1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision polynomial evaluation function for scalar 3*f3087befSAndrew Turner * atan(x) and atan2(y,x). 4*f3087befSAndrew Turner * 5*f3087befSAndrew Turner * Copyright (c) 2021-2024, Arm Limited. 6*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 7*f3087befSAndrew Turner */ 8*f3087befSAndrew Turner 9*f3087befSAndrew Turner #include "math_config.h" 10*f3087befSAndrew Turner #include "poly_scalar_f64.h" 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner /* Polynomial used in fast atan(x) and atan2(y,x) implementations 13*f3087befSAndrew Turner The order 19 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */ 14*f3087befSAndrew Turner static inline double 15*f3087befSAndrew Turner eval_poly (double z, double az, double shift) 16*f3087befSAndrew Turner { 17*f3087befSAndrew Turner /* Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of 18*f3087befSAndrew Turner full scheme to avoid underflow in x^16. */ 19*f3087befSAndrew Turner double z2 = z * z; 20*f3087befSAndrew Turner double x2 = z2 * z2; 21*f3087befSAndrew Turner double x4 = x2 * x2; 22*f3087befSAndrew Turner double x8 = x4 * x4; 23*f3087befSAndrew Turner double y = fma (estrin_11_f64 (z2, x2, x4, x8, __atan_poly_data.poly + 8), 24*f3087befSAndrew Turner x8, estrin_7_f64 (z2, x2, x4, __atan_poly_data.poly)); 25*f3087befSAndrew Turner 26*f3087befSAndrew Turner /* Finalize. y = shift + z + z^3 * P(z^2). */ 27*f3087befSAndrew Turner y = fma (y, z2 * az, az); 28*f3087befSAndrew Turner y = y + shift; 29*f3087befSAndrew Turner 30*f3087befSAndrew Turner return y; 31*f3087befSAndrew Turner } 32*f3087befSAndrew Turner 33*f3087befSAndrew Turner #undef P 34