1/*
2 * Single-precision vector log(1+x) function.
3 *
4 * Copyright (c) 2022-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include "v_math.h"
9#include "pl_sig.h"
10#include "pl_test.h"
11#include "poly_advsimd_f32.h"
12
13const static struct data
14{
15  float32x4_t poly[8], ln2;
16  uint32x4_t tiny_bound, minus_one, four, thresh;
17  int32x4_t three_quarters;
18} data = {
19  .poly = { /* Generated using FPMinimax in [-0.25, 0.5]. First two coefficients
20	       (1, -0.5) are not stored as they can be generated more
21	       efficiently.  */
22	    V4 (0x1.5555aap-2f), V4 (-0x1.000038p-2f), V4 (0x1.99675cp-3f),
23	    V4 (-0x1.54ef78p-3f), V4 (0x1.28a1f4p-3f), V4 (-0x1.0da91p-3f),
24	    V4 (0x1.abcb6p-4f), V4 (-0x1.6f0d5ep-5f) },
25  .ln2 = V4 (0x1.62e43p-1f),
26  .tiny_bound = V4 (0x34000000), /* asuint32(0x1p-23). ulp=0.5 at 0x1p-23.  */
27  .thresh = V4 (0x4b800000), /* asuint32(INFINITY) - tiny_bound.  */
28  .minus_one = V4 (0xbf800000),
29  .four = V4 (0x40800000),
30  .three_quarters = V4 (0x3f400000)
31};
32
33static inline float32x4_t
34eval_poly (float32x4_t m, const float32x4_t *p)
35{
36  /* Approximate log(1+m) on [-0.25, 0.5] using split Estrin scheme.  */
37  float32x4_t p_12 = vfmaq_f32 (v_f32 (-0.5), m, p[0]);
38  float32x4_t p_34 = vfmaq_f32 (p[1], m, p[2]);
39  float32x4_t p_56 = vfmaq_f32 (p[3], m, p[4]);
40  float32x4_t p_78 = vfmaq_f32 (p[5], m, p[6]);
41
42  float32x4_t m2 = vmulq_f32 (m, m);
43  float32x4_t p_02 = vfmaq_f32 (m, m2, p_12);
44  float32x4_t p_36 = vfmaq_f32 (p_34, m2, p_56);
45  float32x4_t p_79 = vfmaq_f32 (p_78, m2, p[7]);
46
47  float32x4_t m4 = vmulq_f32 (m2, m2);
48  float32x4_t p_06 = vfmaq_f32 (p_02, m4, p_36);
49  return vfmaq_f32 (p_06, m4, vmulq_f32 (m4, p_79));
50}
51
52static float32x4_t NOINLINE VPCS_ATTR
53special_case (float32x4_t x, float32x4_t y, uint32x4_t special)
54{
55  return v_call_f32 (log1pf, x, y, special);
56}
57
58/* Vector log1pf approximation using polynomial on reduced interval. Accuracy
59   is roughly 2.02 ULP:
60   log1pf(0x1.21e13ap-2) got 0x1.fe8028p-3 want 0x1.fe802cp-3.  */
61VPCS_ATTR float32x4_t V_NAME_F1 (log1p) (float32x4_t x)
62{
63  const struct data *d = ptr_barrier (&data);
64
65  uint32x4_t ix = vreinterpretq_u32_f32 (x);
66  uint32x4_t ia = vreinterpretq_u32_f32 (vabsq_f32 (x));
67  uint32x4_t special_cases
68      = vorrq_u32 (vcgeq_u32 (vsubq_u32 (ia, d->tiny_bound), d->thresh),
69		   vcgeq_u32 (ix, d->minus_one));
70  float32x4_t special_arg = x;
71
72#if WANT_SIMD_EXCEPT
73  if (unlikely (v_any_u32 (special_cases)))
74    /* Side-step special lanes so fenv exceptions are not triggered
75       inadvertently.  */
76    x = v_zerofy_f32 (x, special_cases);
77#endif
78
79  /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
80			   is in [-0.25, 0.5]):
81     log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
82
83     We approximate log1p(m) with a polynomial, then scale by
84     k*log(2). Instead of doing this directly, we use an intermediate
85     scale factor s = 4*k*log(2) to ensure the scale is representable
86     as a normalised fp32 number.  */
87
88  float32x4_t m = vaddq_f32 (x, v_f32 (1.0f));
89
90  /* Choose k to scale x to the range [-1/4, 1/2].  */
91  int32x4_t k
92      = vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d->three_quarters),
93		   v_s32 (0xff800000));
94  uint32x4_t ku = vreinterpretq_u32_s32 (k);
95
96  /* Scale x by exponent manipulation.  */
97  float32x4_t m_scale
98      = vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku));
99
100  /* Scale up to ensure that the scale factor is representable as normalised
101     fp32 number, and scale m down accordingly.  */
102  float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d->four, ku));
103  m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s));
104
105  /* Evaluate polynomial on the reduced interval.  */
106  float32x4_t p = eval_poly (m_scale, d->poly);
107
108  /* The scale factor to be applied back at the end - by multiplying float(k)
109     by 2^-23 we get the unbiased exponent of k.  */
110  float32x4_t scale_back = vcvtq_f32_s32 (vshrq_n_s32 (k, 23));
111
112  /* Apply the scaling back.  */
113  float32x4_t y = vfmaq_f32 (p, scale_back, d->ln2);
114
115  if (unlikely (v_any_u32 (special_cases)))
116    return special_case (special_arg, y, special_cases);
117  return y;
118}
119
120PL_SIG (V, F, 1, log1p, -0.9, 10.0)
121PL_TEST_ULP (V_NAME_F1 (log1p), 1.53)
122PL_TEST_EXPECT_FENV (V_NAME_F1 (log1p), WANT_SIMD_EXCEPT)
123PL_TEST_SYM_INTERVAL (V_NAME_F1 (log1p), 0.0, 0x1p-23, 30000)
124PL_TEST_SYM_INTERVAL (V_NAME_F1 (log1p), 0x1p-23, 1, 50000)
125PL_TEST_INTERVAL (V_NAME_F1 (log1p), 1, inf, 50000)
126PL_TEST_INTERVAL (V_NAME_F1 (log1p), -1.0, -inf, 1000)
127