## Computer Evaluation of Mathematical Functions |

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absolute-error function accuracy accurate approximates F(x approximation interval approximation to F(x arccos arcsin argument range asymptotic expansion binary Business Machines Corp chapter Chebyshev polynomials check values compute approximate continued fraction convergence critical points decimal places denote the polynomial derive digits double-precision equations erfc error function Exercise floating-point arithmetic formula function evaluation routine function F(x graph IBM System/360 integer International Business Machines Maclaurin series mantissa manufacturer supplied Fortran Math maximum absolute error maximum relative error minimax absolute error minimax approximation minimax polynomial approximations minimax relative error nested multiplication Newton's method nodes number of iterations odd function Pn(x polynomial of degree polynomial or rational polynomial P*(x power series procedure propagation of rounding range-reduction rational approximation rational function relative-error function Remez rounding error shifted Chebyshev series single-precision square-root routine standard error function starting approximation supplied Fortran library tanh fix tion Tn(x truncation error unstable zero