1 /*
2 * Single-precision log function.
3 *
4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 * See https://llvm.org/LICENSE.txt for license information.
6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 */
8
9 #include <math.h>
10 #include <stdint.h>
11 #include "math_config.h"
12
13 /*
14 LOGF_TABLE_BITS = 4
15 LOGF_POLY_ORDER = 4
16
17 ULP error: 0.818 (nearest rounding.)
18 Relative error: 1.957 * 2^-26 (before rounding.)
19 */
20
21 #define T __logf_data.tab
22 #define A __logf_data.poly
23 #define Ln2 __logf_data.ln2
24 #define N (1 << LOGF_TABLE_BITS)
25 #define OFF 0x3f330000
26
27 float
logf(float x)28 logf (float x)
29 {
30 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
31 double_t z, r, r2, y, y0, invc, logc;
32 uint32_t ix, iz, tmp;
33 int k, i;
34
35 ix = asuint (x);
36 #if WANT_ROUNDING
37 /* Fix sign of zero with downward rounding when x==1. */
38 if (unlikely (ix == 0x3f800000))
39 return 0;
40 #endif
41 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
42 {
43 /* x < 0x1p-126 or inf or nan. */
44 if (ix * 2 == 0)
45 return __math_divzerof (1);
46 if (ix == 0x7f800000) /* log(inf) == inf. */
47 return x;
48 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
49 return __math_invalidf (x);
50 /* x is subnormal, normalize it. */
51 ix = asuint (x * 0x1p23f);
52 ix -= 23 << 23;
53 }
54
55 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
56 The range is split into N subintervals.
57 The ith subinterval contains z and c is near its center. */
58 tmp = ix - OFF;
59 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
60 k = (int32_t) tmp >> 23; /* arithmetic shift */
61 iz = ix - (tmp & 0x1ff << 23);
62 invc = T[i].invc;
63 logc = T[i].logc;
64 z = (double_t) asfloat (iz);
65
66 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
67 r = z * invc - 1;
68 y0 = logc + (double_t) k * Ln2;
69
70 /* Pipelined polynomial evaluation to approximate log1p(r). */
71 r2 = r * r;
72 y = A[1] * r + A[2];
73 y = A[0] * r2 + y;
74 y = y * r2 + (y0 + r);
75 return eval_as_float (y);
76 }
77 #if USE_GLIBC_ABI
78 strong_alias (logf, __logf_finite)
79 hidden_alias (logf, __ieee754_logf)
80 #endif
81