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 "include/mathlib.h"
10#include "pl_sig.h"
11#include "pl_test.h"
12#include "poly_sve_f32.h"
13
14/* For x < -SpecialBound, the result is subnormal and not handled correctly by
15   FEXPA.  */
16#define SpecialBound 37.9
17
18static const struct data
19{
20  float poly[5];
21  float shift, log10_2, log2_10_hi, log2_10_lo, special_bound;
22} data = {
23  /* Coefficients generated using Remez algorithm with minimisation of relative
24     error.
25     rel error: 0x1.89dafa3p-24
26     abs error: 0x1.167d55p-23 in [-log10(2)/2, log10(2)/2]
27     maxerr: 0.52 +0.5 ulp.  */
28  .poly = { 0x1.26bb16p+1f, 0x1.5350d2p+1f, 0x1.04744ap+1f, 0x1.2d8176p+0f,
29	    0x1.12b41ap-1f },
30  /* 1.5*2^17 + 127, a shift value suitable for FEXPA.  */
31  .shift = 0x1.903f8p17f,
32  .log10_2 = 0x1.a934fp+1,
33  .log2_10_hi = 0x1.344136p-2,
34  .log2_10_lo = -0x1.ec10cp-27,
35  .special_bound = SpecialBound,
36};
37
38static svfloat32_t NOINLINE
39special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
40{
41  return sv_call_f32 (exp10f, x, y, special);
42}
43
44/* Single-precision SVE exp10f routine. Implements the same algorithm
45   as AdvSIMD exp10f.
46   Worst case error is 1.02 ULPs.
47   _ZGVsMxv_exp10f(-0x1.040488p-4) got 0x1.ba5f9ep-1
48				  want 0x1.ba5f9cp-1.  */
49svfloat32_t SV_NAME_F1 (exp10) (svfloat32_t x, const svbool_t pg)
50{
51  const struct data *d = ptr_barrier (&data);
52  /* exp10(x) = 2^(n/N) * 10^r = 2^n * (1 + poly (r)),
53     with poly(r) in [1/sqrt(2), sqrt(2)] and
54     x = r + n * log10(2) / N, with r in [-log10(2)/2N, log10(2)/2N].  */
55
56  /* Load some constants in quad-word chunks to minimise memory access (last
57     lane is wasted).  */
58  svfloat32_t log10_2_and_inv = svld1rq (svptrue_b32 (), &d->log10_2);
59
60  /* n = round(x/(log10(2)/N)).  */
61  svfloat32_t shift = sv_f32 (d->shift);
62  svfloat32_t z = svmla_lane (shift, x, log10_2_and_inv, 0);
63  svfloat32_t n = svsub_x (pg, z, shift);
64
65  /* r = x - n*log10(2)/N.  */
66  svfloat32_t r = svmls_lane (x, n, log10_2_and_inv, 1);
67  r = svmls_lane (r, n, log10_2_and_inv, 2);
68
69  svbool_t special = svacgt (pg, x, d->special_bound);
70  svfloat32_t scale = svexpa (svreinterpret_u32 (z));
71
72  /* Polynomial evaluation: poly(r) ~ exp10(r)-1.  */
73  svfloat32_t r2 = svmul_x (pg, r, r);
74  svfloat32_t poly
75      = svmla_x (pg, svmul_x (pg, r, d->poly[0]),
76		 sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1), r2);
77
78  if (unlikely (svptest_any (pg, special)))
79    return special_case (x, svmla_x (pg, scale, scale, poly), special);
80
81  return svmla_x (pg, scale, scale, poly);
82}
83
84PL_SIG (SV, F, 1, exp10, -9.9, 9.9)
85PL_TEST_ULP (SV_NAME_F1 (exp10), 0.52)
86PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp10), 0, SpecialBound, 50000)
87PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp10), SpecialBound, inf, 50000)
88