SPRAD27A July   2022  – August 2022 AM2431 , AM2432 , AM2434 , AM2631 , AM2631-Q1 , AM2632 , AM2632-Q1 , AM2634 , AM2634-Q1 , AM2732 , AM2732-Q1 , AM6411 , AM6412 , AM6421 , AM6422 , AM6441 , AM6442

 

  1.   Abstract
  2.   Trademarks
  3. 1Introduction
  4. 2Trigonometric Optimizations
    1. 2.1 Lookup Table-Based Approximation
    2. 2.2 Polynomial Approximation
      1. 2.2.1 Optimizing Sine and Cosine
        1. 2.2.1.1 Sine Cosine Polynomials From Sollya
      2. 2.2.2 Optimizing Arctangent and Arctangent2
        1. 2.2.2.1 Arctangent Polynomials
  5. 3Trig Library Benchmarks
    1. 3.1 C Math.h Library
    2. 3.2 Arm “Fast Math Functions” in CMSIS
    3. 3.3 TI Arm Trig Library
    4. 3.4 Table of Results
  6. 4Optimizations
    1. 4.1 Branch Prediction
    2. 4.2 Floating-Point Single-Precision Instructions
    3. 4.3 Memory Placement
    4. 4.4 Compiler
  7.   Revision History

2.1 Lookup Table-Based Approximation

Up until recently, lookup table-based approximations were considered faster than polynomial-based approximations. Lookup table-based approximations pre-compute N values of the target function and then index them into the table to select the two closest points and perform an interpolation between them. When using lookup table-based approximations, the accuracy can be adjusted by changing either the size of the lookup or the order of the interpolation function. However, this comes with the tradeoff of more memory usage and longer function times. This is the technique used by the Fast Math Functions in the Arm CMSIS Library where they use a table size of 512 entries to cover 0-2PI and then do a linear interpolation between the closest values.