1 /*
2 * Helper for single-precision routines which calculate log(1 + x) and do not
3 * need special-case handling
4 *
5 * Copyright (c) 2022-2024, Arm Limited.
6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7 */
8
9 #ifndef MATH_V_LOG1PF_INLINE_H
10 #define MATH_V_LOG1PF_INLINE_H
11
12 #include "v_math.h"
13 #include "v_poly_f32.h"
14
15 struct v_log1pf_data
16 {
17 uint32x4_t four;
18 int32x4_t three_quarters;
19 float c0, c3, c5, c7;
20 float32x4_t c4, c6, c1, c2, ln2;
21 };
22
23 /* Polynomial generated using FPMinimax in [-0.25, 0.5]. First two coefficients
24 (1, -0.5) are not stored as they can be generated more efficiently. */
25 #define V_LOG1PF_CONSTANTS_TABLE \
26 { \
27 .c0 = 0x1.5555aap-2f, .c1 = V4 (-0x1.000038p-2f), \
28 .c2 = V4 (0x1.99675cp-3f), .c3 = -0x1.54ef78p-3f, \
29 .c4 = V4 (0x1.28a1f4p-3f), .c5 = -0x1.0da91p-3f, \
30 .c6 = V4 (0x1.abcb6p-4f), .c7 = -0x1.6f0d5ep-5f, \
31 .ln2 = V4 (0x1.62e43p-1f), .four = V4 (0x40800000), \
32 .three_quarters = V4 (0x3f400000) \
33 }
34
35 static inline float32x4_t
eval_poly(float32x4_t m,const struct v_log1pf_data * d)36 eval_poly (float32x4_t m, const struct v_log1pf_data *d)
37 {
38 /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner. */
39 float32x4_t c0357 = vld1q_f32 (&d->c0);
40 float32x4_t q = vfmaq_laneq_f32 (v_f32 (-0.5), m, c0357, 0);
41 float32x4_t m2 = vmulq_f32 (m, m);
42 float32x4_t p67 = vfmaq_laneq_f32 (d->c6, m, c0357, 3);
43 float32x4_t p45 = vfmaq_laneq_f32 (d->c4, m, c0357, 2);
44 float32x4_t p23 = vfmaq_laneq_f32 (d->c2, m, c0357, 1);
45 float32x4_t p = vfmaq_f32 (p45, m2, p67);
46 p = vfmaq_f32 (p23, m2, p);
47 p = vfmaq_f32 (d->c1, m, p);
48 p = vmulq_f32 (m2, p);
49 p = vfmaq_f32 (m, m2, p);
50 return vfmaq_f32 (p, m2, q);
51 }
52
53 static inline float32x4_t
log1pf_inline(float32x4_t x,const struct v_log1pf_data * d)54 log1pf_inline (float32x4_t x, const struct v_log1pf_data *d)
55 {
56 /* Helper for calculating log(x + 1). */
57
58 /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
59 is in [-0.25, 0.5]):
60 log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
61
62 We approximate log1p(m) with a polynomial, then scale by
63 k*log(2). Instead of doing this directly, we use an intermediate
64 scale factor s = 4*k*log(2) to ensure the scale is representable
65 as a normalised fp32 number. */
66 float32x4_t m = vaddq_f32 (x, v_f32 (1.0f));
67
68 /* Choose k to scale x to the range [-1/4, 1/2]. */
69 int32x4_t k
70 = vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d->three_quarters),
71 v_s32 (0xff800000));
72 uint32x4_t ku = vreinterpretq_u32_s32 (k);
73
74 /* Scale up to ensure that the scale factor is representable as normalised
75 fp32 number, and scale m down accordingly. */
76 float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d->four, ku));
77
78 /* Scale x by exponent manipulation. */
79 float32x4_t m_scale
80 = vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku));
81 m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s));
82
83 /* Evaluate polynomial on the reduced interval. */
84 float32x4_t p = eval_poly (m_scale, d);
85
86 /* The scale factor to be applied back at the end - by multiplying float(k)
87 by 2^-23 we get the unbiased exponent of k. */
88 float32x4_t scale_back = vmulq_f32 (vcvtq_f32_s32 (k), v_f32 (0x1.0p-23f));
89
90 /* Apply the scaling back. */
91 return vfmaq_f32 (p, scale_back, d->ln2);
92 }
93
94 #endif // MATH_V_LOG1PF_INLINE_H
95