1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-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 "v_poly_f64.h"
10*f3087befSAndrew Turner #include "test_sig.h"
11*f3087befSAndrew Turner #include "test_defs.h"
12*f3087befSAndrew Turner
13*f3087befSAndrew Turner #define N (1 << V_EXP_TABLE_BITS)
14*f3087befSAndrew Turner #define IndexMask (N - 1)
15*f3087befSAndrew Turner #define BigBound 1022.0
16*f3087befSAndrew Turner #define UOFlowBound 1280.0
17*f3087befSAndrew Turner #define TinyBound 0x2000000000000000 /* asuint64(0x1p-511). */
18*f3087befSAndrew Turner
19*f3087befSAndrew Turner static const struct data
20*f3087befSAndrew Turner {
21*f3087befSAndrew Turner float64x2_t poly[4];
22*f3087befSAndrew Turner float64x2_t shift, scale_big_bound, scale_uoflow_bound;
23*f3087befSAndrew Turner } data = {
24*f3087befSAndrew Turner /* Coefficients are computed using Remez algorithm with
25*f3087befSAndrew Turner minimisation of the absolute error. */
26*f3087befSAndrew Turner .poly = { V2 (0x1.62e42fefa3686p-1), V2 (0x1.ebfbdff82c241p-3),
27*f3087befSAndrew Turner V2 (0x1.c6b09b16de99ap-5), V2 (0x1.3b2abf5571ad8p-7) },
28*f3087befSAndrew Turner .shift = V2 (0x1.8p52 / N),
29*f3087befSAndrew Turner .scale_big_bound = V2 (BigBound),
30*f3087befSAndrew Turner .scale_uoflow_bound = V2 (UOFlowBound),
31*f3087befSAndrew Turner };
32*f3087befSAndrew Turner
33*f3087befSAndrew Turner static inline uint64x2_t
lookup_sbits(uint64x2_t i)34*f3087befSAndrew Turner lookup_sbits (uint64x2_t i)
35*f3087befSAndrew Turner {
36*f3087befSAndrew Turner return (uint64x2_t){ __v_exp_data[i[0] & IndexMask],
37*f3087befSAndrew Turner __v_exp_data[i[1] & IndexMask] };
38*f3087befSAndrew Turner }
39*f3087befSAndrew Turner
40*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT
41*f3087befSAndrew Turner
42*f3087befSAndrew Turner # define Thres 0x2080000000000000 /* asuint64(512.0) - TinyBound. */
43*f3087befSAndrew Turner
44*f3087befSAndrew Turner /* Call scalar exp2 as a fallback. */
45*f3087befSAndrew Turner static float64x2_t VPCS_ATTR NOINLINE
special_case(float64x2_t x,float64x2_t y,uint64x2_t is_special)46*f3087befSAndrew Turner special_case (float64x2_t x, float64x2_t y, uint64x2_t is_special)
47*f3087befSAndrew Turner {
48*f3087befSAndrew Turner return v_call_f64 (exp2, x, y, is_special);
49*f3087befSAndrew Turner }
50*f3087befSAndrew Turner
51*f3087befSAndrew Turner #else
52*f3087befSAndrew Turner
53*f3087befSAndrew Turner # define SpecialOffset 0x6000000000000000 /* 0x1p513. */
54*f3087befSAndrew Turner /* SpecialBias1 + SpecialBias1 = asuint(1.0). */
55*f3087befSAndrew Turner # define SpecialBias1 0x7000000000000000 /* 0x1p769. */
56*f3087befSAndrew Turner # define SpecialBias2 0x3010000000000000 /* 0x1p-254. */
57*f3087befSAndrew Turner
58*f3087befSAndrew Turner static inline float64x2_t VPCS_ATTR
special_case(float64x2_t s,float64x2_t y,float64x2_t n,const struct data * d)59*f3087befSAndrew Turner special_case (float64x2_t s, float64x2_t y, float64x2_t n,
60*f3087befSAndrew Turner const struct data *d)
61*f3087befSAndrew Turner {
62*f3087befSAndrew Turner /* 2^(n/N) may overflow, break it up into s1*s2. */
63*f3087befSAndrew Turner uint64x2_t b = vandq_u64 (vclezq_f64 (n), v_u64 (SpecialOffset));
64*f3087befSAndrew Turner float64x2_t s1 = vreinterpretq_f64_u64 (vsubq_u64 (v_u64 (SpecialBias1), b));
65*f3087befSAndrew Turner float64x2_t s2 = vreinterpretq_f64_u64 (vaddq_u64 (
66*f3087befSAndrew Turner vsubq_u64 (vreinterpretq_u64_f64 (s), v_u64 (SpecialBias2)), b));
67*f3087befSAndrew Turner uint64x2_t cmp = vcagtq_f64 (n, d->scale_uoflow_bound);
68*f3087befSAndrew Turner float64x2_t r1 = vmulq_f64 (s1, s1);
69*f3087befSAndrew Turner float64x2_t r0 = vmulq_f64 (vfmaq_f64 (s2, s2, y), s1);
70*f3087befSAndrew Turner return vbslq_f64 (cmp, r1, r0);
71*f3087befSAndrew Turner }
72*f3087befSAndrew Turner
73*f3087befSAndrew Turner #endif
74*f3087befSAndrew Turner
75*f3087befSAndrew Turner /* Fast vector implementation of exp2.
76*f3087befSAndrew Turner Maximum measured error is 1.65 ulp.
77*f3087befSAndrew Turner _ZGVnN2v_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1
78*f3087befSAndrew Turner want 0x1.f8db0d4df721dp-1. */
79*f3087befSAndrew Turner VPCS_ATTR
V_NAME_D1(exp2)80*f3087befSAndrew Turner float64x2_t V_NAME_D1 (exp2) (float64x2_t x)
81*f3087befSAndrew Turner {
82*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
83*f3087befSAndrew Turner uint64x2_t cmp;
84*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT
85*f3087befSAndrew Turner uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x));
86*f3087befSAndrew Turner cmp = vcgeq_u64 (vsubq_u64 (ia, v_u64 (TinyBound)), v_u64 (Thres));
87*f3087befSAndrew Turner /* Mask special lanes and retain a copy of x for passing to special-case
88*f3087befSAndrew Turner handler. */
89*f3087befSAndrew Turner float64x2_t xc = x;
90*f3087befSAndrew Turner x = v_zerofy_f64 (x, cmp);
91*f3087befSAndrew Turner #else
92*f3087befSAndrew Turner cmp = vcagtq_f64 (x, d->scale_big_bound);
93*f3087befSAndrew Turner #endif
94*f3087befSAndrew Turner
95*f3087befSAndrew Turner /* n = round(x/N). */
96*f3087befSAndrew Turner float64x2_t z = vaddq_f64 (d->shift, x);
97*f3087befSAndrew Turner uint64x2_t u = vreinterpretq_u64_f64 (z);
98*f3087befSAndrew Turner float64x2_t n = vsubq_f64 (z, d->shift);
99*f3087befSAndrew Turner
100*f3087befSAndrew Turner /* r = x - n/N. */
101*f3087befSAndrew Turner float64x2_t r = vsubq_f64 (x, n);
102*f3087befSAndrew Turner
103*f3087befSAndrew Turner /* s = 2^(n/N). */
104*f3087befSAndrew Turner uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS);
105*f3087befSAndrew Turner u = lookup_sbits (u);
106*f3087befSAndrew Turner float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e));
107*f3087befSAndrew Turner
108*f3087befSAndrew Turner /* y ~ exp2(r) - 1. */
109*f3087befSAndrew Turner float64x2_t r2 = vmulq_f64 (r, r);
110*f3087befSAndrew Turner float64x2_t y = v_pairwise_poly_3_f64 (r, r2, d->poly);
111*f3087befSAndrew Turner y = vmulq_f64 (r, y);
112*f3087befSAndrew Turner
113*f3087befSAndrew Turner if (unlikely (v_any_u64 (cmp)))
114*f3087befSAndrew Turner #if !WANT_SIMD_EXCEPT
115*f3087befSAndrew Turner return special_case (s, y, n, d);
116*f3087befSAndrew Turner #else
117*f3087befSAndrew Turner return special_case (xc, vfmaq_f64 (s, s, y), cmp);
118*f3087befSAndrew Turner #endif
119*f3087befSAndrew Turner return vfmaq_f64 (s, s, y);
120*f3087befSAndrew Turner }
121*f3087befSAndrew Turner
122*f3087befSAndrew Turner TEST_SIG (V, D, 1, exp2, -9.9, 9.9)
123*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (exp2), 1.15)
124*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (exp2), WANT_SIMD_EXCEPT)
125*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (exp2), 0, TinyBound, 5000)
126*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (exp2), TinyBound, BigBound, 10000)
127*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (exp2), BigBound, UOFlowBound, 5000)
128*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (exp2), UOFlowBound, inf, 10000)
129