1 /* 2 * Double-precision polynomial evaluation function for scalar and vector atan(x) 3 * and atan2(y,x). 4 * 5 * Copyright (c) 2021-2023, Arm Limited. 6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 7 */ 8 9 #include "math_config.h" 10 #include "estrin.h" 11 12 #if V_SUPPORTED 13 14 #include "v_math.h" 15 16 #define DBL_T v_f64_t 17 #define P(i) v_f64 (__atan_poly_data.poly[i]) 18 19 #else 20 21 #define DBL_T double 22 #define P(i) __atan_poly_data.poly[i] 23 24 #endif 25 26 /* Polynomial used in fast atan(x) and atan2(y,x) implementations 27 The order 19 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */ 28 static inline DBL_T 29 eval_poly (DBL_T z, DBL_T az, DBL_T shift) 30 { 31 /* Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of 32 full scheme to avoid underflow in x^16. */ 33 DBL_T z2 = z * z; 34 DBL_T x2 = z2 * z2; 35 DBL_T x4 = x2 * x2; 36 DBL_T x8 = x4 * x4; 37 DBL_T y 38 = FMA (ESTRIN_11_ (z2, x2, x4, x8, P, 8), x8, ESTRIN_7 (z2, x2, x4, P)); 39 40 /* Finalize. y = shift + z + z^3 * P(z^2). */ 41 y = FMA (y, z2 * az, az); 42 y = y + shift; 43 44 return y; 45 } 46 47 #undef DBL_T 48 #undef FMA 49 #undef P 50