1 /*
2 * Single-precision vector log(x + 1) 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 "pl_sig.h"
10 #include "pl_test.h"
11 #include "poly_sve_f32.h"
12
13 static const struct data
14 {
15 float poly[8];
16 float ln2, exp_bias;
17 uint32_t four, three_quarters;
18 } data = {.poly = {/* Do not store first term of polynomial, which is -0.5, as
19 this can be fmov-ed directly instead of including it in
20 the main load-and-mla polynomial schedule. */
21 0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f,
22 -0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f,
23 0x1.abcb6p-4f, -0x1.6f0d5ep-5f},
24 .ln2 = 0x1.62e43p-1f,
25 .exp_bias = 0x1p-23f,
26 .four = 0x40800000,
27 .three_quarters = 0x3f400000};
28
29 #define SignExponentMask 0xff800000
30
31 static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t special)32 special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
33 {
34 return sv_call_f32 (log1pf, x, y, special);
35 }
36
37 /* Vector log1pf approximation using polynomial on reduced interval. Worst-case
38 error is 1.27 ULP very close to 0.5.
39 _ZGVsMxv_log1pf(0x1.fffffep-2) got 0x1.9f324p-2
40 want 0x1.9f323ep-2. */
SV_NAME_F1(log1p)41 svfloat32_t SV_NAME_F1 (log1p) (svfloat32_t x, svbool_t pg)
42 {
43 const struct data *d = ptr_barrier (&data);
44 /* x < -1, Inf/Nan. */
45 svbool_t special = svcmpeq (pg, svreinterpret_u32 (x), 0x7f800000);
46 special = svorn_z (pg, special, svcmpge (pg, x, -1));
47
48 /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
49 is in [-0.25, 0.5]):
50 log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
51
52 We approximate log1p(m) with a polynomial, then scale by
53 k*log(2). Instead of doing this directly, we use an intermediate
54 scale factor s = 4*k*log(2) to ensure the scale is representable
55 as a normalised fp32 number. */
56 svfloat32_t m = svadd_x (pg, x, 1);
57
58 /* Choose k to scale x to the range [-1/4, 1/2]. */
59 svint32_t k
60 = svand_x (pg, svsub_x (pg, svreinterpret_s32 (m), d->three_quarters),
61 sv_s32 (SignExponentMask));
62
63 /* Scale x by exponent manipulation. */
64 svfloat32_t m_scale = svreinterpret_f32 (
65 svsub_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (k)));
66
67 /* Scale up to ensure that the scale factor is representable as normalised
68 fp32 number, and scale m down accordingly. */
69 svfloat32_t s = svreinterpret_f32 (svsubr_x (pg, k, d->four));
70 m_scale = svadd_x (pg, m_scale, svmla_x (pg, sv_f32 (-1), s, 0.25));
71
72 /* Evaluate polynomial on reduced interval. */
73 svfloat32_t ms2 = svmul_x (pg, m_scale, m_scale),
74 ms4 = svmul_x (pg, ms2, ms2);
75 svfloat32_t p = sv_estrin_7_f32_x (pg, m_scale, ms2, ms4, d->poly);
76 p = svmad_x (pg, m_scale, p, -0.5);
77 p = svmla_x (pg, m_scale, m_scale, svmul_x (pg, m_scale, p));
78
79 /* The scale factor to be applied back at the end - by multiplying float(k)
80 by 2^-23 we get the unbiased exponent of k. */
81 svfloat32_t scale_back = svmul_x (pg, svcvt_f32_x (pg, k), d->exp_bias);
82
83 /* Apply the scaling back. */
84 svfloat32_t y = svmla_x (pg, p, scale_back, d->ln2);
85
86 if (unlikely (svptest_any (pg, special)))
87 return special_case (x, y, special);
88
89 return y;
90 }
91
92 PL_SIG (SV, F, 1, log1p, -0.9, 10.0)
93 PL_TEST_ULP (SV_NAME_F1 (log1p), 0.77)
94 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (log1p), 0, 0x1p-23, 5000)
95 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (log1p), 0x1p-23, 1, 5000)
96 PL_TEST_INTERVAL (SV_NAME_F1 (log1p), 1, inf, 10000)
97 PL_TEST_INTERVAL (SV_NAME_F1 (log1p), -1, -inf, 10)
98