1 /*
2 * Helper for single-precision routines which calculate log(1 + x) and do not
3 * need special-case handling
4 *
5 * Copyright (c) 2022-2023, Arm Limited.
6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7 */
8
9 #ifndef PL_MATH_V_LOG1PF_INLINE_H
10 #define PL_MATH_V_LOG1PF_INLINE_H
11
12 #include "v_math.h"
13 #include "poly_advsimd_f32.h"
14
15 struct v_log1pf_data
16 {
17 float32x4_t poly[8], ln2;
18 uint32x4_t four;
19 int32x4_t three_quarters;
20 };
21
22 /* Polynomial generated using FPMinimax in [-0.25, 0.5]. First two coefficients
23 (1, -0.5) are not stored as they can be generated more efficiently. */
24 #define V_LOG1PF_CONSTANTS_TABLE \
25 { \
26 .poly \
27 = { V4 (0x1.5555aap-2f), V4 (-0x1.000038p-2f), V4 (0x1.99675cp-3f), \
28 V4 (-0x1.54ef78p-3f), V4 (0x1.28a1f4p-3f), V4 (-0x1.0da91p-3f), \
29 V4 (0x1.abcb6p-4f), V4 (-0x1.6f0d5ep-5f) }, \
30 .ln2 = V4 (0x1.62e43p-1f), .four = V4 (0x40800000), \
31 .three_quarters = V4 (0x3f400000) \
32 }
33
34 static inline float32x4_t
eval_poly(float32x4_t m,const float32x4_t * c)35 eval_poly (float32x4_t m, const float32x4_t *c)
36 {
37 /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner (main routine
38 uses split Estrin, but this way reduces register pressure in the calling
39 routine). */
40 float32x4_t q = vfmaq_f32 (v_f32 (-0.5), m, c[0]);
41 float32x4_t m2 = vmulq_f32 (m, m);
42 q = vfmaq_f32 (m, m2, q);
43 float32x4_t p = v_pw_horner_6_f32 (m, m2, c + 1);
44 p = vmulq_f32 (m2, p);
45 return vfmaq_f32 (q, m2, p);
46 }
47
48 static inline float32x4_t
log1pf_inline(float32x4_t x,const struct v_log1pf_data d)49 log1pf_inline (float32x4_t x, const struct v_log1pf_data d)
50 {
51 /* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no
52 special-case handling. See that file for details of the algorithm. */
53 float32x4_t m = vaddq_f32 (x, v_f32 (1.0f));
54 int32x4_t k
55 = vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d.three_quarters),
56 v_s32 (0xff800000));
57 uint32x4_t ku = vreinterpretq_u32_s32 (k);
58 float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d.four, ku));
59 float32x4_t m_scale
60 = vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku));
61 m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s));
62 float32x4_t p = eval_poly (m_scale, d.poly);
63 float32x4_t scale_back = vmulq_f32 (vcvtq_f32_s32 (k), v_f32 (0x1.0p-23f));
64 return vfmaq_f32 (p, scale_back, d.ln2);
65 }
66
67 #endif // PL_MATH_V_LOG1PF_INLINE_H
68