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