xref: /freebsd/contrib/arm-optimized-routines/pl/math/sv_log10f_3u5.c (revision 6580f5c38dd5b01aeeaed16b370f1a12423437f0)
1 /*
2  * Single-precision SVE log10 function.
3  *
4  * Copyright (c) 2022-2023, 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 
12 static const struct data
13 {
14   float poly_0246[4];
15   float poly_1357[4];
16   float ln2, inv_ln10;
17 } data = {
18   .poly_1357 = {
19     /* Coefficients copied from the AdvSIMD routine, then rearranged so that coeffs
20        1, 3, 5 and 7 can be loaded as a single quad-word, hence used with _lane
21        variant of MLA intrinsic.  */
22     0x1.2879c8p-3f, 0x1.6408f8p-4f, 0x1.f0e514p-5f, 0x1.f5f76ap-5f
23   },
24   .poly_0246 = { -0x1.bcb79cp-3f, -0x1.bcd472p-4f, -0x1.246f8p-4f,
25 		 -0x1.0fc92cp-4f },
26   .ln2 = 0x1.62e43p-1f,
27   .inv_ln10 = 0x1.bcb7b2p-2f,
28 };
29 
30 #define Min 0x00800000
31 #define Max 0x7f800000
32 #define Thres 0x7f000000  /* Max - Min.  */
33 #define Offset 0x3f2aaaab /* 0.666667.  */
34 #define MantissaMask 0x007fffff
35 
36 static svfloat32_t NOINLINE
37 special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
38 {
39   return sv_call_f32 (log10f, x, y, special);
40 }
41 
42 /* Optimised implementation of SVE log10f using the same algorithm and
43    polynomial as AdvSIMD log10f.
44    Maximum error is 3.31ulps:
45    SV_NAME_F1 (log10)(0x1.555c16p+0) got 0x1.ffe2fap-4
46 				    want 0x1.ffe2f4p-4.  */
47 svfloat32_t SV_NAME_F1 (log10) (svfloat32_t x, const svbool_t pg)
48 {
49   const struct data *d = ptr_barrier (&data);
50   svuint32_t ix = svreinterpret_u32 (x);
51   svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres);
52 
53   /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3.  */
54   ix = svsub_x (pg, ix, Offset);
55   svfloat32_t n = svcvt_f32_x (
56       pg, svasr_x (pg, svreinterpret_s32 (ix), 23)); /* signextend.  */
57   ix = svand_x (pg, ix, MantissaMask);
58   ix = svadd_x (pg, ix, Offset);
59   svfloat32_t r = svsub_x (pg, svreinterpret_f32 (ix), 1.0f);
60 
61   /* y = log10(1+r) + n*log10(2)
62      log10(1+r) ~ r * InvLn(10) + P(r)
63      where P(r) is a polynomial. Use order 9 for log10(1+x), i.e. order 8 for
64      log10(1+x)/x, with x in [-1/3, 1/3] (offset=2/3).  */
65   svfloat32_t r2 = svmul_x (pg, r, r);
66   svfloat32_t r4 = svmul_x (pg, r2, r2);
67   svfloat32_t p_1357 = svld1rq (svptrue_b32 (), &d->poly_1357[0]);
68   svfloat32_t q_01 = svmla_lane (sv_f32 (d->poly_0246[0]), r, p_1357, 0);
69   svfloat32_t q_23 = svmla_lane (sv_f32 (d->poly_0246[1]), r, p_1357, 1);
70   svfloat32_t q_45 = svmla_lane (sv_f32 (d->poly_0246[2]), r, p_1357, 2);
71   svfloat32_t q_67 = svmla_lane (sv_f32 (d->poly_0246[3]), r, p_1357, 3);
72   svfloat32_t q_47 = svmla_x (pg, q_45, r2, q_67);
73   svfloat32_t q_03 = svmla_x (pg, q_01, r2, q_23);
74   svfloat32_t y = svmla_x (pg, q_03, r4, q_47);
75 
76   /* Using hi = Log10(2)*n + r*InvLn(10) is faster but less accurate.  */
77   svfloat32_t hi = svmla_x (pg, r, n, d->ln2);
78   hi = svmul_x (pg, hi, d->inv_ln10);
79 
80   if (unlikely (svptest_any (pg, special)))
81     return special_case (x, svmla_x (svnot_z (pg, special), hi, r2, y),
82 			 special);
83   return svmla_x (pg, hi, r2, y);
84 }
85 
86 PL_SIG (SV, F, 1, log10, 0.01, 11.1)
87 PL_TEST_ULP (SV_NAME_F1 (log10), 2.82)
88 PL_TEST_INTERVAL (SV_NAME_F1 (log10), -0.0, -0x1p126, 100)
89 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 0x1p-149, 0x1p-126, 4000)
90 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 0x1p-126, 0x1p-23, 50000)
91 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 0x1p-23, 1.0, 50000)
92 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 1.0, 100, 50000)
93 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 100, inf, 50000)
94