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 |
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 (f: 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 (f: 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 (i: 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 (x: y); |
76 | } |
77 | #if USE_GLIBC_ABI |
78 | strong_alias (logf, __logf_finite) |
79 | hidden_alias (logf, __ieee754_logf) |
80 | #endif |
81 | |