1 /*
2  * Single-precision vector log function.
3  *
4  * Copyright (c) 2019, Arm Limited.
5  * SPDX-License-Identifier: MIT
6  */
7 
8 #include "mathlib.h"
9 #include "v_math.h"
10 #if V_SUPPORTED
11 
12 static const float Poly[] = {
13   /* 3.34 ulp error */
14   -0x1.3e737cp-3f, 0x1.5a9aa2p-3f, -0x1.4f9934p-3f, 0x1.961348p-3f,
15   -0x1.00187cp-2f, 0x1.555d7cp-2f, -0x1.ffffc8p-2f,
16 };
17 #define P7 v_f32 (Poly[0])
18 #define P6 v_f32 (Poly[1])
19 #define P5 v_f32 (Poly[2])
20 #define P4 v_f32 (Poly[3])
21 #define P3 v_f32 (Poly[4])
22 #define P2 v_f32 (Poly[5])
23 #define P1 v_f32 (Poly[6])
24 
25 #define Ln2 v_f32 (0x1.62e43p-1f) /* 0x3f317218 */
26 #define Min v_u32 (0x00800000)
27 #define Max v_u32 (0x7f800000)
28 #define Mask v_u32 (0x007fffff)
29 #define Off v_u32 (0x3f2aaaab) /* 0.666667 */
30 
31 VPCS_ATTR
32 __attribute__ ((noinline)) static v_f32_t
33 specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
34 {
35   /* Fall back to scalar code.  */
36   return v_call_f32 (logf, x, y, cmp);
37 }
38 
39 VPCS_ATTR
40 v_f32_t
41 V_NAME(logf) (v_f32_t x)
42 {
43   v_f32_t n, p, q, r, r2, y;
44   v_u32_t u, cmp;
45 
46   u = v_as_u32_f32 (x);
47   cmp = v_cond_u32 (u - Min >= Max - Min);
48 
49   /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3 */
50   u -= Off;
51   n = v_to_f32_s32 (v_as_s32_u32 (u) >> 23); /* signextend */
52   u &= Mask;
53   u += Off;
54   r = v_as_f32_u32 (u) - v_f32 (1.0f);
55 
56   /* y = log(1+r) + n*ln2.  */
57   r2 = r * r;
58   /* n*ln2 + r + r2*(P1 + r*P2 + r2*(P3 + r*P4 + r2*(P5 + r*P6 + r2*P7))).  */
59   p = v_fma_f32 (P6, r, P5);
60   q = v_fma_f32 (P4, r, P3);
61   y = v_fma_f32 (P2, r, P1);
62   p = v_fma_f32 (P7, r2, p);
63   q = v_fma_f32 (p, r2, q);
64   y = v_fma_f32 (q, r2, y);
65   p = v_fma_f32 (Ln2, n, r);
66   y = v_fma_f32 (y, r2, p);
67 
68   if (unlikely (v_any_u32 (cmp)))
69     return specialcase (x, y, cmp);
70   return y;
71 }
72 VPCS_ALIAS
73 #endif
74