mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 11:37:35 +00:00
56 lines
1.4 KiB
C
56 lines
1.4 KiB
C
|
#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"
|
||
|
|
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 /* COSMOPOLITAN_LIBC_TINYMATH_ATAN_COMMON_H_ */
|