2 * Single-precision log function.
4 * Copyright (c) 2017-2018, Arm Limited.
5 * SPDX-License-Identifier: MIT
11 #include "logf_data.h"
17 ULP error: 0.818 (nearest rounding.)
18 Relative error: 1.957 * 2^-26 (before rounding.)
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
29 double_t z, r, r2, y, y0, invc, logc;
34 /* Fix sign of zero with downward rounding when x==1. */
35 if (WANT_ROUNDING && predict_false(ix == 0x3f800000))
37 if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
38 /* x < 0x1p-126 or inf or nan. */
40 return __math_divzerof(1);
41 if (ix == 0x7f800000) /* log(inf) == inf. */
43 if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
44 return __math_invalidf(x);
45 /* x is subnormal, normalize it. */
46 ix = asuint(x * 0x1p23f);
50 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
51 The range is split into N subintervals.
52 The ith subinterval contains z and c is near its center. */
54 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
55 k = (int32_t)tmp >> 23; /* arithmetic shift */
56 iz = ix - (tmp & 0x1ff << 23);
59 z = (double_t)asfloat(iz);
61 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
63 y0 = logc + (double_t)k * Ln2;
65 /* Pipelined polynomial evaluation to approximate log1p(r). */
69 y = y * r2 + (y0 + r);
70 return eval_as_float(y);