#ifndef COSMOPOLITAN_LIBC_TINYMATH_ATAN_COMMON_H_ #define COSMOPOLITAN_LIBC_TINYMATH_ATAN_COMMON_H_ #include "libc/tinymath/atan_data.internal.h" #include "libc/tinymath/estrin_wrap.internal.h" #include "libc/tinymath/horner.internal.h" #if !(__ASSEMBLER__ + __LINKER__ + 0) COSMOPOLITAN_C_START_ // clang-format off /* * Double-precision polynomial evaluation function for scalar and vector atan(x) * and atan2(y,x). * * Copyright (c) 2021-2023, Arm Limited. * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception */ #if WANT_VMATH #define DBL_T float64x2_t #define P(i) v_f64 (__atan_poly_data.poly[i]) #else #define DBL_T double #define P(i) __atan_poly_data.poly[i] #endif /* Polynomial used in fast atan(x) and atan2(y,x) implementations The order 19 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */ static inline DBL_T eval_poly (DBL_T z, DBL_T az, DBL_T shift) { /* Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of full scheme to avoid underflow in x^16. */ DBL_T z2 = z * z; DBL_T x2 = z2 * z2; DBL_T x4 = x2 * x2; DBL_T x8 = x4 * x4; DBL_T y = FMA (ESTRIN_11_ (z2, x2, x4, x8, P, 8), x8, ESTRIN_7 (z2, x2, x4, P)); /* Finalize. y = shift + z + z^3 * P(z^2). */ y = FMA (y, z2 * az, az); y = y + shift; return y; } #undef DBL_T #undef FMA #undef P COSMOPOLITAN_C_END_ #endif /* !(__ASSEMBLER__ + __LINKER__ + 0) */ #endif /* COSMOPOLITAN_LIBC_TINYMATH_ATAN_COMMON_H_ */