1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision vector exp(x) - 1 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 #include "sv_math.h"
9*f3087befSAndrew Turner #include "test_sig.h"
10*f3087befSAndrew Turner #include "test_defs.h"
11*f3087befSAndrew Turner
12*f3087befSAndrew Turner /* Largest value of x for which expm1(x) should round to -1. */
13*f3087befSAndrew Turner #define SpecialBound 0x1.5ebc4p+6f
14*f3087befSAndrew Turner
15*f3087befSAndrew Turner static const struct data
16*f3087befSAndrew Turner {
17*f3087befSAndrew Turner /* These 4 are grouped together so they can be loaded as one quadword, then
18*f3087befSAndrew Turner used with _lane forms of svmla/svmls. */
19*f3087befSAndrew Turner float c2, c4, ln2_hi, ln2_lo;
20*f3087befSAndrew Turner float c0, inv_ln2, c1, c3, special_bound;
21*f3087befSAndrew Turner } data = {
22*f3087befSAndrew Turner /* Generated using fpminimax. */
23*f3087befSAndrew Turner .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3,
24*f3087befSAndrew Turner .c2 = 0x1.555736p-5, .c3 = 0x1.12287cp-7,
25*f3087befSAndrew Turner .c4 = 0x1.6b55a2p-10, .inv_ln2 = 0x1.715476p+0f,
26*f3087befSAndrew Turner .special_bound = SpecialBound, .ln2_lo = 0x1.7f7d1cp-20f,
27*f3087befSAndrew Turner .ln2_hi = 0x1.62e4p-1f,
28*f3087befSAndrew Turner
29*f3087befSAndrew Turner };
30*f3087befSAndrew Turner
31*f3087befSAndrew Turner static svfloat32_t NOINLINE
special_case(svfloat32_t x,svbool_t pg)32*f3087befSAndrew Turner special_case (svfloat32_t x, svbool_t pg)
33*f3087befSAndrew Turner {
34*f3087befSAndrew Turner return sv_call_f32 (expm1f, x, x, pg);
35*f3087befSAndrew Turner }
36*f3087befSAndrew Turner
37*f3087befSAndrew Turner /* Single-precision SVE exp(x) - 1. Maximum error is 1.52 ULP:
38*f3087befSAndrew Turner _ZGVsMxv_expm1f(0x1.8f4ebcp-2) got 0x1.e859dp-2
39*f3087befSAndrew Turner want 0x1.e859d4p-2. */
SV_NAME_F1(expm1)40*f3087befSAndrew Turner svfloat32_t SV_NAME_F1 (expm1) (svfloat32_t x, svbool_t pg)
41*f3087befSAndrew Turner {
42*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
43*f3087befSAndrew Turner
44*f3087befSAndrew Turner /* Large, NaN/Inf. */
45*f3087befSAndrew Turner svbool_t special = svnot_z (pg, svaclt (pg, x, d->special_bound));
46*f3087befSAndrew Turner
47*f3087befSAndrew Turner if (unlikely (svptest_any (pg, special)))
48*f3087befSAndrew Turner return special_case (x, pg);
49*f3087befSAndrew Turner
50*f3087befSAndrew Turner /* This vector is reliant on layout of data - it contains constants
51*f3087befSAndrew Turner that can be used with _lane forms of svmla/svmls. Values are:
52*f3087befSAndrew Turner [ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */
53*f3087befSAndrew Turner svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2);
54*f3087befSAndrew Turner
55*f3087befSAndrew Turner /* Reduce argument to smaller range:
56*f3087befSAndrew Turner Let i = round(x / ln2)
57*f3087befSAndrew Turner and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
58*f3087befSAndrew Turner exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
59*f3087befSAndrew Turner where 2^i is exact because i is an integer. */
60*f3087befSAndrew Turner svfloat32_t j = svmul_x (svptrue_b32 (), x, d->inv_ln2);
61*f3087befSAndrew Turner j = svrinta_x (pg, j);
62*f3087befSAndrew Turner
63*f3087befSAndrew Turner svfloat32_t f = svmls_lane (x, j, lane_constants, 2);
64*f3087befSAndrew Turner f = svmls_lane (f, j, lane_constants, 3);
65*f3087befSAndrew Turner
66*f3087befSAndrew Turner /* Approximate expm1(f) using polynomial.
67*f3087befSAndrew Turner Taylor expansion for expm1(x) has the form:
68*f3087befSAndrew Turner x + ax^2 + bx^3 + cx^4 ....
69*f3087befSAndrew Turner So we calculate the polynomial P(f) = a + bf + cf^2 + ...
70*f3087befSAndrew Turner and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
71*f3087befSAndrew Turner svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), f, lane_constants, 0);
72*f3087befSAndrew Turner svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), f, lane_constants, 1);
73*f3087befSAndrew Turner svfloat32_t f2 = svmul_x (svptrue_b32 (), f, f);
74*f3087befSAndrew Turner svfloat32_t p = svmla_x (pg, p12, f2, p34);
75*f3087befSAndrew Turner
76*f3087befSAndrew Turner p = svmla_x (pg, sv_f32 (d->c0), f, p);
77*f3087befSAndrew Turner p = svmla_x (pg, f, f2, p);
78*f3087befSAndrew Turner
79*f3087befSAndrew Turner /* Assemble the result.
80*f3087befSAndrew Turner expm1(x) ~= 2^i * (p + 1) - 1
81*f3087befSAndrew Turner Let t = 2^i. */
82*f3087befSAndrew Turner svfloat32_t t = svscale_x (pg, sv_f32 (1.0f), svcvt_s32_x (pg, j));
83*f3087befSAndrew Turner return svmla_x (pg, svsub_x (pg, t, 1.0f), p, t);
84*f3087befSAndrew Turner }
85*f3087befSAndrew Turner
86*f3087befSAndrew Turner TEST_SIG (SV, F, 1, expm1, -9.9, 9.9)
87*f3087befSAndrew Turner TEST_ULP (SV_NAME_F1 (expm1), 1.02)
88*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_F1 (expm1))
89*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (expm1), 0, SpecialBound, 100000)
90*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_F1 (expm1), SpecialBound, inf, 1000)
91*f3087befSAndrew Turner CLOSE_SVE_ATTR
92