xref: /freebsd/contrib/arm-optimized-routines/pl/math/sv_log1pf_1u3.c (revision 95eb4b873b6a8b527c5bd78d7191975dfca38998)
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
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.  */
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