1 /*
2 * Single-precision SVE 2^x function.
3 *
4 * Copyright (c) 2023-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "test_sig.h"
10 #include "test_defs.h"
11
12 #define Thres 0x1.5d5e2ap+6f
13
14 static const struct data
15 {
16 float c0, c2, c4, c1, c3;
17 float shift, thres;
18 } data = {
19 /* Coefficients copied from the polynomial in AdvSIMD variant. */
20 .c0 = 0x1.62e422p-1f,
21 .c1 = 0x1.ebf9bcp-3f,
22 .c2 = 0x1.c6bd32p-5f,
23 .c3 = 0x1.3ce9e4p-7f,
24 .c4 = 0x1.59977ap-10f,
25 /* 1.5*2^17 + 127. */
26 .shift = 0x1.803f8p17f,
27 /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
28 correctly by FEXPA. */
29 .thres = Thres,
30 };
31
32 static inline svfloat32_t
sv_exp2f_inline(svfloat32_t x,const svbool_t pg,const struct data * d)33 sv_exp2f_inline (svfloat32_t x, const svbool_t pg, const struct data *d)
34 {
35 /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
36 x = n + r, with r in [-1/2, 1/2]. */
37 svfloat32_t z = svadd_x (svptrue_b32 (), x, d->shift);
38 svfloat32_t n = svsub_x (svptrue_b32 (), z, d->shift);
39 svfloat32_t r = svsub_x (svptrue_b32 (), x, n);
40
41 svfloat32_t scale = svexpa (svreinterpret_u32 (z));
42
43 /* Polynomial evaluation: poly(r) ~ exp2(r)-1.
44 Evaluate polynomial use hybrid scheme - offset ESTRIN by 1 for
45 coefficients 1 to 4, and apply most significant coefficient directly. */
46 svfloat32_t even_coeffs = svld1rq (svptrue_b32 (), &d->c0);
47 svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r);
48 svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, even_coeffs, 1);
49 svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, even_coeffs, 2);
50 svfloat32_t p14 = svmla_x (pg, p12, r2, p34);
51 svfloat32_t p0 = svmul_lane (r, even_coeffs, 0);
52 svfloat32_t poly = svmla_x (pg, p0, r2, p14);
53
54 return svmla_x (pg, scale, scale, poly);
55 }
56
57 static svfloat32_t NOINLINE
special_case(svfloat32_t x,svbool_t special,const struct data * d)58 special_case (svfloat32_t x, svbool_t special, const struct data *d)
59 {
60 return sv_call_f32 (exp2f, x, sv_exp2f_inline (x, svptrue_b32 (), d),
61 special);
62 }
63
64 /* Single-precision SVE exp2f routine. Implements the same algorithm
65 as AdvSIMD exp2f.
66 Worst case error is 1.04 ULPs.
67 _ZGVsMxv_exp2f(-0x1.af994ap-3) got 0x1.ba6a66p-1
68 want 0x1.ba6a64p-1. */
SV_NAME_F1(exp2)69 svfloat32_t SV_NAME_F1 (exp2) (svfloat32_t x, const svbool_t pg)
70 {
71 const struct data *d = ptr_barrier (&data);
72 svbool_t special = svacgt (pg, x, d->thres);
73 if (unlikely (svptest_any (special, special)))
74 return special_case (x, special, d);
75 return sv_exp2f_inline (x, pg, d);
76 }
77
78 TEST_SIG (SV, F, 1, exp2, -9.9, 9.9)
79 TEST_ULP (SV_NAME_F1 (exp2), 0.54)
80 TEST_DISABLE_FENV (SV_NAME_F1 (exp2))
81 TEST_SYM_INTERVAL (SV_NAME_F1 (exp2), 0, Thres, 50000)
82 TEST_SYM_INTERVAL (SV_NAME_F1 (exp2), Thres, inf, 50000)
83 CLOSE_SVE_ATTR
84