78 lines
2.8 KiB
C
78 lines
2.8 KiB
C
/*
|
|
* 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
|