1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision vector 2^x function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2019-2024, Arm Limited.
5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*f3087befSAndrew Turner */
7*f3087befSAndrew Turner
8*f3087befSAndrew Turner #include "v_math.h"
9*f3087befSAndrew Turner #include "test_defs.h"
10*f3087befSAndrew Turner
11*f3087befSAndrew Turner static const struct data
12*f3087befSAndrew Turner {
13*f3087befSAndrew Turner float32x4_t c0, c1, c2, c3, c4, c5, shift;
14*f3087befSAndrew Turner uint32x4_t exponent_bias;
15*f3087befSAndrew Turner float32x4_t special_bound, scale_thresh;
16*f3087befSAndrew Turner uint32x4_t special_offset, special_bias;
17*f3087befSAndrew Turner } data = {
18*f3087befSAndrew Turner .shift = V4 (0x1.8p23f),
19*f3087befSAndrew Turner .exponent_bias = V4 (0x3f800000),
20*f3087befSAndrew Turner .special_bound = V4 (126.0f),
21*f3087befSAndrew Turner .scale_thresh = V4 (192.0f),
22*f3087befSAndrew Turner .special_offset = V4 (0x82000000),
23*f3087befSAndrew Turner .special_bias = V4 (0x7f000000),
24*f3087befSAndrew Turner /* maxerr: 0.878 ulp. */
25*f3087befSAndrew Turner .c0 = V4 (0x1.416b5ep-13f),
26*f3087befSAndrew Turner .c1 = V4 (0x1.5f082ep-10f),
27*f3087befSAndrew Turner .c2 = V4 (0x1.3b2dep-7f),
28*f3087befSAndrew Turner .c3 = V4 (0x1.c6af7cp-5f),
29*f3087befSAndrew Turner .c4 = V4 (0x1.ebfbdcp-3f),
30*f3087befSAndrew Turner .c5 = V4 (0x1.62e43p-1f),
31*f3087befSAndrew Turner };
32*f3087befSAndrew Turner
33*f3087befSAndrew Turner static float32x4_t VPCS_ATTR NOINLINE
specialcase(float32x4_t p,float32x4_t n,uint32x4_t e,const struct data * d)34*f3087befSAndrew Turner specialcase (float32x4_t p, float32x4_t n, uint32x4_t e, const struct data *d)
35*f3087befSAndrew Turner {
36*f3087befSAndrew Turner /* 2^n may overflow, break it up into s1*s2. */
37*f3087befSAndrew Turner uint32x4_t b = vandq_u32 (vclezq_f32 (n), d->special_offset);
38*f3087befSAndrew Turner float32x4_t s1 = vreinterpretq_f32_u32 (vaddq_u32 (b, d->special_bias));
39*f3087befSAndrew Turner float32x4_t s2 = vreinterpretq_f32_u32 (vsubq_u32 (e, b));
40*f3087befSAndrew Turner uint32x4_t cmp = vcagtq_f32 (n, d->scale_thresh);
41*f3087befSAndrew Turner float32x4_t r1 = vmulq_f32 (s1, s1);
42*f3087befSAndrew Turner float32x4_t r0 = vmulq_f32 (vmulq_f32 (p, s1), s2);
43*f3087befSAndrew Turner return vreinterpretq_f32_u32 ((cmp & vreinterpretq_u32_f32 (r1))
44*f3087befSAndrew Turner | (~cmp & vreinterpretq_u32_f32 (r0)));
45*f3087befSAndrew Turner }
46*f3087befSAndrew Turner
47*f3087befSAndrew Turner float32x4_t VPCS_ATTR
_ZGVnN4v_exp2f_1u(float32x4_t x)48*f3087befSAndrew Turner _ZGVnN4v_exp2f_1u (float32x4_t x)
49*f3087befSAndrew Turner {
50*f3087befSAndrew Turner /* exp2(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]
51*f3087befSAndrew Turner x = n + r, with r in [-1/2, 1/2]. */
52*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
53*f3087befSAndrew Turner float32x4_t n = vrndaq_f32 (x);
54*f3087befSAndrew Turner float32x4_t r = x - n;
55*f3087befSAndrew Turner uint32x4_t e = vreinterpretq_u32_s32 (vcvtaq_s32_f32 (x)) << 23;
56*f3087befSAndrew Turner float32x4_t scale = vreinterpretq_f32_u32 (e + d->exponent_bias);
57*f3087befSAndrew Turner uint32x4_t cmp = vcagtq_f32 (n, d->special_bound);
58*f3087befSAndrew Turner
59*f3087befSAndrew Turner float32x4_t p = vfmaq_f32 (d->c1, d->c0, r);
60*f3087befSAndrew Turner p = vfmaq_f32 (d->c2, p, r);
61*f3087befSAndrew Turner p = vfmaq_f32 (d->c3, p, r);
62*f3087befSAndrew Turner p = vfmaq_f32 (d->c4, p, r);
63*f3087befSAndrew Turner p = vfmaq_f32 (d->c5, p, r);
64*f3087befSAndrew Turner p = vfmaq_f32 (v_f32 (1.0f), p, r);
65*f3087befSAndrew Turner if (unlikely (v_any_u32 (cmp)))
66*f3087befSAndrew Turner return specialcase (p, n, e, d);
67*f3087befSAndrew Turner return scale * p;
68*f3087befSAndrew Turner }
69*f3087befSAndrew Turner
70*f3087befSAndrew Turner TEST_ULP (_ZGVnN4v_exp2f_1u, 0.4)
71*f3087befSAndrew Turner TEST_DISABLE_FENV (_ZGVnN4v_exp2f_1u)
72*f3087befSAndrew Turner TEST_INTERVAL (_ZGVnN4v_exp2f_1u, 0, 0xffff0000, 10000)
73*f3087befSAndrew Turner TEST_SYM_INTERVAL (_ZGVnN4v_exp2f_1u, 0x1p-14, 0x1p8, 500000)
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