/* chbevl.c * * Evaluate Chebyshev series * * * * SYNOPSIS: * * int N; * double x, y, coef[N], chebevl(); * * y = chbevl( x, coef, N ); * * * * DESCRIPTION: * * Evaluates the series * * N-1 * - ' * y = > coef[i] T (x/2) * - i * i=0 * * of Chebyshev polynomials Ti at argument x/2. * * Coefficients are stored in reverse order, i.e. the zero * order term is last in the array. Note N is the number of * coefficients, not the order. * * If coefficients are for the interval a to b, x must * have been transformed to x -> 2(2x - b - a)/(b-a) before * entering the routine. This maps x from (a, b) to (-1, 1), * over which the Chebyshev polynomials are defined. * * If the coefficients are for the inverted interval, in * which (a, b) is mapped to (1/b, 1/a), the transformation * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity, * this becomes x -> 4a/x - 1. * * * * SPEED: * * Taking advantage of the recurrence properties of the * Chebyshev polynomials, the routine requires one more * addition per loop than evaluating a nested polynomial of * the same degree. * */ /* chbevl.c */ /* Cephes Math Library Release 2.0: April, 1987 Copyright 1985, 1987 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ double chbevl (double x, double *array, int n) { double b0, b1, b2, *p = array; int i; b0 = *p++; b1 = 0.0; i = n - 1; do { b2 = b1; b1 = b0; b0 = x * b1 - b2 + *p++; } while (--i); return 0.5 * (b0-b2); }

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