1 /*
2 * Single-precision log function.
3 *
4 * Copyright (c) 2017-2023, 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 #include "math_config.h"
11
12 /*
13 LOGF_TABLE_BITS = 4
14 LOGF_POLY_ORDER = 4
15
16 ULP error: 0.818 (nearest rounding.)
17 Relative error: 1.957 * 2^-26 (before rounding.)
18 */
19
20 #define T __logf_data.tab
21 #define A __logf_data.poly
22 #define Ln2 __logf_data.ln2
23 #define N (1 << LOGF_TABLE_BITS)
24 #define OFF 0x3f330000
25
26 float
logf(float x)27 logf (float x)
28 {
29 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
30 double_t z, r, r2, y, y0, invc, logc;
31 uint32_t ix, iz, tmp;
32 int k, i;
33
34 ix = asuint (x);
35 #if WANT_ROUNDING
36 /* Fix sign of zero with downward rounding when x==1. */
37 if (unlikely (ix == 0x3f800000))
38 return 0;
39 #endif
40 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
41 {
42 /* x < 0x1p-126 or inf or nan. */
43 if (ix * 2 == 0)
44 return __math_divzerof (1);
45 if (ix == 0x7f800000) /* log(inf) == inf. */
46 return x;
47 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
48 return __math_invalidf (x);
49 /* x is subnormal, normalize it. */
50 ix = asuint (x * 0x1p23f);
51 ix -= 23 << 23;
52 }
53
54 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
55 The range is split into N subintervals.
56 The ith subinterval contains z and c is near its center. */
57 tmp = ix - OFF;
58 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
59 k = (int32_t) tmp >> 23; /* arithmetic shift */
60 iz = ix - (tmp & 0xff800000);
61 invc = T[i].invc;
62 logc = T[i].logc;
63 z = (double_t) asfloat (iz);
64
65 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
66 r = z * invc - 1;
67 y0 = logc + (double_t) k * Ln2;
68
69 /* Pipelined polynomial evaluation to approximate log1p(r). */
70 r2 = r * r;
71 y = A[1] * r + A[2];
72 y = A[0] * r2 + y;
73 y = y * r2 + (y0 + r);
74 return eval_as_float (y);
75 }
76 #if USE_GLIBC_ABI
77 strong_alias (logf, __logf_finite)
78 hidden_alias (logf, __ieee754_logf)
79 #endif
80