1 /*
2 * Single-precision SVE 2^x function.
3 *
4 * Copyright (c) 2023-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "poly_sve_f32.h"
10 #include "pl_sig.h"
11 #include "pl_test.h"
12
13 #define Thres 0x1.5d5e2ap+6f
14
15 static const struct data
16 {
17 float poly[5];
18 float shift, thres;
19 } data = {
20 /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
21 compatibility with polynomial helpers. */
22 .poly = { 0x1.62e422p-1f, 0x1.ebf9bcp-3f, 0x1.c6bd32p-5f, 0x1.3ce9e4p-7f,
23 0x1.59977ap-10f },
24 /* 1.5*2^17 + 127. */
25 .shift = 0x1.903f8p17f,
26 /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
27 correctly by FEXPA. */
28 .thres = Thres,
29 };
30
31 static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t special)32 special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
33 {
34 return sv_call_f32 (exp2f, x, y, special);
35 }
36
37 /* Single-precision SVE exp2f routine. Implements the same algorithm
38 as AdvSIMD exp2f.
39 Worst case error is 1.04 ULPs.
40 SV_NAME_F1 (exp2)(0x1.943b9p-1) got 0x1.ba7eb2p+0
41 want 0x1.ba7ebp+0. */
SV_NAME_F1(exp2)42 svfloat32_t SV_NAME_F1 (exp2) (svfloat32_t x, const svbool_t pg)
43 {
44 const struct data *d = ptr_barrier (&data);
45 /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
46 x = n + r, with r in [-1/2, 1/2]. */
47 svfloat32_t shift = sv_f32 (d->shift);
48 svfloat32_t z = svadd_x (pg, x, shift);
49 svfloat32_t n = svsub_x (pg, z, shift);
50 svfloat32_t r = svsub_x (pg, x, n);
51
52 svbool_t special = svacgt (pg, x, d->thres);
53 svfloat32_t scale = svexpa (svreinterpret_u32 (z));
54
55 /* Polynomial evaluation: poly(r) ~ exp2(r)-1.
56 Evaluate polynomial use hybrid scheme - offset ESTRIN by 1 for
57 coefficients 1 to 4, and apply most significant coefficient directly. */
58 svfloat32_t r2 = svmul_x (pg, r, r);
59 svfloat32_t p14 = sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1);
60 svfloat32_t p0 = svmul_x (pg, r, d->poly[0]);
61 svfloat32_t poly = svmla_x (pg, p0, r2, p14);
62
63 if (unlikely (svptest_any (pg, special)))
64 return special_case (x, svmla_x (pg, scale, scale, poly), special);
65
66 return svmla_x (pg, scale, scale, poly);
67 }
68
69 PL_SIG (SV, F, 1, exp2, -9.9, 9.9)
70 PL_TEST_ULP (SV_NAME_F1 (exp2), 0.55)
71 PL_TEST_INTERVAL (SV_NAME_F1 (exp2), 0, Thres, 40000)
72 PL_TEST_INTERVAL (SV_NAME_F1 (exp2), 1, Thres, 50000)
73 PL_TEST_INTERVAL (SV_NAME_F1 (exp2), Thres, inf, 50000)
74 PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0, -0x1p-23, 40000)
75 PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0x1p-23, -1, 50000)
76 PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -1, -0x1p23, 50000)
77 PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0x1p23, -inf, 50000)
78