1 /* Double-precision vector (Advanced SIMD) exp function.
2
3 Copyright (C) 2023 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 #define N (1 << V_EXP_TABLE_BITS)
23 #define IndexMask (N - 1)
24
25 const static volatile struct
26 {
27 float64x2_t poly[3];
28 float64x2_t inv_ln2, ln2_hi, ln2_lo, shift;
29 #if !WANT_SIMD_EXCEPT
30 float64x2_t special_bound, scale_thresh;
31 #endif
32 } data = {
33 /* maxerr: 1.88 +0.5 ulp
34 rel error: 1.4337*2^-53
35 abs error: 1.4299*2^-53 in [ -ln2/256, ln2/256 ]. */
36 .poly = { V2 (0x1.ffffffffffd43p-2), V2 (0x1.55555c75adbb2p-3),
37 V2 (0x1.55555da646206p-5) },
38 #if !WANT_SIMD_EXCEPT
39 .scale_thresh = V2 (163840.0), /* 1280.0 * N. */
40 .special_bound = V2 (704.0),
41 #endif
42 .inv_ln2 = V2 (0x1.71547652b82fep7), /* N/ln2. */
43 .ln2_hi = V2 (0x1.62e42fefa39efp-8), /* ln2/N. */
44 .ln2_lo = V2 (0x1.abc9e3b39803f3p-63),
45 .shift = V2 (0x1.8p+52)
46 };
47
48 #define C(i) data.poly[i]
49 #define Tab __v_exp_data
50
51 #if WANT_SIMD_EXCEPT
52
53 # define TinyBound v_u64 (0x2000000000000000) /* asuint64 (0x1p-511). */
54 # define BigBound v_u64 (0x4080000000000000) /* asuint64 (0x1p9). */
55 # define SpecialBound v_u64 (0x2080000000000000) /* BigBound - TinyBound. */
56
57 static inline float64x2_t VPCS_ATTR
58 special_case (float64x2_t x, float64x2_t y, uint64x2_t cmp)
59 {
60 /* If fenv exceptions are to be triggered correctly, fall back to the scalar
61 routine to special lanes. */
62 return v_call_f64 (exp, x, y, cmp);
63 }
64
65 #else
66
67 # define SpecialOffset v_u64 (0x6000000000000000) /* 0x1p513. */
68 /* SpecialBias1 + SpecialBias1 = asuint(1.0). */
69 # define SpecialBias1 v_u64 (0x7000000000000000) /* 0x1p769. */
70 # define SpecialBias2 v_u64 (0x3010000000000000) /* 0x1p-254. */
71
72 static float64x2_t VPCS_ATTR NOINLINE
73 special_case (float64x2_t s, float64x2_t y, float64x2_t n)
74 {
75 /* 2^(n/N) may overflow, break it up into s1*s2. */
76 uint64x2_t b = vandq_u64 (vcltzq_f64 (n), SpecialOffset);
77 float64x2_t s1 = vreinterpretq_f64_u64 (vsubq_u64 (SpecialBias1, b));
78 float64x2_t s2 = vreinterpretq_f64_u64 (
79 vaddq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (s), SpecialBias2), b));
80 uint64x2_t cmp = vcagtq_f64 (n, data.scale_thresh);
81 float64x2_t r1 = vmulq_f64 (s1, s1);
82 float64x2_t r0 = vmulq_f64 (vfmaq_f64 (s2, y, s2), s1);
83 return vbslq_f64 (cmp, r1, r0);
84 }
85
86 #endif
87
88 float64x2_t VPCS_ATTR V_NAME_D1 (exp) (float64x2_t x)
89 {
90 float64x2_t n, r, r2, s, y, z;
91 uint64x2_t cmp, u, e;
92
93 #if WANT_SIMD_EXCEPT
94 /* If any lanes are special, mask them with 1 and retain a copy of x to allow
95 special_case to fix special lanes later. This is only necessary if fenv
96 exceptions are to be triggered correctly. */
97 float64x2_t xm = x;
98 uint64x2_t iax = vreinterpretq_u64_f64 (vabsq_f64 (x));
99 cmp = vcgeq_u64 (vsubq_u64 (iax, TinyBound), SpecialBound);
100 if (__glibc_unlikely (v_any_u64 (cmp)))
101 x = vbslq_f64 (cmp, v_f64 (1), x);
102 #else
103 cmp = vcagtq_f64 (x, data.special_bound);
104 #endif
105
106 /* n = round(x/(ln2/N)). */
107 z = vfmaq_f64 (data.shift, x, data.inv_ln2);
108 u = vreinterpretq_u64_f64 (z);
109 n = vsubq_f64 (z, data.shift);
110
111 /* r = x - n*ln2/N. */
112 r = x;
113 r = vfmsq_f64 (r, data.ln2_hi, n);
114 r = vfmsq_f64 (r, data.ln2_lo, n);
115
116 e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS);
117
118 /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4. */
119 r2 = vmulq_f64 (r, r);
120 y = vfmaq_f64 (C (0), C (1), r);
121 y = vfmaq_f64 (y, C (2), r2);
122 y = vfmaq_f64 (r, y, r2);
123
124 /* s = 2^(n/N). */
125 u = (uint64x2_t){ Tab[u[0] & IndexMask], Tab[u[1] & IndexMask] };
126 s = vreinterpretq_f64_u64 (vaddq_u64 (u, e));
127
128 if (__glibc_unlikely (v_any_u64 (cmp)))
129 #if WANT_SIMD_EXCEPT
130 return special_case (xm, vfmaq_f64 (s, y, s), cmp);
131 #else
132 return special_case (s, y, n);
133 #endif
134
135 return vfmaq_f64 (s, y, s);
136 }