1 /*
2 * Single-precision vector log function.
3 *
4 * Copyright (c) 2019-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "mathlib.h"
9 #include "v_math.h"
10
11 static const struct data
12 {
13 uint32x4_t min_norm;
14 uint16x8_t special_bound;
15 float32x4_t poly[7];
16 float32x4_t ln2, tiny_bound;
17 uint32x4_t off, mantissa_mask;
18 } data = {
19 /* 3.34 ulp error. */
20 .poly = { V4 (-0x1.3e737cp-3f), V4 (0x1.5a9aa2p-3f), V4 (-0x1.4f9934p-3f),
21 V4 (0x1.961348p-3f), V4 (-0x1.00187cp-2f), V4 (0x1.555d7cp-2f),
22 V4 (-0x1.ffffc8p-2f) },
23 .ln2 = V4 (0x1.62e43p-1f),
24 .tiny_bound = V4 (0x1p-126),
25 .min_norm = V4 (0x00800000),
26 .special_bound = V8 (0x7f00), /* asuint32(inf) - min_norm. */
27 .off = V4 (0x3f2aaaab), /* 0.666667. */
28 .mantissa_mask = V4 (0x007fffff)
29 };
30
31 #define P(i) d->poly[7 - i]
32
33 static float32x4_t VPCS_ATTR NOINLINE
special_case(float32x4_t x,float32x4_t y,float32x4_t r2,float32x4_t p,uint16x4_t cmp)34 special_case (float32x4_t x, float32x4_t y, float32x4_t r2, float32x4_t p,
35 uint16x4_t cmp)
36 {
37 /* Fall back to scalar code. */
38 return v_call_f32 (logf, x, vfmaq_f32 (p, y, r2), vmovl_u16 (cmp));
39 }
40
V_NAME_F1(log)41 float32x4_t VPCS_ATTR V_NAME_F1 (log) (float32x4_t x)
42 {
43 const struct data *d = ptr_barrier (&data);
44 float32x4_t n, p, q, r, r2, y;
45 uint32x4_t u;
46 uint16x4_t cmp;
47
48 u = vreinterpretq_u32_f32 (x);
49 cmp = vcge_u16 (vsubhn_u32 (u, d->min_norm),
50 vget_low_u16 (d->special_bound));
51
52 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
53 u = vsubq_u32 (u, d->off);
54 n = vcvtq_f32_s32 (
55 vshrq_n_s32 (vreinterpretq_s32_u32 (u), 23)); /* signextend. */
56 u = vandq_u32 (u, d->mantissa_mask);
57 u = vaddq_u32 (u, d->off);
58 r = vsubq_f32 (vreinterpretq_f32_u32 (u), v_f32 (1.0f));
59
60 /* y = log(1+r) + n*ln2. */
61 r2 = vmulq_f32 (r, r);
62 /* n*ln2 + r + r2*(P1 + r*P2 + r2*(P3 + r*P4 + r2*(P5 + r*P6 + r2*P7))). */
63 p = vfmaq_f32 (P (5), P (6), r);
64 q = vfmaq_f32 (P (3), P (4), r);
65 y = vfmaq_f32 (P (1), P (2), r);
66 p = vfmaq_f32 (p, P (7), r2);
67 q = vfmaq_f32 (q, p, r2);
68 y = vfmaq_f32 (y, q, r2);
69 p = vfmaq_f32 (r, d->ln2, n);
70
71 if (unlikely (v_any_u16h (cmp)))
72 return special_case (x, y, r2, p, cmp);
73 return vfmaq_f32 (p, y, r2);
74 }
75