1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Single-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 #ifndef PL_MATH_ATANF_COMMON_H 10*f3087befSAndrew Turner #define PL_MATH_ATANF_COMMON_H 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner #include "math_config.h" 13*f3087befSAndrew Turner #include "poly_scalar_f32.h" 14*f3087befSAndrew Turner 15*f3087befSAndrew Turner /* Polynomial used in fast atanf(x) and atan2f(y,x) implementations 16*f3087befSAndrew Turner The order 7 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */ 17*f3087befSAndrew Turner static inline float 18*f3087befSAndrew Turner eval_poly (float z, float az, float shift) 19*f3087befSAndrew Turner { 20*f3087befSAndrew Turner /* Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However, 21*f3087befSAndrew Turner a standard implementation using z8 creates spurious underflow 22*f3087befSAndrew Turner in the very last fma (when z^8 is small enough). 23*f3087befSAndrew Turner Therefore, we split the last fma into a mul and and an fma. 24*f3087befSAndrew Turner Horner and single-level Estrin have higher errors that exceed 25*f3087befSAndrew Turner threshold. */ 26*f3087befSAndrew Turner float z2 = z * z; 27*f3087befSAndrew Turner float z4 = z2 * z2; 28*f3087befSAndrew Turner 29*f3087befSAndrew Turner /* Then assemble polynomial. */ 30*f3087befSAndrew Turner float y = fmaf ( 31*f3087befSAndrew Turner z4, z4 * pairwise_poly_3_f32 (z2, z4, __atanf_poly_data.poly + 4), 32*f3087befSAndrew Turner pairwise_poly_3_f32 (z2, z4, __atanf_poly_data.poly)); 33*f3087befSAndrew Turner /* Finalize: 34*f3087befSAndrew Turner y = shift + z * P(z^2). */ 35*f3087befSAndrew Turner return fmaf (y, z2 * az, az) + shift; 36*f3087befSAndrew Turner } 37*f3087befSAndrew Turner 38*f3087befSAndrew Turner #endif // PL_MATH_ATANF_COMMON_H 39