Standard Fast DCT algorithm

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I’m looking for a standard Fast DCT algorithm that the industry has settled on.

From what I can tell, there are various papers which describe different algorithms e.g.:

  1. A Fast Computational Algorithm for the Discrete Cosine Transform (Chen, Smith, Fralick, 1977)
  2. A new algorithm to compute the discrete cosine Transform (Lee, 1984)

plus maybe c. 2,000 other papers in the field.

The algorithm in 2) seems objectively more efficient than the algorithm in 1), because it uses fewer arithmetic operations.

But is the approach of 2) industry standard for software/hardware implementation? Or is there something else which is more efficient, or has lower rounding error?