Tilewise Operations
11. Tensor Manipulation
12. experimental::Device C++ APIs
13. Software Interrupt and Host Synchronization

Reading FixedPoint Fractional Bit Error Plots

Some kernels documented in this CCL API Reference may include FixedPoint32 Fractional Bit error plots. These error plots show the maximum absolute error between the algorithm's CCL (quadratic) implementation and the adapted CPU implementation (performed in float64 arithmetic using NumPy/SciPy libraries) across all q number of fractional bits that could be used for an input value's FixedPoint32 representation.

When reading these plots, the x-axis will always show the number of fractional bits used in the input's FixedPoint32 representation and the y-axis displays the maximum absolute error between the CCL implementation and the CPU implementation of the algorithm.

NOTE: Please note that the graph is a semi-log plot; the x-axis uses a linear scale while the y-axis employs a logarithmic scale with a base of 2. In addition to the error curve, we overlay a curve representing machine epsilon, which is equal to 2^-frac_bits.

When interpreting the results of these graphs, an accurate algorithm is one with a maximum absolute error near machine epsilon, i.e. when the curve most closely approximates the machine epsilon curve. Some algorithms produce outputs with a different number of fractional bits than the input. In these cases, we compare the error to the machine epsilon corresponding to the output's number of fractional bits.