1/*
2 * Single-precision SVE 2^x function.
3 *
4 * Copyright (c) 2023, 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
13static const struct data
14{
15  float poly[5];
16  float shift, thres;
17} data = {
18  /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
19     compatibility with polynomial helpers.  */
20  .poly = { 0x1.62e422p-1f, 0x1.ebf9bcp-3f, 0x1.c6bd32p-5f, 0x1.3ce9e4p-7f,
21	    0x1.59977ap-10f },
22  /* 1.5*2^17 + 127.  */
23  .shift = 0x1.903f8p17f,
24  /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
25     correctly by FEXPA.  */
26  .thres = 0x1.5d5e2ap+6f,
27};
28
29static svfloat32_t NOINLINE
30special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
31{
32  return sv_call_f32 (exp2f, x, y, special);
33}
34
35/* Single-precision SVE exp2f routine. Implements the same algorithm
36   as AdvSIMD exp2f.
37   Worst case error is 1.04 ULPs.
38   SV_NAME_F1 (exp2)(0x1.943b9p-1) got 0x1.ba7eb2p+0
39				  want 0x1.ba7ebp+0.  */
40svfloat32_t SV_NAME_F1 (exp2) (svfloat32_t x, const svbool_t pg)
41{
42  const struct data *d = ptr_barrier (&data);
43  /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
44    x = n + r, with r in [-1/2, 1/2].  */
45  svfloat32_t shift = sv_f32 (d->shift);
46  svfloat32_t z = svadd_x (pg, x, shift);
47  svfloat32_t n = svsub_x (pg, z, shift);
48  svfloat32_t r = svsub_x (pg, x, n);
49
50  svbool_t special = svacgt (pg, x, d->thres);
51  svfloat32_t scale = svexpa (svreinterpret_u32 (z));
52
53  /* Polynomial evaluation: poly(r) ~ exp2(r)-1.
54     Evaluate polynomial use hybrid scheme - offset ESTRIN by 1 for
55     coefficients 1 to 4, and apply most significant coefficient directly.  */
56  svfloat32_t r2 = svmul_x (pg, r, r);
57  svfloat32_t p14 = sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1);
58  svfloat32_t p0 = svmul_x (pg, r, d->poly[0]);
59  svfloat32_t poly = svmla_x (pg, p0, r2, p14);
60
61  if (unlikely (svptest_any (pg, special)))
62    return special_case (x, svmla_x (pg, scale, scale, poly), special);
63
64  return svmla_x (pg, scale, scale, poly);
65}
66
67PL_SIG (SV, F, 1, exp2, -9.9, 9.9)
68PL_TEST_ULP (SV_NAME_F1 (exp2), 0.55)
69PL_TEST_INTERVAL (SV_NAME_F1 (exp2), 0, Thres, 40000)
70PL_TEST_INTERVAL (SV_NAME_F1 (exp2), Thres, 1, 50000)
71PL_TEST_INTERVAL (SV_NAME_F1 (exp2), 1, Thres, 50000)
72PL_TEST_INTERVAL (SV_NAME_F1 (exp2), Thres, inf, 50000)
73PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0, -0x1p-23, 40000)
74PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0x1p-23, -1, 50000)
75PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -1, -0x1p23, 50000)
76PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0x1p23, -inf, 50000)
77PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0, ScaleThres, 40000)
78PL_TEST_INTERVAL (SV_NAME_F1 (exp2), ScaleThres, -1, 50000)
79PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -1, ScaleThres, 50000)
80PL_TEST_INTERVAL (SV_NAME_F1 (exp2), ScaleThres, -inf, 50000)
81