Approximations for hand calculators using small integer coefficients

Author:

Derenzo Stephen E.

Abstract

Methods are presented for deriving approximations containing small integer coefficients. This approach is useful for electronic hand calculators and programmable calculators, where it is important to minimize the number of keystrokes necessary to evaluate the function. For example, the probability P ( x ) P(x) of exceeding x standard deviations of either sign (Gaussian probability integral) is approximated by \[ P ( x ) EXP [ ( 83 x + 351 ) x + 562 703 / x + 165 ] P(x) \approx {\text {EXP}}\left [ { - \frac {{(83x + 351)x + 562}}{{703/x + 165}}} \right ] \] with a relative error less than 0.042

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference9 articles.

1. Approximations for Digital Computers

2. J. F. HART ET AL., Computer Approximations, Wiley, New York, 1968.

3. For cases where the absolute error 𝑔(𝑥)-𝑓(𝑥) is important, 𝑤(𝑥) is equal to a constant. For cases where the relative error (𝑔(𝑥)-𝑓(𝑥))/𝑓(𝑥) is important, 𝑤(𝑥) is proportional to 1/𝑓(𝑥).

4. STEPHEN E. DERENZO, Lawrence Radiation Laboratory Group A Programming Note P-190, Berkeley, Calif., 1969. Most other minimizing codes can also be used.

5. STEPHEN E. DERENZO, Lawrence Berkeley Laboratory Report No. LBL-3804, Berkeley, Calif., March, 1975. (Available from the author.)

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