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/*
* Helper for vector double-precision routines which calculate log(1 + x) and do
* not need special-case handling
*
* Copyright (c) 2022-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#ifndef PL_MATH_V_LOG1P_INLINE_H
#define PL_MATH_V_LOG1P_INLINE_H
#include "v_math.h"
#include "pairwise_horner.h"
#define Ln2Hi v_f64 (0x1.62e42fefa3800p-1)
#define Ln2Lo v_f64 (0x1.ef35793c76730p-45)
#define HfRt2Top 0x3fe6a09e00000000 /* top32(asuint64(sqrt(2)/2)) << 32. */
#define OneMHfRt2Top \
0x00095f6200000000 /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) \
<< 32. */
#define OneTop 0x3ff
#define BottomMask 0xffffffff
#define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */
#define C(i) v_f64 (__log1p_data.coeffs[i])
static inline v_f64_t
log1p_inline (v_f64_t x)
{
/* Helper for calculating log(x + 1). Copied from v_log1p_2u5.c, with several
modifications:
- No special-case handling - this should be dealt with by the caller.
- Pairwise Horner polynomial evaluation for improved accuracy.
- Optionally simulate the shortcut for k=0, used in the scalar routine,
using v_sel, for improved accuracy when the argument to log1p is close to
0. This feature is enabled by defining WANT_V_LOG1P_K0_SHORTCUT as 1 in
the source of the caller before including this file.
See v_log1pf_2u1.c for details of the algorithm. */
v_f64_t m = x + 1;
v_u64_t mi = v_as_u64_f64 (m);
v_u64_t u = mi + OneMHfRt2Top;
v_s64_t ki = v_as_s64_u64 (u >> 52) - OneTop;
v_f64_t k = v_to_f64_s64 (ki);
/* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */
v_u64_t utop = (u & 0x000fffff00000000) + HfRt2Top;
v_u64_t u_red = utop | (mi & BottomMask);
v_f64_t f = v_as_f64_u64 (u_red) - 1;
/* Correction term c/m. */
v_f64_t cm = (x - (m - 1)) / m;
#ifndef WANT_V_LOG1P_K0_SHORTCUT
#error \
"Cannot use v_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0"
#elif WANT_V_LOG1P_K0_SHORTCUT
/* Shortcut if k is 0 - set correction term to 0 and f to x. The result is
that the approximation is solely the polynomial. */
v_u64_t k0 = k == 0;
if (unlikely (v_any_u64 (k0)))
{
cm = v_sel_f64 (k0, v_f64 (0), cm);
f = v_sel_f64 (k0, x, f);
}
#endif
/* Approximate log1p(f) on the reduced input using a polynomial. */
v_f64_t f2 = f * f;
v_f64_t p = PAIRWISE_HORNER_18 (f, f2, C);
/* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */
v_f64_t ylo = v_fma_f64 (k, Ln2Lo, cm);
v_f64_t yhi = v_fma_f64 (k, Ln2Hi, f);
return v_fma_f64 (f2, p, ylo + yhi);
}
#endif // PL_MATH_V_LOG1P_INLINE_H
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