2 * Single-precision log2 function.
4 * Copyright (c) 2017-2018, Arm Limited.
5 * SPDX-License-Identifier: MIT
11 #include "log2f_data.h"
17 ULP error: 0.752 (nearest rounding.)
18 Relative error: 1.9 * 2^-26 (before rounding.)
21 #define N (1 << LOG2F_TABLE_BITS)
22 #define T __log2f_data.tab
23 #define A __log2f_data.poly
24 #define OFF 0x3f330000
28 double_t z, r, r2, p, y, y0, invc, logc;
29 uint32_t ix, iz, top, tmp;
33 /* Fix sign of zero with downward rounding when x==1. */
34 if (WANT_ROUNDING && predict_false(ix == 0x3f800000))
36 if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
37 /* x < 0x1p-126 or inf or nan. */
39 return __math_divzerof(1);
40 if (ix == 0x7f800000) /* log2(inf) == inf. */
42 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
43 return __math_invalidf(x);
44 /* x is subnormal, normalize it. */
45 ix = asuint(x * 0x1p23f);
49 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
50 The range is split into N subintervals.
51 The ith subinterval contains z and c is near its center. */
53 i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N;
54 top = tmp & 0xff800000;
56 k = (int32_t)tmp >> 23; /* arithmetic shift */
59 z = (double_t)asfloat(iz);
61 /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
63 y0 = logc + (double_t)k;
65 /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
71 return eval_as_float(y);