1 /*
2 * Helper for vector double-precision routines which calculate log(1 + x) and do
3 * not need special-case handling
4 *
5 * Copyright (c) 2022-2023, Arm Limited.
6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7 */
8 #ifndef PL_MATH_V_LOG1P_INLINE_H
9 #define PL_MATH_V_LOG1P_INLINE_H
10
11 #include "v_math.h"
12 #include "pairwise_horner.h"
13
14 #define Ln2Hi v_f64 (0x1.62e42fefa3800p-1)
15 #define Ln2Lo v_f64 (0x1.ef35793c76730p-45)
16 #define HfRt2Top 0x3fe6a09e00000000 /* top32(asuint64(sqrt(2)/2)) << 32. */
17 #define OneMHfRt2Top \
18 0x00095f6200000000 /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) \
19 << 32. */
20 #define OneTop 0x3ff
21 #define BottomMask 0xffffffff
22 #define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */
23
24 #define C(i) v_f64 (__log1p_data.coeffs[i])
25
26 static inline v_f64_t
log1p_inline(v_f64_t x)27 log1p_inline (v_f64_t x)
28 {
29 /* Helper for calculating log(x + 1). Copied from v_log1p_2u5.c, with several
30 modifications:
31 - No special-case handling - this should be dealt with by the caller.
32 - Pairwise Horner polynomial evaluation for improved accuracy.
33 - Optionally simulate the shortcut for k=0, used in the scalar routine,
34 using v_sel, for improved accuracy when the argument to log1p is close to
35 0. This feature is enabled by defining WANT_V_LOG1P_K0_SHORTCUT as 1 in
36 the source of the caller before including this file.
37 See v_log1pf_2u1.c for details of the algorithm. */
38 v_f64_t m = x + 1;
39 v_u64_t mi = v_as_u64_f64 (m);
40 v_u64_t u = mi + OneMHfRt2Top;
41
42 v_s64_t ki = v_as_s64_u64 (u >> 52) - OneTop;
43 v_f64_t k = v_to_f64_s64 (ki);
44
45 /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */
46 v_u64_t utop = (u & 0x000fffff00000000) + HfRt2Top;
47 v_u64_t u_red = utop | (mi & BottomMask);
48 v_f64_t f = v_as_f64_u64 (u_red) - 1;
49
50 /* Correction term c/m. */
51 v_f64_t cm = (x - (m - 1)) / m;
52
53 #ifndef WANT_V_LOG1P_K0_SHORTCUT
54 #error \
55 "Cannot use v_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0"
56 #elif WANT_V_LOG1P_K0_SHORTCUT
57 /* Shortcut if k is 0 - set correction term to 0 and f to x. The result is
58 that the approximation is solely the polynomial. */
59 v_u64_t k0 = k == 0;
60 if (unlikely (v_any_u64 (k0)))
61 {
62 cm = v_sel_f64 (k0, v_f64 (0), cm);
63 f = v_sel_f64 (k0, x, f);
64 }
65 #endif
66
67 /* Approximate log1p(f) on the reduced input using a polynomial. */
68 v_f64_t f2 = f * f;
69 v_f64_t p = PAIRWISE_HORNER_18 (f, f2, C);
70
71 /* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */
72 v_f64_t ylo = v_fma_f64 (k, Ln2Lo, cm);
73 v_f64_t yhi = v_fma_f64 (k, Ln2Hi, f);
74 return v_fma_f64 (f2, p, ylo + yhi);
75 }
76
77 #endif // PL_MATH_V_LOG1P_INLINE_H
78