1/* Single-precision 2^x function.
2 Copyright (C) 2017-2018 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <http://www.gnu.org/licenses/>. */
18
19#include <math.h>
20#include <stdint.h>
21#include <shlib-compat.h>
22#include <libm-alias-float.h>
23#include "math_config.h"
24
25/*
26EXP2F_TABLE_BITS = 5
27EXP2F_POLY_ORDER = 3
28
29ULP error: 0.502 (nearest rounding.)
30Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
31Wrong count: 168353 (all nearest rounding wrong results with fma.)
32Non-nearest ULP error: 1 (rounded ULP error)
33*/
34
35#define N (1 << EXP2F_TABLE_BITS)
36#define T __exp2f_data.tab
37#define C __exp2f_data.poly
38#define SHIFT __exp2f_data.shift_scaled
39
40static inline uint32_t
41top12 (float x)
42{
43 return asuint (x) >> 20;
44}
45
46float
47__exp2f (float x)
48{
49 uint32_t abstop;
50 uint64_t ki, t;
51 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
52 double_t kd, xd, z, r, r2, y, s;
53
54 xd = (double_t) x;
55 abstop = top12 (x) & 0x7ff;
56 if (__glibc_unlikely (abstop >= top12 (128.0f)))
57 {
58 /* |x| >= 128 or x is nan. */
59 if (asuint (x) == asuint (-INFINITY))
60 return 0.0f;
61 if (abstop >= top12 (INFINITY))
62 return x + x;
63 if (x > 0.0f)
64 return __math_oflowf (0);
65 if (x <= -150.0f)
66 return __math_uflowf (0);
67#if WANT_ERRNO_UFLOW
68 if (x < -149.0f)
69 return __math_may_uflowf (0);
70#endif
71 }
72
73 /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */
74 kd = math_narrow_eval ((double) (xd + SHIFT)); /* Needs to be double. */
75 ki = asuint64 (kd);
76 kd -= SHIFT; /* k/N for int k. */
77 r = xd - kd;
78
79 /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
80 t = T[ki % N];
81 t += ki << (52 - EXP2F_TABLE_BITS);
82 s = asdouble (t);
83 z = C[0] * r + C[1];
84 r2 = r * r;
85 y = C[2] * r + 1;
86 y = z * r2 + y;
87 y = y * s;
88 return (float) y;
89}
90#ifndef __exp2f
91strong_alias (__exp2f, __ieee754_exp2f)
92strong_alias (__exp2f, __exp2f_finite)
93versioned_symbol (libm, __exp2f, exp2f, GLIBC_2_27);
94libm_alias_float_other (__exp2, exp2)
95#endif
96