1*412f47f9SXin Li /*
2*412f47f9SXin Li * Single-precision vector e^x function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2019-2023, Arm Limited.
5*412f47f9SXin Li * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*412f47f9SXin Li */
7*412f47f9SXin Li
8*412f47f9SXin Li #include "sv_math.h"
9*412f47f9SXin Li #include "pl_sig.h"
10*412f47f9SXin Li #include "pl_test.h"
11*412f47f9SXin Li
12*412f47f9SXin Li static const struct data
13*412f47f9SXin Li {
14*412f47f9SXin Li float poly[5];
15*412f47f9SXin Li float inv_ln2, ln2_hi, ln2_lo, shift, thres;
16*412f47f9SXin Li } data = {
17*412f47f9SXin Li /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
18*412f47f9SXin Li compatibility with polynomial helpers. */
19*412f47f9SXin Li .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f,
20*412f47f9SXin Li 0x1.0e4020p-7f },
21*412f47f9SXin Li .inv_ln2 = 0x1.715476p+0f,
22*412f47f9SXin Li .ln2_hi = 0x1.62e4p-1f,
23*412f47f9SXin Li .ln2_lo = 0x1.7f7d1cp-20f,
24*412f47f9SXin Li /* 1.5*2^17 + 127. */
25*412f47f9SXin Li .shift = 0x1.903f8p17f,
26*412f47f9SXin Li /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
27*412f47f9SXin Li correctly by FEXPA. */
28*412f47f9SXin Li .thres = 0x1.5d5e2ap+6f,
29*412f47f9SXin Li };
30*412f47f9SXin Li
31*412f47f9SXin Li #define C(i) sv_f32 (d->poly[i])
32*412f47f9SXin Li #define ExponentBias 0x3f800000
33*412f47f9SXin Li
34*412f47f9SXin Li static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t special)35*412f47f9SXin Li special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
36*412f47f9SXin Li {
37*412f47f9SXin Li return sv_call_f32 (expf, x, y, special);
38*412f47f9SXin Li }
39*412f47f9SXin Li
40*412f47f9SXin Li /* Optimised single-precision SVE exp function.
41*412f47f9SXin Li Worst-case error is 1.04 ulp:
42*412f47f9SXin Li SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4
43*412f47f9SXin Li want 0x1.ba74bap+4. */
SV_NAME_F1(exp)44*412f47f9SXin Li svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg)
45*412f47f9SXin Li {
46*412f47f9SXin Li const struct data *d = ptr_barrier (&data);
47*412f47f9SXin Li
48*412f47f9SXin Li /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
49*412f47f9SXin Li x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
50*412f47f9SXin Li
51*412f47f9SXin Li /* Load some constants in quad-word chunks to minimise memory access (last
52*412f47f9SXin Li lane is wasted). */
53*412f47f9SXin Li svfloat32_t invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->inv_ln2);
54*412f47f9SXin Li
55*412f47f9SXin Li /* n = round(x/(ln2/N)). */
56*412f47f9SXin Li svfloat32_t z = svmla_lane (sv_f32 (d->shift), x, invln2_and_ln2, 0);
57*412f47f9SXin Li svfloat32_t n = svsub_x (pg, z, d->shift);
58*412f47f9SXin Li
59*412f47f9SXin Li /* r = x - n*ln2/N. */
60*412f47f9SXin Li svfloat32_t r = svmls_lane (x, n, invln2_and_ln2, 1);
61*412f47f9SXin Li r = svmls_lane (r, n, invln2_and_ln2, 2);
62*412f47f9SXin Li
63*412f47f9SXin Li /* scale = 2^(n/N). */
64*412f47f9SXin Li svbool_t is_special_case = svacgt (pg, x, d->thres);
65*412f47f9SXin Li svfloat32_t scale = svexpa (svreinterpret_u32 (z));
66*412f47f9SXin Li
67*412f47f9SXin Li /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */
68*412f47f9SXin Li svfloat32_t p12 = svmla_x (pg, C (1), C (2), r);
69*412f47f9SXin Li svfloat32_t p34 = svmla_x (pg, C (3), C (4), r);
70*412f47f9SXin Li svfloat32_t r2 = svmul_x (pg, r, r);
71*412f47f9SXin Li svfloat32_t p14 = svmla_x (pg, p12, p34, r2);
72*412f47f9SXin Li svfloat32_t p0 = svmul_x (pg, r, C (0));
73*412f47f9SXin Li svfloat32_t poly = svmla_x (pg, p0, r2, p14);
74*412f47f9SXin Li
75*412f47f9SXin Li if (unlikely (svptest_any (pg, is_special_case)))
76*412f47f9SXin Li return special_case (x, svmla_x (pg, scale, scale, poly), is_special_case);
77*412f47f9SXin Li
78*412f47f9SXin Li return svmla_x (pg, scale, scale, poly);
79*412f47f9SXin Li }
80*412f47f9SXin Li
81*412f47f9SXin Li PL_SIG (SV, F, 1, exp, -9.9, 9.9)
82*412f47f9SXin Li PL_TEST_ULP (SV_NAME_F1 (exp), 0.55)
83*412f47f9SXin Li PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 0, 0x1p-23, 40000)
84*412f47f9SXin Li PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 0x1p-23, 1, 50000)
85*412f47f9SXin Li PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 1, 0x1p23, 50000)
86*412f47f9SXin Li PL_TEST_SYM_INTERVAL (SV_NAME_F1 (exp), 0x1p23, inf, 50000)
87