1 /* Single-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 static const struct data
23 {
24 float32x4_t poly[5];
25 float32x4_t shift, inv_ln2, ln2_hi, ln2_lo;
26 uint32x4_t exponent_bias;
27 #if !WANT_SIMD_EXCEPT
28 float32x4_t special_bound, scale_thresh;
29 #endif
30 } data = {
31 /* maxerr: 1.45358 +0.5 ulp. */
32 .poly = { V4 (0x1.0e4020p-7f), V4 (0x1.573e2ep-5f), V4 (0x1.555e66p-3f),
33 V4 (0x1.fffdb6p-2f), V4 (0x1.ffffecp-1f) },
34 .shift = V4 (0x1.8p23f),
35 .inv_ln2 = V4 (0x1.715476p+0f),
36 .ln2_hi = V4 (0x1.62e4p-1f),
37 .ln2_lo = V4 (0x1.7f7d1cp-20f),
38 .exponent_bias = V4 (0x3f800000),
39 #if !WANT_SIMD_EXCEPT
40 .special_bound = V4 (126.0f),
41 .scale_thresh = V4 (192.0f),
42 #endif
43 };
44
45 #define C(i) d->poly[i]
46
47 #if WANT_SIMD_EXCEPT
48
49 # define TinyBound v_u32 (0x20000000) /* asuint (0x1p-63). */
50 # define BigBound v_u32 (0x42800000) /* asuint (0x1p6). */
51 # define SpecialBound v_u32 (0x22800000) /* BigBound - TinyBound. */
52
53 static float32x4_t VPCS_ATTR NOINLINE
54 special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
55 {
56 /* If fenv exceptions are to be triggered correctly, fall back to the scalar
57 routine to special lanes. */
58 return v_call_f32 (expf, x, y, cmp);
59 }
60
61 #else
62
63 # define SpecialOffset v_u32 (0x82000000)
64 # define SpecialBias v_u32 (0x7f000000)
65
66 static float32x4_t VPCS_ATTR NOINLINE
67 special_case (float32x4_t poly, float32x4_t n, uint32x4_t e, uint32x4_t cmp1,
68 float32x4_t scale, const struct data *d)
69 {
70 /* 2^n may overflow, break it up into s1*s2. */
71 uint32x4_t b = vandq_u32 (vclezq_f32 (n), SpecialOffset);
72 float32x4_t s1 = vreinterpretq_f32_u32 (vaddq_u32 (b, SpecialBias));
73 float32x4_t s2 = vreinterpretq_f32_u32 (vsubq_u32 (e, b));
74 uint32x4_t cmp2 = vcagtq_f32 (n, d->scale_thresh);
75 float32x4_t r2 = vmulq_f32 (s1, s1);
76 float32x4_t r1 = vmulq_f32 (vfmaq_f32 (s2, poly, s2), s1);
77 /* Similar to r1 but avoids double rounding in the subnormal range. */
78 float32x4_t r0 = vfmaq_f32 (scale, poly, scale);
79 float32x4_t r = vbslq_f32 (cmp1, r1, r0);
80 return vbslq_f32 (cmp2, r2, r);
81 }
82
83 #endif
84
85 float32x4_t VPCS_ATTR V_NAME_F1 (exp) (float32x4_t x)
86 {
87 const struct data *d = ptr_barrier (&data);
88 float32x4_t n, r, r2, scale, p, q, poly, z;
89 uint32x4_t cmp, e;
90
91 #if WANT_SIMD_EXCEPT
92 /* asuint(x) - TinyBound >= BigBound - TinyBound. */
93 cmp = vcgeq_u32 (
94 vsubq_u32 (vandq_u32 (vreinterpretq_u32_f32 (x), v_u32 (0x7fffffff)),
95 TinyBound),
96 SpecialBound);
97 float32x4_t xm = x;
98 /* If any lanes are special, mask them with 1 and retain a copy of x to allow
99 special case handler to fix special lanes later. This is only necessary if
100 fenv exceptions are to be triggered correctly. */
101 if (__glibc_unlikely (v_any_u32 (cmp)))
102 x = vbslq_f32 (cmp, v_f32 (1), x);
103 #endif
104
105 /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
106 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
107 z = vfmaq_f32 (d->shift, x, d->inv_ln2);
108 n = vsubq_f32 (z, d->shift);
109 r = vfmsq_f32 (x, n, d->ln2_hi);
110 r = vfmsq_f32 (r, n, d->ln2_lo);
111 e = vshlq_n_u32 (vreinterpretq_u32_f32 (z), 23);
112 scale = vreinterpretq_f32_u32 (vaddq_u32 (e, d->exponent_bias));
113
114 #if !WANT_SIMD_EXCEPT
115 cmp = vcagtq_f32 (n, d->special_bound);
116 #endif
117
118 r2 = vmulq_f32 (r, r);
119 p = vfmaq_f32 (C (1), C (0), r);
120 q = vfmaq_f32 (C (3), C (2), r);
121 q = vfmaq_f32 (q, p, r2);
122 p = vmulq_f32 (C (4), r);
123 poly = vfmaq_f32 (p, q, r2);
124
125 if (__glibc_unlikely (v_any_u32 (cmp)))
126 #if WANT_SIMD_EXCEPT
127 return special_case (xm, vfmaq_f32 (scale, poly, scale), cmp);
128 #else
129 return special_case (poly, n, e, cmp, scale, d);
130 #endif
131
132 return vfmaq_f32 (scale, poly, scale);
133 }