2 * Single-precision log2 function.
4 * Copyright (c) 2017-2018, Arm Limited.
5 * SPDX-License-Identifier: MIT
10 #include "math_config.h"
16 ULP error: 0.752 (nearest rounding.)
17 Relative error: 1.9 * 2^-26 (before rounding.)
20 #define N (1 << LOG2F_TABLE_BITS)
21 #define T __log2f_data.tab
22 #define A __log2f_data.poly
23 #define OFF 0x3f330000
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;
35 /* Fix sign of zero with downward rounding when x==1. */
36 if (unlikely (ix == 0x3f800000))
39 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
41 /* x < 0x1p-126 or inf or nan. */
43 return __math_divzerof (1);
44 if (ix == 0x7f800000) /* log2(inf) == inf. */
46 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
47 return __math_invalidf (x);
48 /* x is subnormal, normalize it. */
49 ix = asuint (x * 0x1p23f);
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. */
57 i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
58 top = tmp & 0xff800000;
60 k = (int32_t) tmp >> 23; /* arithmetic shift */
63 z = (double_t) asfloat (iz);
65 /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
67 y0 = logc + (double_t) k;
69 /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
75 return eval_as_float (y);
78 strong_alias (log2f, __log2f_finite)
79 hidden_alias (log2f, __ieee754_log2f)