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 Trigonometric Optimizations

The most commonly used trigonometric functions are sine, cosine, arcsine, arccosine, arctangent, and atan2. Trigonometric optimization techniques for these functions fall into two categories:

  • Lookup table-based approximations
  • Polynomial approximations

These techniques are described in the following sections and the polynomial-based optimization techniques used by the TI Arm® Trigonometric Library are discussed.