1/*
2 * Double-precision vector 2^x function.
3 *
4 * Copyright (c) 2019-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include "v_math.h"
9#include "poly_advsimd_f64.h"
10#include "pl_sig.h"
11#include "pl_test.h"
12
13#define N (1 << V_EXP_TABLE_BITS)
14#define IndexMask (N - 1)
15#define BigBound 1022.0
16#define UOFlowBound 1280.0
17
18static const struct data
19{
20  float64x2_t poly[4];
21  float64x2_t shift, scale_big_bound, scale_uoflow_bound;
22} data = {
23  /* Coefficients are computed using Remez algorithm with
24     minimisation of the absolute error.  */
25  .poly = { V2 (0x1.62e42fefa3686p-1), V2 (0x1.ebfbdff82c241p-3),
26	    V2 (0x1.c6b09b16de99ap-5), V2 (0x1.3b2abf5571ad8p-7) },
27  .shift = V2 (0x1.8p52 / N),
28  .scale_big_bound = V2 (BigBound),
29  .scale_uoflow_bound = V2 (UOFlowBound),
30};
31
32static inline uint64x2_t
33lookup_sbits (uint64x2_t i)
34{
35  return (uint64x2_t){ __v_exp_data[i[0] & IndexMask],
36		       __v_exp_data[i[1] & IndexMask] };
37}
38
39#if WANT_SIMD_EXCEPT
40
41# define TinyBound 0x2000000000000000 /* asuint64(0x1p-511).  */
42# define Thres 0x2080000000000000     /* asuint64(512.0) - TinyBound.  */
43
44/* Call scalar exp2 as a fallback.  */
45static float64x2_t VPCS_ATTR NOINLINE
46special_case (float64x2_t x, float64x2_t y, uint64x2_t is_special)
47{
48  return v_call_f64 (exp2, x, y, is_special);
49}
50
51#else
52
53# define SpecialOffset 0x6000000000000000 /* 0x1p513.  */
54/* SpecialBias1 + SpecialBias1 = asuint(1.0).  */
55# define SpecialBias1 0x7000000000000000 /* 0x1p769.  */
56# define SpecialBias2 0x3010000000000000 /* 0x1p-254.  */
57
58static inline float64x2_t VPCS_ATTR
59special_case (float64x2_t s, float64x2_t y, float64x2_t n,
60	      const struct data *d)
61{
62  /* 2^(n/N) may overflow, break it up into s1*s2.  */
63  uint64x2_t b = vandq_u64 (vclezq_f64 (n), v_u64 (SpecialOffset));
64  float64x2_t s1 = vreinterpretq_f64_u64 (vsubq_u64 (v_u64 (SpecialBias1), b));
65  float64x2_t s2 = vreinterpretq_f64_u64 (
66    vaddq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (s), v_u64 (SpecialBias2)), b));
67  uint64x2_t cmp = vcagtq_f64 (n, d->scale_uoflow_bound);
68  float64x2_t r1 = vmulq_f64 (s1, s1);
69  float64x2_t r0 = vmulq_f64 (vfmaq_f64 (s2, s2, y), s1);
70  return vbslq_f64 (cmp, r1, r0);
71}
72
73#endif
74
75/* Fast vector implementation of exp2.
76   Maximum measured error is 1.65 ulp.
77   _ZGVnN2v_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1
78				       want 0x1.f8db0d4df721dp-1.  */
79VPCS_ATTR
80float64x2_t V_NAME_D1 (exp2) (float64x2_t x)
81{
82  const struct data *d = ptr_barrier (&data);
83  uint64x2_t cmp;
84#if WANT_SIMD_EXCEPT
85  uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x));
86  cmp = vcgeq_u64 (vsubq_u64 (ia, v_u64 (TinyBound)), v_u64 (Thres));
87  /* Mask special lanes and retain a copy of x for passing to special-case
88     handler.  */
89  float64x2_t xc = x;
90  x = v_zerofy_f64 (x, cmp);
91#else
92  cmp = vcagtq_f64 (x, d->scale_big_bound);
93#endif
94
95  /* n = round(x/N).  */
96  float64x2_t z = vaddq_f64 (d->shift, x);
97  uint64x2_t u = vreinterpretq_u64_f64 (z);
98  float64x2_t n = vsubq_f64 (z, d->shift);
99
100  /* r = x - n/N.  */
101  float64x2_t r = vsubq_f64 (x, n);
102
103  /* s = 2^(n/N).  */
104  uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS);
105  u = lookup_sbits (u);
106  float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e));
107
108  /* y ~ exp2(r) - 1.  */
109  float64x2_t r2 = vmulq_f64 (r, r);
110  float64x2_t y = v_pairwise_poly_3_f64 (r, r2, d->poly);
111  y = vmulq_f64 (r, y);
112
113  if (unlikely (v_any_u64 (cmp)))
114#if !WANT_SIMD_EXCEPT
115    return special_case (s, y, n, d);
116#else
117    return special_case (xc, vfmaq_f64 (s, s, y), cmp);
118#endif
119  return vfmaq_f64 (s, s, y);
120}
121
122PL_SIG (V, D, 1, exp2, -9.9, 9.9)
123PL_TEST_ULP (V_NAME_D1 (exp2), 1.15)
124PL_TEST_EXPECT_FENV (V_NAME_D1 (exp2), WANT_SIMD_EXCEPT)
125PL_TEST_SYM_INTERVAL (V_NAME_D1 (exp2), 0, TinyBound, 5000)
126PL_TEST_SYM_INTERVAL (V_NAME_D1 (exp2), TinyBound, BigBound, 10000)
127PL_TEST_SYM_INTERVAL (V_NAME_D1 (exp2), BigBound, UOFlowBound, 5000)
128PL_TEST_SYM_INTERVAL (V_NAME_D1 (exp2), UOFlowBound, inf, 10000)
129