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
18 static 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
38 static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t special)39 special_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. */
SV_NAME_F1(exp10)49 svfloat32_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
84 PL_SIG (SV, F, 1, exp10, -9.9, 9.9)
85 PL_TEST_ULP (SV_NAME_F1 (exp10), 0.52)
86 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp10), 0, SpecialBound, 50000)
87 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp10), SpecialBound, inf, 50000)
88