1 /*
2 * Single-precision 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 <math.h>
9 #include <stdint.h>
10
11 #include "math_config.h"
12 #include "pl_sig.h"
13 #include "pl_test.h"
14
15 /* Data associated to logf:
16
17 LOGF_TABLE_BITS = 4
18 LOGF_POLY_ORDER = 4
19
20 ULP error: 0.818 (nearest rounding.)
21 Relative error: 1.957 * 2^-26 (before rounding.). */
22
23 #define T __logf_data.tab
24 #define A __logf_data.poly
25 #define Ln2 __logf_data.ln2
26 #define InvLn10 __logf_data.invln10
27 #define N (1 << LOGF_TABLE_BITS)
28 #define OFF 0x3f330000
29
30 /* This naive implementation of log10f mimics that of log
31 then simply scales the result by 1/log(10) to switch from base e to
32 base 10. Hence, most computations are carried out in double precision.
33 Scaling before rounding to single precision is both faster and more accurate.
34
35 ULP error: 0.797 ulp (nearest rounding.). */
36 float
log10f(float x)37 log10f (float x)
38 {
39 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
40 double_t z, r, r2, y, y0, invc, logc;
41 uint32_t ix, iz, tmp;
42 int k, i;
43
44 ix = asuint (x);
45 #if WANT_ROUNDING
46 /* Fix sign of zero with downward rounding when x==1. */
47 if (unlikely (ix == 0x3f800000))
48 return 0;
49 #endif
50 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
51 {
52 /* x < 0x1p-126 or inf or nan. */
53 if (ix * 2 == 0)
54 return __math_divzerof (1);
55 if (ix == 0x7f800000) /* log(inf) == inf. */
56 return x;
57 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
58 return __math_invalidf (x);
59 /* x is subnormal, normalize it. */
60 ix = asuint (x * 0x1p23f);
61 ix -= 23 << 23;
62 }
63
64 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
65 The range is split into N subintervals.
66 The ith subinterval contains z and c is near its center. */
67 tmp = ix - OFF;
68 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
69 k = (int32_t) tmp >> 23; /* arithmetic shift. */
70 iz = ix - (tmp & 0xff800000);
71 invc = T[i].invc;
72 logc = T[i].logc;
73 z = (double_t) asfloat (iz);
74
75 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
76 r = z * invc - 1;
77 y0 = logc + (double_t) k * Ln2;
78
79 /* Pipelined polynomial evaluation to approximate log1p(r). */
80 r2 = r * r;
81 y = A[1] * r + A[2];
82 y = A[0] * r2 + y;
83 y = y * r2 + (y0 + r);
84
85 /* Multiply by 1/log(10). */
86 y = y * InvLn10;
87
88 return eval_as_float (y);
89 }
90
91 PL_SIG (S, F, 1, log10, 0.01, 11.1)
92 PL_TEST_ULP (log10f, 0.30)
93 PL_TEST_INTERVAL (log10f, 0, 0xffff0000, 10000)
94 PL_TEST_INTERVAL (log10f, 0x1p-127, 0x1p-26, 50000)
95 PL_TEST_INTERVAL (log10f, 0x1p-26, 0x1p3, 50000)
96 PL_TEST_INTERVAL (log10f, 0x1p-4, 0x1p4, 50000)
97 PL_TEST_INTERVAL (log10f, 0, inf, 50000)
98