1 /*
2  * Single-precision log2 function.
3  *
4  * Copyright (c) 2017-2018, Arm Limited.
5  * SPDX-License-Identifier: MIT
6  */
7 
8 #include <math.h>
9 #include <stdint.h>
10 #include "math_config.h"
11 
12 /*
13 LOG2F_TABLE_BITS = 4
14 LOG2F_POLY_ORDER = 4
15 
16 ULP error: 0.752 (nearest rounding.)
17 Relative error: 1.9 * 2^-26 (before rounding.)
18 */
19 
20 #define N (1 << LOG2F_TABLE_BITS)
21 #define T __log2f_data.tab
22 #define A __log2f_data.poly
23 #define OFF 0x3f330000
24 
25 float
26 log2f (float x)
27 {
28   /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
29   double_t z, r, r2, p, y, y0, invc, logc;
30   uint32_t ix, iz, top, tmp;
31   int k, i;
32 
33   ix = asuint (x);
34 #if WANT_ROUNDING
35   /* Fix sign of zero with downward rounding when x==1.  */
36   if (unlikely (ix == 0x3f800000))
37     return 0;
38 #endif
39   if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
40     {
41       /* x < 0x1p-126 or inf or nan.  */
42       if (ix * 2 == 0)
43 	return __math_divzerof (1);
44       if (ix == 0x7f800000) /* log2(inf) == inf.  */
45 	return x;
46       if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
47 	return __math_invalidf (x);
48       /* x is subnormal, normalize it.  */
49       ix = asuint (x * 0x1p23f);
50       ix -= 23 << 23;
51     }
52 
53   /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
54      The range is split into N subintervals.
55      The ith subinterval contains z and c is near its center.  */
56   tmp = ix - OFF;
57   i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
58   top = tmp & 0xff800000;
59   iz = ix - top;
60   k = (int32_t) tmp >> 23; /* arithmetic shift */
61   invc = T[i].invc;
62   logc = T[i].logc;
63   z = (double_t) asfloat (iz);
64 
65   /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
66   r = z * invc - 1;
67   y0 = logc + (double_t) k;
68 
69   /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
70   r2 = r * r;
71   y = A[1] * r + A[2];
72   y = A[0] * r2 + y;
73   p = A[3] * r + y0;
74   y = y * r2 + p;
75   return eval_as_float (y);
76 }
77 #if USE_GLIBC_ABI
78 strong_alias (log2f, __log2f_finite)
79 hidden_alias (log2f, __ieee754_log2f)
80 #endif
81