1 /*
2 * Single-precision vector log function.
3 *
4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 * See https://llvm.org/LICENSE.txt for license information.
6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 */
8
9 #include "mathlib.h"
10 #include "v_math.h"
11 #if V_SUPPORTED
12
13 static const float Poly[] = {
14 /* 3.34 ulp error */
15 -0x1.3e737cp-3f, 0x1.5a9aa2p-3f, -0x1.4f9934p-3f, 0x1.961348p-3f,
16 -0x1.00187cp-2f, 0x1.555d7cp-2f, -0x1.ffffc8p-2f,
17 };
18 #define P7 v_f32 (Poly[0])
19 #define P6 v_f32 (Poly[1])
20 #define P5 v_f32 (Poly[2])
21 #define P4 v_f32 (Poly[3])
22 #define P3 v_f32 (Poly[4])
23 #define P2 v_f32 (Poly[5])
24 #define P1 v_f32 (Poly[6])
25
26 #define Ln2 v_f32 (0x1.62e43p-1f) /* 0x3f317218 */
27 #define Min v_u32 (0x00800000)
28 #define Max v_u32 (0x7f800000)
29 #define Mask v_u32 (0x007fffff)
30 #define Off v_u32 (0x3f2aaaab) /* 0.666667 */
31
32 VPCS_ATTR
33 __attribute__ ((noinline)) static v_f32_t
specialcase(v_f32_t x,v_f32_t y,v_u32_t cmp)34 specialcase (v_f32_t x, v_f32_t y, v_u32_t cmp)
35 {
36 /* Fall back to scalar code. */
37 return v_call_f32 (logf, x, y, cmp);
38 }
39
40 VPCS_ATTR
41 v_f32_t
V_NAME(logf)42 V_NAME(logf) (v_f32_t x)
43 {
44 v_f32_t n, p, q, r, r2, y;
45 v_u32_t u, cmp;
46
47 u = v_as_u32_f32 (x);
48 cmp = v_cond_u32 (u - Min >= Max - Min);
49
50 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3 */
51 u -= Off;
52 n = v_to_f32_s32 (v_as_s32_u32 (u) >> 23); /* signextend */
53 u &= Mask;
54 u += Off;
55 r = v_as_f32_u32 (u) - v_f32 (1.0f);
56
57 /* y = log(1+r) + n*ln2. */
58 r2 = r * r;
59 /* n*ln2 + r + r2*(P1 + r*P2 + r2*(P3 + r*P4 + r2*(P5 + r*P6 + r2*P7))). */
60 p = v_fma_f32 (P6, r, P5);
61 q = v_fma_f32 (P4, r, P3);
62 y = v_fma_f32 (P2, r, P1);
63 p = v_fma_f32 (P7, r2, p);
64 q = v_fma_f32 (p, r2, q);
65 y = v_fma_f32 (q, r2, y);
66 p = v_fma_f32 (Ln2, n, r);
67 y = v_fma_f32 (y, r2, p);
68
69 if (unlikely (v_any_u32 (cmp)))
70 return specialcase (x, y, cmp);
71 return y;
72 }
73 VPCS_ALIAS
74 #endif
75