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 "sv_math.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 static const struct data
13 {
14 float poly_0135[4];
15 float poly_246[3];
16 float ln2;
17 } data = {
18 .poly_0135 = {
19 /* Coefficients copied from the AdvSIMD routine in math/, then rearranged so
20 that coeffs 0, 1, 3 and 5 can be loaded as a single quad-word, hence used
21 with _lane variant of MLA intrinsic. */
22 -0x1.3e737cp-3f, 0x1.5a9aa2p-3f, 0x1.961348p-3f, 0x1.555d7cp-2f
23 },
24 .poly_246 = { -0x1.4f9934p-3f, -0x1.00187cp-2f, -0x1.ffffc8p-2f },
25 .ln2 = 0x1.62e43p-1f
26 };
27
28 #define Min (0x00800000)
29 #define Max (0x7f800000)
30 #define Thresh (0x7f000000) /* Max - Min. */
31 #define Mask (0x007fffff)
32 #define Off (0x3f2aaaab) /* 0.666667. */
33
34 float optr_aor_log_f32 (float);
35
36 static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t cmp)37 special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
38 {
39 return sv_call_f32 (optr_aor_log_f32, x, y, cmp);
40 }
41
42 /* Optimised implementation of SVE logf, using the same algorithm and
43 polynomial as the AdvSIMD routine. Maximum error is 3.34 ULPs:
44 SV_NAME_F1 (log)(0x1.557298p+0) got 0x1.26edecp-2
45 want 0x1.26ede6p-2. */
SV_NAME_F1(log)46 svfloat32_t SV_NAME_F1 (log) (svfloat32_t x, const svbool_t pg)
47 {
48 const struct data *d = ptr_barrier (&data);
49
50 svuint32_t u = svreinterpret_u32 (x);
51 svbool_t cmp = svcmpge (pg, svsub_x (pg, u, Min), Thresh);
52
53 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
54 u = svsub_x (pg, u, Off);
55 svfloat32_t n = svcvt_f32_x (
56 pg, svasr_x (pg, svreinterpret_s32 (u), 23)); /* Sign-extend. */
57 u = svand_x (pg, u, Mask);
58 u = svadd_x (pg, u, Off);
59 svfloat32_t r = svsub_x (pg, svreinterpret_f32 (u), 1.0f);
60
61 /* y = log(1+r) + n*ln2. */
62 svfloat32_t r2 = svmul_x (pg, r, r);
63 /* n*ln2 + r + r2*(P6 + r*P5 + r2*(P4 + r*P3 + r2*(P2 + r*P1 + r2*P0))). */
64 svfloat32_t p_0135 = svld1rq (svptrue_b32 (), &d->poly_0135[0]);
65 svfloat32_t p = svmla_lane (sv_f32 (d->poly_246[0]), r, p_0135, 1);
66 svfloat32_t q = svmla_lane (sv_f32 (d->poly_246[1]), r, p_0135, 2);
67 svfloat32_t y = svmla_lane (sv_f32 (d->poly_246[2]), r, p_0135, 3);
68 p = svmla_lane (p, r2, p_0135, 0);
69
70 q = svmla_x (pg, q, r2, p);
71 y = svmla_x (pg, y, r2, q);
72 p = svmla_x (pg, r, n, d->ln2);
73
74 if (unlikely (svptest_any (pg, cmp)))
75 return special_case (x, svmla_x (svnot_z (pg, cmp), p, r2, y), cmp);
76 return svmla_x (pg, p, r2, y);
77 }
78
79 PL_SIG (SV, F, 1, log, 0.01, 11.1)
80 PL_TEST_ULP (SV_NAME_F1 (log), 2.85)
81 PL_TEST_INTERVAL (SV_NAME_F1 (log), -0.0, -inf, 100)
82 PL_TEST_INTERVAL (SV_NAME_F1 (log), 0, 0x1p-126, 100)
83 PL_TEST_INTERVAL (SV_NAME_F1 (log), 0x1p-126, 0x1p-23, 50000)
84 PL_TEST_INTERVAL (SV_NAME_F1 (log), 0x1p-23, 1.0, 50000)
85 PL_TEST_INTERVAL (SV_NAME_F1 (log), 1.0, 100, 50000)
86 PL_TEST_INTERVAL (SV_NAME_F1 (log), 100, inf, 50000)
87