1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Helper for single-precision routines which calculate log(1 + x) and do not
3*f3087befSAndrew Turner * need special-case handling
4*f3087befSAndrew Turner *
5*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited.
6*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7*f3087befSAndrew Turner */
8*f3087befSAndrew Turner
9*f3087befSAndrew Turner #ifndef MATH_V_LOG1PF_INLINE_H
10*f3087befSAndrew Turner #define MATH_V_LOG1PF_INLINE_H
11*f3087befSAndrew Turner
12*f3087befSAndrew Turner #include "v_math.h"
13*f3087befSAndrew Turner #include "v_poly_f32.h"
14*f3087befSAndrew Turner
15*f3087befSAndrew Turner struct v_log1pf_data
16*f3087befSAndrew Turner {
17*f3087befSAndrew Turner uint32x4_t four;
18*f3087befSAndrew Turner int32x4_t three_quarters;
19*f3087befSAndrew Turner float c0, c3, c5, c7;
20*f3087befSAndrew Turner float32x4_t c4, c6, c1, c2, ln2;
21*f3087befSAndrew Turner };
22*f3087befSAndrew Turner
23*f3087befSAndrew Turner /* Polynomial generated using FPMinimax in [-0.25, 0.5]. First two coefficients
24*f3087befSAndrew Turner (1, -0.5) are not stored as they can be generated more efficiently. */
25*f3087befSAndrew Turner #define V_LOG1PF_CONSTANTS_TABLE \
26*f3087befSAndrew Turner { \
27*f3087befSAndrew Turner .c0 = 0x1.5555aap-2f, .c1 = V4 (-0x1.000038p-2f), \
28*f3087befSAndrew Turner .c2 = V4 (0x1.99675cp-3f), .c3 = -0x1.54ef78p-3f, \
29*f3087befSAndrew Turner .c4 = V4 (0x1.28a1f4p-3f), .c5 = -0x1.0da91p-3f, \
30*f3087befSAndrew Turner .c6 = V4 (0x1.abcb6p-4f), .c7 = -0x1.6f0d5ep-5f, \
31*f3087befSAndrew Turner .ln2 = V4 (0x1.62e43p-1f), .four = V4 (0x40800000), \
32*f3087befSAndrew Turner .three_quarters = V4 (0x3f400000) \
33*f3087befSAndrew Turner }
34*f3087befSAndrew Turner
35*f3087befSAndrew Turner static inline float32x4_t
eval_poly(float32x4_t m,const struct v_log1pf_data * d)36*f3087befSAndrew Turner eval_poly (float32x4_t m, const struct v_log1pf_data *d)
37*f3087befSAndrew Turner {
38*f3087befSAndrew Turner /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner. */
39*f3087befSAndrew Turner float32x4_t c0357 = vld1q_f32 (&d->c0);
40*f3087befSAndrew Turner float32x4_t q = vfmaq_laneq_f32 (v_f32 (-0.5), m, c0357, 0);
41*f3087befSAndrew Turner float32x4_t m2 = vmulq_f32 (m, m);
42*f3087befSAndrew Turner float32x4_t p67 = vfmaq_laneq_f32 (d->c6, m, c0357, 3);
43*f3087befSAndrew Turner float32x4_t p45 = vfmaq_laneq_f32 (d->c4, m, c0357, 2);
44*f3087befSAndrew Turner float32x4_t p23 = vfmaq_laneq_f32 (d->c2, m, c0357, 1);
45*f3087befSAndrew Turner float32x4_t p = vfmaq_f32 (p45, m2, p67);
46*f3087befSAndrew Turner p = vfmaq_f32 (p23, m2, p);
47*f3087befSAndrew Turner p = vfmaq_f32 (d->c1, m, p);
48*f3087befSAndrew Turner p = vmulq_f32 (m2, p);
49*f3087befSAndrew Turner p = vfmaq_f32 (m, m2, p);
50*f3087befSAndrew Turner return vfmaq_f32 (p, m2, q);
51*f3087befSAndrew Turner }
52*f3087befSAndrew Turner
53*f3087befSAndrew Turner static inline float32x4_t
log1pf_inline(float32x4_t x,const struct v_log1pf_data * d)54*f3087befSAndrew Turner log1pf_inline (float32x4_t x, const struct v_log1pf_data *d)
55*f3087befSAndrew Turner {
56*f3087befSAndrew Turner /* Helper for calculating log(x + 1). */
57*f3087befSAndrew Turner
58*f3087befSAndrew Turner /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
59*f3087befSAndrew Turner is in [-0.25, 0.5]):
60*f3087befSAndrew Turner log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
61*f3087befSAndrew Turner
62*f3087befSAndrew Turner We approximate log1p(m) with a polynomial, then scale by
63*f3087befSAndrew Turner k*log(2). Instead of doing this directly, we use an intermediate
64*f3087befSAndrew Turner scale factor s = 4*k*log(2) to ensure the scale is representable
65*f3087befSAndrew Turner as a normalised fp32 number. */
66*f3087befSAndrew Turner float32x4_t m = vaddq_f32 (x, v_f32 (1.0f));
67*f3087befSAndrew Turner
68*f3087befSAndrew Turner /* Choose k to scale x to the range [-1/4, 1/2]. */
69*f3087befSAndrew Turner int32x4_t k
70*f3087befSAndrew Turner = vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d->three_quarters),
71*f3087befSAndrew Turner v_s32 (0xff800000));
72*f3087befSAndrew Turner uint32x4_t ku = vreinterpretq_u32_s32 (k);
73*f3087befSAndrew Turner
74*f3087befSAndrew Turner /* Scale up to ensure that the scale factor is representable as normalised
75*f3087befSAndrew Turner fp32 number, and scale m down accordingly. */
76*f3087befSAndrew Turner float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d->four, ku));
77*f3087befSAndrew Turner
78*f3087befSAndrew Turner /* Scale x by exponent manipulation. */
79*f3087befSAndrew Turner float32x4_t m_scale
80*f3087befSAndrew Turner = vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku));
81*f3087befSAndrew Turner m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s));
82*f3087befSAndrew Turner
83*f3087befSAndrew Turner /* Evaluate polynomial on the reduced interval. */
84*f3087befSAndrew Turner float32x4_t p = eval_poly (m_scale, d);
85*f3087befSAndrew Turner
86*f3087befSAndrew Turner /* The scale factor to be applied back at the end - by multiplying float(k)
87*f3087befSAndrew Turner by 2^-23 we get the unbiased exponent of k. */
88*f3087befSAndrew Turner float32x4_t scale_back = vmulq_f32 (vcvtq_f32_s32 (k), v_f32 (0x1.0p-23f));
89*f3087befSAndrew Turner
90*f3087befSAndrew Turner /* Apply the scaling back. */
91*f3087befSAndrew Turner return vfmaq_f32 (p, scale_back, d->ln2);
92*f3087befSAndrew Turner }
93*f3087befSAndrew Turner
94*f3087befSAndrew Turner #endif // MATH_V_LOG1PF_INLINE_H
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