expf.c
2.3 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
/*
* Single-precision e^x function.
*
* Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
* See https://llvm.org/LICENSE.txt for license information.
* SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
*/
#include <math.h>
#include <stdint.h>
#include "math_config.h"
/*
EXP2F_TABLE_BITS = 5
EXP2F_POLY_ORDER = 3
ULP error: 0.502 (nearest rounding.)
Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
Wrong count: 170635 (all nearest rounding wrong results with fma.)
Non-nearest ULP error: 1 (rounded ULP error)
*/
#define N (1 << EXP2F_TABLE_BITS)
#define InvLn2N __exp2f_data.invln2_scaled
#define T __exp2f_data.tab
#define C __exp2f_data.poly_scaled
static inline uint32_t
top12 (float x)
{
return asuint (x) >> 20;
}
float
expf (float x)
{
uint32_t abstop;
uint64_t ki, t;
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
double_t kd, xd, z, r, r2, y, s;
xd = (double_t) x;
abstop = top12 (x) & 0x7ff;
if (unlikely (abstop >= top12 (88.0f)))
{
/* |x| >= 88 or x is nan. */
if (asuint (x) == asuint (-INFINITY))
return 0.0f;
if (abstop >= top12 (INFINITY))
return x + x;
if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
return __math_oflowf (0);
if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
return __math_uflowf (0);
#if WANT_ERRNO_UFLOW
if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
return __math_may_uflowf (0);
#endif
}
/* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
z = InvLn2N * xd;
/* Round and convert z to int, the result is in [-150*N, 128*N] and
ideally nearest int is used, otherwise the magnitude of r can be
bigger which gives larger approximation error. */
#if TOINT_INTRINSICS
kd = roundtoint (z);
ki = converttoint (z);
#else
# define SHIFT __exp2f_data.shift
kd = eval_as_double (z + SHIFT);
ki = asuint64 (kd);
kd -= SHIFT;
#endif
r = z - kd;
/* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
t = T[ki % N];
t += ki << (52 - EXP2F_TABLE_BITS);
s = asdouble (t);
z = C[0] * r + C[1];
r2 = r * r;
y = C[2] * r + 1;
y = z * r2 + y;
y = y * s;
return eval_as_float (y);
}
#if USE_GLIBC_ABI
strong_alias (expf, __expf_finite)
hidden_alias (expf, __ieee754_expf)
#endif