1/*
2 * Single-precision log function.
3 *
4 * Copyright (c) 2017-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include <math.h>
9#include <stdint.h>
10#include "math_config.h"
11
12/*
13LOGF_TABLE_BITS = 4
14LOGF_POLY_ORDER = 4
15
16ULP error: 0.818 (nearest rounding.)
17Relative error: 1.957 * 2^-26 (before rounding.)
18*/
19
20#define T __logf_data.tab
21#define A __logf_data.poly
22#define Ln2 __logf_data.ln2
23#define N (1 << LOGF_TABLE_BITS)
24#define OFF 0x3f330000
25
26float
27logf (float x)
28{
29  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
30  double_t z, r, r2, y, y0, invc, logc;
31  uint32_t ix, iz, tmp;
32  int k, i;
33
34  ix = asuint (x);
35#if WANT_ROUNDING
36  /* Fix sign of zero with downward rounding when x==1.  */
37  if (unlikely (ix == 0x3f800000))
38    return 0;
39#endif
40  if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
41    {
42      /* x < 0x1p-126 or inf or nan.  */
43      if (ix * 2 == 0)
44	return __math_divzerof (1);
45      if (ix == 0x7f800000) /* log(inf) == inf.  */
46	return x;
47      if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
48	return __math_invalidf (x);
49      /* x is subnormal, normalize it.  */
50      ix = asuint (x * 0x1p23f);
51      ix -= 23 << 23;
52    }
53
54  /* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
55     The range is split into N subintervals.
56     The ith subinterval contains z and c is near its center.  */
57  tmp = ix - OFF;
58  i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
59  k = (int32_t) tmp >> 23; /* arithmetic shift */
60  iz = ix - (tmp & 0xff800000);
61  invc = T[i].invc;
62  logc = T[i].logc;
63  z = (double_t) asfloat (iz);
64
65  /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
66  r = z * invc - 1;
67  y0 = logc + (double_t) k * Ln2;
68
69  /* Pipelined polynomial evaluation to approximate log1p(r).  */
70  r2 = r * r;
71  y = A[1] * r + A[2];
72  y = A[0] * r2 + y;
73  y = y * r2 + (y0 + r);
74  return eval_as_float (y);
75}
76#if USE_GLIBC_ABI
77strong_alias (logf, __logf_finite)
78hidden_alias (logf, __ieee754_logf)
79#endif
80