New Skill Forged: Elementary Functions: Algorithms and Implementation

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New Skill Forged

Elementary Functions: Algorithms and Implementation, 2nd Ed. by Jean-Michel Muller. 270 pages.

Rigorous treatment of transcendental function implementation: IEEE 754 fundamentals (ULPs, rounding modes, FMA, subnormals), polynomial approximation via Chebyshev/Remez minimax, Horner/Estrin evaluation, range reduction (Cody-Waite, Payne-Hanek for large arguments), CORDIC for sin/cos/atan, and correct-rounding via Ziv’s multilevel strategy.

What this skill teaches Claude to do:

  • Evaluate polynomials efficiently using Horner’s method (sequential) or Estrin’s method (pipelined)
  • Design minimax polynomial approximations using Chebyshev polynomials and the Remez algorithm
  • Implement range reduction for exp/log/sin/cos using Cody-Waite or Payne-Hanek techniques
  • …and 3 more

Browse the full skill at /skills/elementary-functions

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