1*412f47f9SXin Li /*
2*412f47f9SXin Li * Single-precision SVE 2^x function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2023-2024, 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 "poly_sve_f32.h"
10*412f47f9SXin Li #include "pl_sig.h"
11*412f47f9SXin Li #include "pl_test.h"
12*412f47f9SXin Li
13*412f47f9SXin Li #define Thres 0x1.5d5e2ap+6f
14*412f47f9SXin Li
15*412f47f9SXin Li static const struct data
16*412f47f9SXin Li {
17*412f47f9SXin Li float poly[5];
18*412f47f9SXin Li float shift, thres;
19*412f47f9SXin Li } data = {
20*412f47f9SXin Li /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
21*412f47f9SXin Li compatibility with polynomial helpers. */
22*412f47f9SXin Li .poly = { 0x1.62e422p-1f, 0x1.ebf9bcp-3f, 0x1.c6bd32p-5f, 0x1.3ce9e4p-7f,
23*412f47f9SXin Li 0x1.59977ap-10f },
24*412f47f9SXin Li /* 1.5*2^17 + 127. */
25*412f47f9SXin Li .shift = 0x1.903f8p17f,
26*412f47f9SXin Li /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
27*412f47f9SXin Li correctly by FEXPA. */
28*412f47f9SXin Li .thres = Thres,
29*412f47f9SXin Li };
30*412f47f9SXin Li
31*412f47f9SXin Li static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t special)32*412f47f9SXin Li special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
33*412f47f9SXin Li {
34*412f47f9SXin Li return sv_call_f32 (exp2f, x, y, special);
35*412f47f9SXin Li }
36*412f47f9SXin Li
37*412f47f9SXin Li /* Single-precision SVE exp2f routine. Implements the same algorithm
38*412f47f9SXin Li as AdvSIMD exp2f.
39*412f47f9SXin Li Worst case error is 1.04 ULPs.
40*412f47f9SXin Li SV_NAME_F1 (exp2)(0x1.943b9p-1) got 0x1.ba7eb2p+0
41*412f47f9SXin Li want 0x1.ba7ebp+0. */
SV_NAME_F1(exp2)42*412f47f9SXin Li svfloat32_t SV_NAME_F1 (exp2) (svfloat32_t x, const svbool_t pg)
43*412f47f9SXin Li {
44*412f47f9SXin Li const struct data *d = ptr_barrier (&data);
45*412f47f9SXin Li /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
46*412f47f9SXin Li x = n + r, with r in [-1/2, 1/2]. */
47*412f47f9SXin Li svfloat32_t shift = sv_f32 (d->shift);
48*412f47f9SXin Li svfloat32_t z = svadd_x (pg, x, shift);
49*412f47f9SXin Li svfloat32_t n = svsub_x (pg, z, shift);
50*412f47f9SXin Li svfloat32_t r = svsub_x (pg, x, n);
51*412f47f9SXin Li
52*412f47f9SXin Li svbool_t special = svacgt (pg, x, d->thres);
53*412f47f9SXin Li svfloat32_t scale = svexpa (svreinterpret_u32 (z));
54*412f47f9SXin Li
55*412f47f9SXin Li /* Polynomial evaluation: poly(r) ~ exp2(r)-1.
56*412f47f9SXin Li Evaluate polynomial use hybrid scheme - offset ESTRIN by 1 for
57*412f47f9SXin Li coefficients 1 to 4, and apply most significant coefficient directly. */
58*412f47f9SXin Li svfloat32_t r2 = svmul_x (pg, r, r);
59*412f47f9SXin Li svfloat32_t p14 = sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1);
60*412f47f9SXin Li svfloat32_t p0 = svmul_x (pg, r, d->poly[0]);
61*412f47f9SXin Li svfloat32_t poly = svmla_x (pg, p0, r2, p14);
62*412f47f9SXin Li
63*412f47f9SXin Li if (unlikely (svptest_any (pg, special)))
64*412f47f9SXin Li return special_case (x, svmla_x (pg, scale, scale, poly), special);
65*412f47f9SXin Li
66*412f47f9SXin Li return svmla_x (pg, scale, scale, poly);
67*412f47f9SXin Li }
68*412f47f9SXin Li
69*412f47f9SXin Li PL_SIG (SV, F, 1, exp2, -9.9, 9.9)
70*412f47f9SXin Li PL_TEST_ULP (SV_NAME_F1 (exp2), 0.55)
71*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (exp2), 0, Thres, 40000)
72*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (exp2), 1, Thres, 50000)
73*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (exp2), Thres, inf, 50000)
74*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0, -0x1p-23, 40000)
75*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0x1p-23, -1, 50000)
76*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -1, -0x1p23, 50000)
77*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0x1p23, -inf, 50000)
78