1/* Double-precision vector (SVE) 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 "sv_math.h"
21#include "poly_sve_f64.h"
22
23#define SpecialBound 307.0 /* floor (log10 (2^1023)). */
24
25static const struct data
26{
27 double poly[5];
28 double shift, log10_2, log2_10_hi, log2_10_lo, scale_thres, special_bound;
29} data = {
30 /* Coefficients generated using Remez algorithm.
31 rel error: 0x1.9fcb9b3p-60
32 abs error: 0x1.a20d9598p-60 in [ -log10(2)/128, log10(2)/128 ]
33 max ulp err 0.52 +0.5. */
34 .poly = { 0x1.26bb1bbb55516p1, 0x1.53524c73cd32ap1, 0x1.0470591daeafbp1,
35 0x1.2bd77b1361ef6p0, 0x1.142b5d54e9621p-1 },
36 /* 1.5*2^46+1023. This value is further explained below. */
37 .shift = 0x1.800000000ffc0p+46,
38 .log10_2 = 0x1.a934f0979a371p1, /* 1/log2(10). */
39 .log2_10_hi = 0x1.34413509f79ffp-2, /* log2(10). */
40 .log2_10_lo = -0x1.9dc1da994fd21p-59,
41 .scale_thres = 1280.0,
42 .special_bound = SpecialBound,
43};
44
45#define SpecialOffset 0x6000000000000000 /* 0x1p513. */
46/* SpecialBias1 + SpecialBias1 = asuint(1.0). */
47#define SpecialBias1 0x7000000000000000 /* 0x1p769. */
48#define SpecialBias2 0x3010000000000000 /* 0x1p-254. */
49
50/* Update of both special and non-special cases, if any special case is
51 detected. */
52static inline svfloat64_t
53special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
54 const struct data *d)
55{
56 /* s=2^n may overflow, break it up into s=s1*s2,
57 such that exp = s + s*y can be computed as s1*(s2+s2*y)
58 and s1*s1 overflows only if n>0. */
59
60 /* If n<=0 then set b to 0x6, 0 otherwise. */
61 svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */
62 svuint64_t b = svdup_u64_z (p_sign, SpecialOffset);
63
64 /* Set s1 to generate overflow depending on sign of exponent n. */
65 svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
66 /* Offset s to avoid overflow in final result if n is below threshold. */
67 svfloat64_t s2 = svreinterpret_f64 (
68 svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
69
70 /* |n| > 1280 => 2^(n) overflows. */
71 svbool_t p_cmp = svacgt (pg, n, d->scale_thres);
72
73 svfloat64_t r1 = svmul_x (pg, s1, s1);
74 svfloat64_t r2 = svmla_x (pg, s2, s2, y);
75 svfloat64_t r0 = svmul_x (pg, r2, s1);
76
77 return svsel (p_cmp, r1, r0);
78}
79
80/* Fast vector implementation of exp10 using FEXPA instruction.
81 Maximum measured error is 1.02 ulp.
82 SV_NAME_D1 (exp10)(-0x1.2862fec805e58p+2) got 0x1.885a89551d782p-16
83 want 0x1.885a89551d781p-16. */
84svfloat64_t SV_NAME_D1 (exp10) (svfloat64_t x, svbool_t pg)
85{
86 const struct data *d = ptr_barrier (&data);
87 svbool_t no_big_scale = svacle (pg, x, d->special_bound);
88 svbool_t special = svnot_z (pg, no_big_scale);
89
90 /* n = round(x/(log10(2)/N)). */
91 svfloat64_t shift = sv_f64 (x: d->shift);
92 svfloat64_t z = svmla_x (pg, shift, x, d->log10_2);
93 svfloat64_t n = svsub_x (pg, z, shift);
94
95 /* r = x - n*log10(2)/N. */
96 svfloat64_t log2_10 = svld1rq (svptrue_b64 (), &d->log2_10_hi);
97 svfloat64_t r = x;
98 r = svmls_lane (r, n, log2_10, 0);
99 r = svmls_lane (r, n, log2_10, 1);
100
101 /* scale = 2^(n/N), computed using FEXPA. FEXPA does not propagate NaNs, so
102 for consistent NaN handling we have to manually propagate them. This
103 comes at significant performance cost. */
104 svuint64_t u = svreinterpret_u64 (z);
105 svfloat64_t scale = svexpa (u);
106
107 /* Approximate exp10(r) using polynomial. */
108 svfloat64_t r2 = svmul_x (pg, r, r);
109 svfloat64_t y = svmla_x (pg, svmul_x (pg, r, d->poly[0]), r2,
110 sv_pairwise_poly_3_f64_x (pg, x: r, x2: r2, poly: d->poly + 1));
111
112 /* Assemble result as exp10(x) = 2^n * exp10(r). If |x| > SpecialBound
113 multiplication may overflow, so use special case routine. */
114 if (__glibc_unlikely (svptest_any (pg, special)))
115 {
116 /* FEXPA zeroes the sign bit, however the sign is meaningful to the
117 special case function so needs to be copied.
118 e = sign bit of u << 46. */
119 svuint64_t e = svand_x (pg, svlsl_x (pg, u, 46), 0x8000000000000000);
120 /* Copy sign to scale. */
121 scale = svreinterpret_f64 (svadd_x (pg, e, svreinterpret_u64 (scale)));
122 return special_case (pg, s: scale, y, n, d);
123 }
124
125 /* No special case. */
126 return svmla_x (pg, scale, scale, y);
127}
128

source code of glibc/sysdeps/aarch64/fpu/exp10_sve.c