| /* Translated into C++ by SciPy developers in 2024. | |
| * Original header with Copyright information appears below. | |
| */ | |
| /* polevl.c | |
| * p1evl.c | |
| * | |
| * Evaluate polynomial | |
| * | |
| * | |
| * | |
| * SYNOPSIS: | |
| * | |
| * int N; | |
| * double x, y, coef[N+1], polevl[]; | |
| * | |
| * y = polevl( x, coef, N ); | |
| * | |
| * | |
| * | |
| * DESCRIPTION: | |
| * | |
| * Evaluates polynomial of degree N: | |
| * | |
| * 2 N | |
| * y = C + C x + C x +...+ C x | |
| * 0 1 2 N | |
| * | |
| * Coefficients are stored in reverse order: | |
| * | |
| * coef[0] = C , ..., coef[N] = C . | |
| * N 0 | |
| * | |
| * The function p1evl() assumes that c_N = 1.0 so that coefficent | |
| * is omitted from the array. Its calling arguments are | |
| * otherwise the same as polevl(). | |
| * | |
| * | |
| * SPEED: | |
| * | |
| * In the interest of speed, there are no checks for out | |
| * of bounds arithmetic. This routine is used by most of | |
| * the functions in the library. Depending on available | |
| * equipment features, the user may wish to rewrite the | |
| * program in microcode or assembly language. | |
| * | |
| */ | |
| /* | |
| * Cephes Math Library Release 2.1: December, 1988 | |
| * Copyright 1984, 1987, 1988 by Stephen L. Moshier | |
| * Direct inquiries to 30 Frost Street, Cambridge, MA 02140 | |
| */ | |
| /* Sources: | |
| * [1] Holin et. al., "Polynomial and Rational Function Evaluation", | |
| * https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/roots/rational.html | |
| */ | |
| /* Scipy changes: | |
| * - 06-23-2016: add code for evaluating rational functions | |
| */ | |
| namespace xsf { | |
| namespace cephes { | |
| XSF_HOST_DEVICE inline double polevl(double x, const double coef[], int N) { | |
| double ans; | |
| int i; | |
| const double *p; | |
| p = coef; | |
| ans = *p++; | |
| i = N; | |
| do { | |
| ans = ans * x + *p++; | |
| } while (--i); | |
| return (ans); | |
| } | |
| /* p1evl() */ | |
| /* N | |
| * Evaluate polynomial when coefficient of x is 1.0. | |
| * That is, C_{N} is assumed to be 1, and that coefficient | |
| * is not included in the input array coef. | |
| * coef must have length N and contain the polynomial coefficients | |
| * stored as | |
| * coef[0] = C_{N-1} | |
| * coef[1] = C_{N-2} | |
| * ... | |
| * coef[N-2] = C_1 | |
| * coef[N-1] = C_0 | |
| * Otherwise same as polevl. | |
| */ | |
| XSF_HOST_DEVICE inline double p1evl(double x, const double coef[], int N) { | |
| double ans; | |
| const double *p; | |
| int i; | |
| p = coef; | |
| ans = x + *p++; | |
| i = N - 1; | |
| do | |
| ans = ans * x + *p++; | |
| while (--i); | |
| return (ans); | |
| } | |
| /* Evaluate a rational function. See [1]. */ | |
| /* The function ratevl is only used once in cephes/lanczos.h. */ | |
| XSF_HOST_DEVICE inline double ratevl(double x, const double num[], int M, const double denom[], int N) { | |
| int i, dir; | |
| double y, num_ans, denom_ans; | |
| double absx = std::abs(x); | |
| const double *p; | |
| if (absx > 1) { | |
| /* Evaluate as a polynomial in 1/x. */ | |
| dir = -1; | |
| p = num + M; | |
| y = 1 / x; | |
| } else { | |
| dir = 1; | |
| p = num; | |
| y = x; | |
| } | |
| /* Evaluate the numerator */ | |
| num_ans = *p; | |
| p += dir; | |
| for (i = 1; i <= M; i++) { | |
| num_ans = num_ans * y + *p; | |
| p += dir; | |
| } | |
| /* Evaluate the denominator */ | |
| if (absx > 1) { | |
| p = denom + N; | |
| } else { | |
| p = denom; | |
| } | |
| denom_ans = *p; | |
| p += dir; | |
| for (i = 1; i <= N; i++) { | |
| denom_ans = denom_ans * y + *p; | |
| p += dir; | |
| } | |
| if (absx > 1) { | |
| i = M - N; | |
| return std::pow(x, i) * num_ans / denom_ans; | |
| } else { | |
| return num_ans / denom_ans; | |
| } | |
| } | |
| } // namespace cephes | |
| } // namespace xsf | |