1*412f47f9SXin Li /*
2*412f47f9SXin Li * Single-precision vector/SVE log2 function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2022-2024, Arm Limited.
5*412f47f9SXin Li * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*412f47f9SXin Li */
7*412f47f9SXin Li
8*412f47f9SXin Li #include "sv_math.h"
9*412f47f9SXin Li #include "pl_sig.h"
10*412f47f9SXin Li #include "pl_test.h"
11*412f47f9SXin Li
12*412f47f9SXin Li static const struct data
13*412f47f9SXin Li {
14*412f47f9SXin Li float poly_02468[5];
15*412f47f9SXin Li float poly_1357[4];
16*412f47f9SXin Li } data = {
17*412f47f9SXin Li .poly_1357 = {
18*412f47f9SXin Li /* Coefficients copied from the AdvSIMD routine, then rearranged so that coeffs
19*412f47f9SXin Li 1, 3, 5 and 7 can be loaded as a single quad-word, hence used with _lane
20*412f47f9SXin Li variant of MLA intrinsic. */
21*412f47f9SXin Li -0x1.715458p-1f, -0x1.7171a4p-2f, -0x1.e5143ep-3f, -0x1.c675bp-3f
22*412f47f9SXin Li },
23*412f47f9SXin Li .poly_02468 = { 0x1.715476p0f, 0x1.ec701cp-2f, 0x1.27a0b8p-2f,
24*412f47f9SXin Li 0x1.9d8ecap-3f, 0x1.9e495p-3f },
25*412f47f9SXin Li };
26*412f47f9SXin Li
27*412f47f9SXin Li #define Min (0x00800000)
28*412f47f9SXin Li #define Max (0x7f800000)
29*412f47f9SXin Li #define Thres (0x7f000000) /* Max - Min. */
30*412f47f9SXin Li #define MantissaMask (0x007fffff)
31*412f47f9SXin Li #define Off (0x3f2aaaab) /* 0.666667. */
32*412f47f9SXin Li
33*412f47f9SXin Li static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t cmp)34*412f47f9SXin Li special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
35*412f47f9SXin Li {
36*412f47f9SXin Li return sv_call_f32 (log2f, x, y, cmp);
37*412f47f9SXin Li }
38*412f47f9SXin Li
39*412f47f9SXin Li /* Optimised implementation of SVE log2f, using the same algorithm
40*412f47f9SXin Li and polynomial as AdvSIMD log2f.
41*412f47f9SXin Li Maximum error is 2.48 ULPs:
42*412f47f9SXin Li SV_NAME_F1 (log2)(0x1.558174p+0) got 0x1.a9be84p-2
43*412f47f9SXin Li want 0x1.a9be8p-2. */
SV_NAME_F1(log2)44*412f47f9SXin Li svfloat32_t SV_NAME_F1 (log2) (svfloat32_t x, const svbool_t pg)
45*412f47f9SXin Li {
46*412f47f9SXin Li const struct data *d = ptr_barrier (&data);
47*412f47f9SXin Li
48*412f47f9SXin Li svuint32_t u = svreinterpret_u32 (x);
49*412f47f9SXin Li svbool_t special = svcmpge (pg, svsub_x (pg, u, Min), Thres);
50*412f47f9SXin Li
51*412f47f9SXin Li /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
52*412f47f9SXin Li u = svsub_x (pg, u, Off);
53*412f47f9SXin Li svfloat32_t n = svcvt_f32_x (
54*412f47f9SXin Li pg, svasr_x (pg, svreinterpret_s32 (u), 23)); /* Sign-extend. */
55*412f47f9SXin Li u = svand_x (pg, u, MantissaMask);
56*412f47f9SXin Li u = svadd_x (pg, u, Off);
57*412f47f9SXin Li svfloat32_t r = svsub_x (pg, svreinterpret_f32 (u), 1.0f);
58*412f47f9SXin Li
59*412f47f9SXin Li /* y = log2(1+r) + n. */
60*412f47f9SXin Li svfloat32_t r2 = svmul_x (pg, r, r);
61*412f47f9SXin Li
62*412f47f9SXin Li /* Evaluate polynomial using pairwise Horner scheme. */
63*412f47f9SXin Li svfloat32_t p_1357 = svld1rq (svptrue_b32 (), &d->poly_1357[0]);
64*412f47f9SXin Li svfloat32_t q_01 = svmla_lane (sv_f32 (d->poly_02468[0]), r, p_1357, 0);
65*412f47f9SXin Li svfloat32_t q_23 = svmla_lane (sv_f32 (d->poly_02468[1]), r, p_1357, 1);
66*412f47f9SXin Li svfloat32_t q_45 = svmla_lane (sv_f32 (d->poly_02468[2]), r, p_1357, 2);
67*412f47f9SXin Li svfloat32_t q_67 = svmla_lane (sv_f32 (d->poly_02468[3]), r, p_1357, 3);
68*412f47f9SXin Li svfloat32_t y = svmla_x (pg, q_67, r2, sv_f32 (d->poly_02468[4]));
69*412f47f9SXin Li y = svmla_x (pg, q_45, r2, y);
70*412f47f9SXin Li y = svmla_x (pg, q_23, r2, y);
71*412f47f9SXin Li y = svmla_x (pg, q_01, r2, y);
72*412f47f9SXin Li
73*412f47f9SXin Li if (unlikely (svptest_any (pg, special)))
74*412f47f9SXin Li return special_case (x, svmla_x (svnot_z (pg, special), n, r, y), special);
75*412f47f9SXin Li return svmla_x (pg, n, r, y);
76*412f47f9SXin Li }
77*412f47f9SXin Li
78*412f47f9SXin Li PL_SIG (SV, F, 1, log2, 0.01, 11.1)
79*412f47f9SXin Li PL_TEST_ULP (SV_NAME_F1 (log2), 1.99)
80*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log2), -0.0, -0x1p126, 4000)
81*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log2), 0.0, 0x1p-126, 4000)
82*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log2), 0x1p-126, 0x1p-23, 50000)
83*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log2), 0x1p-23, 1.0, 50000)
84*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log2), 1.0, 100, 50000)
85*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log2), 100, inf, 50000)
86