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
13 const 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
33 static inline float32x4_t
eval_poly(float32x4_t m,const float32x4_t * p)34 eval_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
52 static float32x4_t NOINLINE VPCS_ATTR
special_case(float32x4_t x,float32x4_t y,uint32x4_t special)53 special_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. */
V_NAME_F1(log1p)61 VPCS_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
120 PL_SIG (V, F, 1, log1p, -0.9, 10.0)
121 PL_TEST_ULP (V_NAME_F1 (log1p), 1.53)
122 PL_TEST_EXPECT_FENV (V_NAME_F1 (log1p), WANT_SIMD_EXCEPT)
123 PL_TEST_SYM_INTERVAL (V_NAME_F1 (log1p), 0.0, 0x1p-23, 30000)
124 PL_TEST_SYM_INTERVAL (V_NAME_F1 (log1p), 0x1p-23, 1, 50000)
125 PL_TEST_INTERVAL (V_NAME_F1 (log1p), 1, inf, 50000)
126 PL_TEST_INTERVAL (V_NAME_F1 (log1p), -1.0, -inf, 1000)
127