1/*
2 * Single-precision vector e^x function.
3 *
4 * Copyright (c) 2019-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include "sv_math.h"
9#include "pl_sig.h"
10#include "pl_test.h"
11
12static const struct data
13{
14  float poly[5];
15  float inv_ln2, ln2_hi, ln2_lo, shift, thres;
16} data = {
17  /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
18     compatibility with polynomial helpers.  */
19  .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f,
20	    0x1.0e4020p-7f },
21  .inv_ln2 = 0x1.715476p+0f,
22  .ln2_hi = 0x1.62e4p-1f,
23  .ln2_lo = 0x1.7f7d1cp-20f,
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 = 0x1.5d5e2ap+6f,
29};
30
31#define C(i) sv_f32 (d->poly[i])
32#define ExponentBias 0x3f800000
33
34static svfloat32_t NOINLINE
35special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
36{
37  return sv_call_f32 (expf, x, y, special);
38}
39
40/* Optimised single-precision SVE exp function.
41   Worst-case error is 1.04 ulp:
42   SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4
43				  want 0x1.ba74bap+4.  */
44svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg)
45{
46  const struct data *d = ptr_barrier (&data);
47
48  /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
49     x = ln2*n + r, with r in [-ln2/2, ln2/2].  */
50
51  /* Load some constants in quad-word chunks to minimise memory access (last
52     lane is wasted).  */
53  svfloat32_t invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->inv_ln2);
54
55  /* n = round(x/(ln2/N)).  */
56  svfloat32_t z = svmla_lane (sv_f32 (d->shift), x, invln2_and_ln2, 0);
57  svfloat32_t n = svsub_x (pg, z, d->shift);
58
59  /* r = x - n*ln2/N.  */
60  svfloat32_t r = svmls_lane (x, n, invln2_and_ln2, 1);
61  r = svmls_lane (r, n, invln2_and_ln2, 2);
62
63  /* scale = 2^(n/N).  */
64  svbool_t is_special_case = svacgt (pg, x, d->thres);
65  svfloat32_t scale = svexpa (svreinterpret_u32 (z));
66
67  /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6.  */
68  svfloat32_t p12 = svmla_x (pg, C (1), C (2), r);
69  svfloat32_t p34 = svmla_x (pg, C (3), C (4), r);
70  svfloat32_t r2 = svmul_x (pg, r, r);
71  svfloat32_t p14 = svmla_x (pg, p12, p34, r2);
72  svfloat32_t p0 = svmul_x (pg, r, C (0));
73  svfloat32_t poly = svmla_x (pg, p0, r2, p14);
74
75  if (unlikely (svptest_any (pg, is_special_case)))
76    return special_case (x, svmla_x (pg, scale, scale, poly), is_special_case);
77
78  return svmla_x (pg, scale, scale, poly);
79}
80
81PL_SIG (SV, F, 1, exp, -9.9, 9.9)
82PL_TEST_ULP (SV_NAME_F1 (exp), 0.55)
83PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 0, 0x1p-23, 40000)
84PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 0x1p-23, 1, 50000)
85PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 1, 0x1p23, 50000)
86PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 0x1p23, inf, 50000)
87