1*412f47f9SXin Li /*
2*412f47f9SXin Li * Single-precision vector log function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2019-2023, 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_0135[4];
15*412f47f9SXin Li float poly_246[3];
16*412f47f9SXin Li float ln2;
17*412f47f9SXin Li } data = {
18*412f47f9SXin Li .poly_0135 = {
19*412f47f9SXin Li /* Coefficients copied from the AdvSIMD routine in math/, then rearranged so
20*412f47f9SXin Li that coeffs 0, 1, 3 and 5 can be loaded as a single quad-word, hence used
21*412f47f9SXin Li with _lane variant of MLA intrinsic. */
22*412f47f9SXin Li -0x1.3e737cp-3f, 0x1.5a9aa2p-3f, 0x1.961348p-3f, 0x1.555d7cp-2f
23*412f47f9SXin Li },
24*412f47f9SXin Li .poly_246 = { -0x1.4f9934p-3f, -0x1.00187cp-2f, -0x1.ffffc8p-2f },
25*412f47f9SXin Li .ln2 = 0x1.62e43p-1f
26*412f47f9SXin Li };
27*412f47f9SXin Li
28*412f47f9SXin Li #define Min (0x00800000)
29*412f47f9SXin Li #define Max (0x7f800000)
30*412f47f9SXin Li #define Thresh (0x7f000000) /* Max - Min. */
31*412f47f9SXin Li #define Mask (0x007fffff)
32*412f47f9SXin Li #define Off (0x3f2aaaab) /* 0.666667. */
33*412f47f9SXin Li
34*412f47f9SXin Li float optr_aor_log_f32 (float);
35*412f47f9SXin Li
36*412f47f9SXin Li static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t cmp)37*412f47f9SXin Li special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
38*412f47f9SXin Li {
39*412f47f9SXin Li return sv_call_f32 (optr_aor_log_f32, x, y, cmp);
40*412f47f9SXin Li }
41*412f47f9SXin Li
42*412f47f9SXin Li /* Optimised implementation of SVE logf, using the same algorithm and
43*412f47f9SXin Li polynomial as the AdvSIMD routine. Maximum error is 3.34 ULPs:
44*412f47f9SXin Li SV_NAME_F1 (log)(0x1.557298p+0) got 0x1.26edecp-2
45*412f47f9SXin Li want 0x1.26ede6p-2. */
SV_NAME_F1(log)46*412f47f9SXin Li svfloat32_t SV_NAME_F1 (log) (svfloat32_t x, const svbool_t pg)
47*412f47f9SXin Li {
48*412f47f9SXin Li const struct data *d = ptr_barrier (&data);
49*412f47f9SXin Li
50*412f47f9SXin Li svuint32_t u = svreinterpret_u32 (x);
51*412f47f9SXin Li svbool_t cmp = svcmpge (pg, svsub_x (pg, u, Min), Thresh);
52*412f47f9SXin Li
53*412f47f9SXin Li /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */
54*412f47f9SXin Li u = svsub_x (pg, u, Off);
55*412f47f9SXin Li svfloat32_t n = svcvt_f32_x (
56*412f47f9SXin Li pg, svasr_x (pg, svreinterpret_s32 (u), 23)); /* Sign-extend. */
57*412f47f9SXin Li u = svand_x (pg, u, Mask);
58*412f47f9SXin Li u = svadd_x (pg, u, Off);
59*412f47f9SXin Li svfloat32_t r = svsub_x (pg, svreinterpret_f32 (u), 1.0f);
60*412f47f9SXin Li
61*412f47f9SXin Li /* y = log(1+r) + n*ln2. */
62*412f47f9SXin Li svfloat32_t r2 = svmul_x (pg, r, r);
63*412f47f9SXin Li /* n*ln2 + r + r2*(P6 + r*P5 + r2*(P4 + r*P3 + r2*(P2 + r*P1 + r2*P0))). */
64*412f47f9SXin Li svfloat32_t p_0135 = svld1rq (svptrue_b32 (), &d->poly_0135[0]);
65*412f47f9SXin Li svfloat32_t p = svmla_lane (sv_f32 (d->poly_246[0]), r, p_0135, 1);
66*412f47f9SXin Li svfloat32_t q = svmla_lane (sv_f32 (d->poly_246[1]), r, p_0135, 2);
67*412f47f9SXin Li svfloat32_t y = svmla_lane (sv_f32 (d->poly_246[2]), r, p_0135, 3);
68*412f47f9SXin Li p = svmla_lane (p, r2, p_0135, 0);
69*412f47f9SXin Li
70*412f47f9SXin Li q = svmla_x (pg, q, r2, p);
71*412f47f9SXin Li y = svmla_x (pg, y, r2, q);
72*412f47f9SXin Li p = svmla_x (pg, r, n, d->ln2);
73*412f47f9SXin Li
74*412f47f9SXin Li if (unlikely (svptest_any (pg, cmp)))
75*412f47f9SXin Li return special_case (x, svmla_x (svnot_z (pg, cmp), p, r2, y), cmp);
76*412f47f9SXin Li return svmla_x (pg, p, r2, y);
77*412f47f9SXin Li }
78*412f47f9SXin Li
79*412f47f9SXin Li PL_SIG (SV, F, 1, log, 0.01, 11.1)
80*412f47f9SXin Li PL_TEST_ULP (SV_NAME_F1 (log), 2.85)
81*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log), -0.0, -inf, 100)
82*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log), 0, 0x1p-126, 100)
83*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log), 0x1p-126, 0x1p-23, 50000)
84*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log), 0x1p-23, 1.0, 50000)
85*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log), 1.0, 100, 50000)
86*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (log), 100, inf, 50000)
87