1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision SVE 10^x function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2023-2024, Arm Limited.
5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*f3087befSAndrew Turner */
7*f3087befSAndrew Turner
8*f3087befSAndrew Turner #define _GNU_SOURCE
9*f3087befSAndrew Turner #include "sv_math.h"
10*f3087befSAndrew Turner #include "test_sig.h"
11*f3087befSAndrew Turner #include "test_defs.h"
12*f3087befSAndrew Turner #include "sv_poly_f32.h"
13*f3087befSAndrew Turner
14*f3087befSAndrew Turner /* For x < -Thres, the result is subnormal and not handled correctly by
15*f3087befSAndrew Turner FEXPA. */
16*f3087befSAndrew Turner #define Thres 37.9
17*f3087befSAndrew Turner
18*f3087befSAndrew Turner static const struct data
19*f3087befSAndrew Turner {
20*f3087befSAndrew Turner float log2_10_lo, c0, c2, c4;
21*f3087befSAndrew Turner float c1, c3, log10_2;
22*f3087befSAndrew Turner float shift, log2_10_hi, thres;
23*f3087befSAndrew Turner } data = {
24*f3087befSAndrew Turner /* Coefficients generated using Remez algorithm with minimisation of relative
25*f3087befSAndrew Turner error.
26*f3087befSAndrew Turner rel error: 0x1.89dafa3p-24
27*f3087befSAndrew Turner abs error: 0x1.167d55p-23 in [-log10(2)/2, log10(2)/2]
28*f3087befSAndrew Turner maxerr: 0.52 +0.5 ulp. */
29*f3087befSAndrew Turner .c0 = 0x1.26bb16p+1f,
30*f3087befSAndrew Turner .c1 = 0x1.5350d2p+1f,
31*f3087befSAndrew Turner .c2 = 0x1.04744ap+1f,
32*f3087befSAndrew Turner .c3 = 0x1.2d8176p+0f,
33*f3087befSAndrew Turner .c4 = 0x1.12b41ap-1f,
34*f3087befSAndrew Turner /* 1.5*2^17 + 127, a shift value suitable for FEXPA. */
35*f3087befSAndrew Turner .shift = 0x1.803f8p17f,
36*f3087befSAndrew Turner .log10_2 = 0x1.a934fp+1,
37*f3087befSAndrew Turner .log2_10_hi = 0x1.344136p-2,
38*f3087befSAndrew Turner .log2_10_lo = -0x1.ec10cp-27,
39*f3087befSAndrew Turner .thres = Thres,
40*f3087befSAndrew Turner };
41*f3087befSAndrew Turner
42*f3087befSAndrew Turner static inline svfloat32_t
sv_exp10f_inline(svfloat32_t x,const svbool_t pg,const struct data * d)43*f3087befSAndrew Turner sv_exp10f_inline (svfloat32_t x, const svbool_t pg, const struct data *d)
44*f3087befSAndrew Turner {
45*f3087befSAndrew Turner /* exp10(x) = 2^(n/N) * 10^r = 2^n * (1 + poly (r)),
46*f3087befSAndrew Turner with poly(r) in [1/sqrt(2), sqrt(2)] and
47*f3087befSAndrew Turner x = r + n * log10(2) / N, with r in [-log10(2)/2N, log10(2)/2N]. */
48*f3087befSAndrew Turner
49*f3087befSAndrew Turner svfloat32_t lane_consts = svld1rq (svptrue_b32 (), &d->log2_10_lo);
50*f3087befSAndrew Turner
51*f3087befSAndrew Turner /* n = round(x/(log10(2)/N)). */
52*f3087befSAndrew Turner svfloat32_t shift = sv_f32 (d->shift);
53*f3087befSAndrew Turner svfloat32_t z = svmad_x (pg, sv_f32 (d->log10_2), x, shift);
54*f3087befSAndrew Turner svfloat32_t n = svsub_x (svptrue_b32 (), z, shift);
55*f3087befSAndrew Turner
56*f3087befSAndrew Turner /* r = x - n*log10(2)/N. */
57*f3087befSAndrew Turner svfloat32_t r = svmsb_x (pg, sv_f32 (d->log2_10_hi), n, x);
58*f3087befSAndrew Turner r = svmls_lane (r, n, lane_consts, 0);
59*f3087befSAndrew Turner
60*f3087befSAndrew Turner svfloat32_t scale = svexpa (svreinterpret_u32 (z));
61*f3087befSAndrew Turner
62*f3087befSAndrew Turner /* Polynomial evaluation: poly(r) ~ exp10(r)-1. */
63*f3087befSAndrew Turner svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, lane_consts, 2);
64*f3087befSAndrew Turner svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, lane_consts, 3);
65*f3087befSAndrew Turner svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r);
66*f3087befSAndrew Turner svfloat32_t p14 = svmla_x (pg, p12, p34, r2);
67*f3087befSAndrew Turner svfloat32_t p0 = svmul_lane (r, lane_consts, 1);
68*f3087befSAndrew Turner svfloat32_t poly = svmla_x (pg, p0, r2, p14);
69*f3087befSAndrew Turner
70*f3087befSAndrew Turner return svmla_x (pg, scale, scale, poly);
71*f3087befSAndrew Turner }
72*f3087befSAndrew Turner
73*f3087befSAndrew Turner static svfloat32_t NOINLINE
special_case(svfloat32_t x,svbool_t special,const struct data * d)74*f3087befSAndrew Turner special_case (svfloat32_t x, svbool_t special, const struct data *d)
75*f3087befSAndrew Turner {
76*f3087befSAndrew Turner return sv_call_f32 (exp10f, x, sv_exp10f_inline (x, svptrue_b32 (), d),
77*f3087befSAndrew Turner special);
78*f3087befSAndrew Turner }
79*f3087befSAndrew Turner
80*f3087befSAndrew Turner /* Single-precision SVE exp10f routine. Implements the same algorithm
81*f3087befSAndrew Turner as AdvSIMD exp10f.
82*f3087befSAndrew Turner Worst case error is 1.02 ULPs.
83*f3087befSAndrew Turner _ZGVsMxv_exp10f(-0x1.040488p-4) got 0x1.ba5f9ep-1
84*f3087befSAndrew Turner want 0x1.ba5f9cp-1. */
SV_NAME_F1(exp10)85*f3087befSAndrew Turner svfloat32_t SV_NAME_F1 (exp10) (svfloat32_t x, const svbool_t pg)
86*f3087befSAndrew Turner {
87*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
88*f3087befSAndrew Turner svbool_t special = svacgt (pg, x, d->thres);
89*f3087befSAndrew Turner if (unlikely (svptest_any (special, special)))
90*f3087befSAndrew Turner return special_case (x, special, d);
91*f3087befSAndrew Turner return sv_exp10f_inline (x, pg, d);
92*f3087befSAndrew Turner }
93*f3087befSAndrew Turner
94*f3087befSAndrew Turner #if WANT_EXP10_TESTS
95*f3087befSAndrew Turner TEST_SIG (SV, F, 1, exp10, -9.9, 9.9)
96*f3087befSAndrew Turner TEST_ULP (SV_NAME_F1 (exp10), 0.52)
97*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_F1 (exp10))
98*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (exp10), 0, Thres, 50000)
99*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (exp10), Thres, inf, 50000)
100*f3087befSAndrew Turner #endif
101*f3087befSAndrew Turner CLOSE_SVE_ATTR
102