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The implementation of expf() explains how approximation in the range [0 - 0.34] is done. The comment describes the "Reme" algorithm for constructing the polynomial. This is a typo and should be the "Remez" algorithm. The remez algorithm (or minimax) is used to calculate the coefficients of polynomials in other implementations of exp(0 and log(). See more: https://en.wikipedia.org/wiki/Remez_algorithm