1/* Double-precision vector (AdvSIMD) exp10 function.
2
3 Copyright (C) 2023-2024 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <https://www.gnu.org/licenses/>. */
19
20#include "v_math.h"
21
22/* Value of |x| above which scale overflows without special treatment. */
23#define SpecialBound 306.0 /* floor (log10 (2^1023)) - 1. */
24/* Value of n above which scale overflows even with special treatment. */
25#define ScaleBound 163840.0 /* 1280.0 * N. */
26
27const static struct data
28{
29 float64x2_t poly[4];
30 float64x2_t log10_2, log2_10_hi, log2_10_lo, shift;
31#if !WANT_SIMD_EXCEPT
32 float64x2_t special_bound, scale_thresh;
33#endif
34} data = {
35 /* Coefficients generated using Remez algorithm.
36 rel error: 0x1.5ddf8f28p-54
37 abs error: 0x1.5ed266c8p-54 in [ -log10(2)/256, log10(2)/256 ]
38 maxerr: 1.14432 +0.5 ulp. */
39 .poly = { V2 (0x1.26bb1bbb5524p1), V2 (0x1.53524c73cecdap1),
40 V2 (0x1.047060efb781cp1), V2 (0x1.2bd76040f0d16p0) },
41 .log10_2 = V2 (0x1.a934f0979a371p8), /* N/log2(10). */
42 .log2_10_hi = V2 (0x1.34413509f79ffp-9), /* log2(10)/N. */
43 .log2_10_lo = V2 (-0x1.9dc1da994fd21p-66),
44 .shift = V2 (0x1.8p+52),
45#if !WANT_SIMD_EXCEPT
46 .scale_thresh = V2 (ScaleBound),
47 .special_bound = V2 (SpecialBound),
48#endif
49};
50
51#define N (1 << V_EXP_TABLE_BITS)
52#define IndexMask v_u64 (N - 1)
53
54#if WANT_SIMD_EXCEPT
55
56# define TinyBound v_u64 (0x2000000000000000) /* asuint64 (0x1p-511). */
57# define BigBound v_u64 (0x4070000000000000) /* asuint64 (0x1p8). */
58# define Thres v_u64 (0x2070000000000000) /* BigBound - TinyBound. */
59
60static float64x2_t VPCS_ATTR NOINLINE
61special_case (float64x2_t x, float64x2_t y, uint64x2_t cmp)
62{
63 /* If fenv exceptions are to be triggered correctly, fall back to the scalar
64 routine for special lanes. */
65 return v_call_f64 (exp10, x, y, cmp);
66}
67
68#else
69
70# define SpecialOffset v_u64 (0x6000000000000000) /* 0x1p513. */
71/* SpecialBias1 + SpecialBias1 = asuint(1.0). */
72# define SpecialBias1 v_u64 (0x7000000000000000) /* 0x1p769. */
73# define SpecialBias2 v_u64 (0x3010000000000000) /* 0x1p-254. */
74
75static inline float64x2_t VPCS_ATTR
76special_case (float64x2_t s, float64x2_t y, float64x2_t n,
77 const struct data *d)
78{
79 /* 2^(n/N) may overflow, break it up into s1*s2. */
80 uint64x2_t b = vandq_u64 (vcltzq_f64 (n), SpecialOffset);
81 float64x2_t s1 = vreinterpretq_f64_u64 (vsubq_u64 (SpecialBias1, b));
82 float64x2_t s2 = vreinterpretq_f64_u64 (
83 vaddq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (s), SpecialBias2), b));
84 uint64x2_t cmp = vcagtq_f64 (n, d->scale_thresh);
85 float64x2_t r1 = vmulq_f64 (s1, s1);
86 float64x2_t r0 = vmulq_f64 (vfmaq_f64 (s2, y, s2), s1);
87 return vbslq_f64 (cmp, r1, r0);
88}
89
90#endif
91
92/* Fast vector implementation of exp10.
93 Maximum measured error is 1.64 ulp.
94 _ZGVnN2v_exp10(0x1.ccd1c9d82cc8cp+0) got 0x1.f8dab6d7fed0cp+5
95 want 0x1.f8dab6d7fed0ap+5. */
96float64x2_t VPCS_ATTR V_NAME_D1 (exp10) (float64x2_t x)
97{
98 const struct data *d = ptr_barrier (&data);
99 uint64x2_t cmp;
100#if WANT_SIMD_EXCEPT
101 /* If any lanes are special, mask them with 1 and retain a copy of x to allow
102 special_case to fix special lanes later. This is only necessary if fenv
103 exceptions are to be triggered correctly. */
104 float64x2_t xm = x;
105 uint64x2_t iax = vreinterpretq_u64_f64 (vabsq_f64 (x));
106 cmp = vcgeq_u64 (vsubq_u64 (iax, TinyBound), Thres);
107 if (__glibc_unlikely (v_any_u64 (cmp)))
108 x = vbslq_f64 (cmp, v_f64 (1), x);
109#else
110 cmp = vcageq_f64 (x, d->special_bound);
111#endif
112
113 /* n = round(x/(log10(2)/N)). */
114 float64x2_t z = vfmaq_f64 (d->shift, x, d->log10_2);
115 uint64x2_t u = vreinterpretq_u64_f64 (z);
116 float64x2_t n = vsubq_f64 (z, d->shift);
117
118 /* r = x - n*log10(2)/N. */
119 float64x2_t r = x;
120 r = vfmsq_f64 (r, d->log2_10_hi, n);
121 r = vfmsq_f64 (r, d->log2_10_lo, n);
122
123 uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS);
124 uint64x2_t i = vandq_u64 (u, IndexMask);
125
126 /* y = exp10(r) - 1 ~= C0 r + C1 r^2 + C2 r^3 + C3 r^4. */
127 float64x2_t r2 = vmulq_f64 (r, r);
128 float64x2_t p = vfmaq_f64 (d->poly[0], r, d->poly[1]);
129 float64x2_t y = vfmaq_f64 (d->poly[2], r, d->poly[3]);
130 p = vfmaq_f64 (p, y, r2);
131 y = vmulq_f64 (r, p);
132
133 /* s = 2^(n/N). */
134 u = v_lookup_u64 (__v_exp_data, i);
135 float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e));
136
137 if (__glibc_unlikely (v_any_u64 (cmp)))
138#if WANT_SIMD_EXCEPT
139 return special_case (xm, vfmaq_f64 (s, y, s), cmp);
140#else
141 return special_case (s, y, n, d);
142#endif
143
144 return vfmaq_f64 (s, y, s);
145}
146

source code of glibc/sysdeps/aarch64/fpu/exp10_advsimd.c