1 /* Single-precision 2^x function.
2 Copyright (C) 2017-2021 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 <https://www.gnu.org/licenses/>. */
18
19 #include <math.h>
20 #include <math-narrow-eval.h>
21 #include <stdint.h>
22 #include <libm-alias-finite.h>
23 #include <libm-alias-float.h>
24 #include "math_config.h"
25
26 /*
27 EXP2F_TABLE_BITS = 5
28 EXP2F_POLY_ORDER = 3
29
30 ULP error: 0.502 (nearest rounding.)
31 Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
32 Wrong count: 168353 (all nearest rounding wrong results with fma.)
33 Non-nearest ULP error: 1 (rounded ULP error)
34 */
35
36 #define N (1 << EXP2F_TABLE_BITS)
37 #define T __exp2f_data.tab
38 #define C __exp2f_data.poly
39 #define SHIFT __exp2f_data.shift_scaled
40
41 static inline uint32_t
top12(float x)42 top12 (float x)
43 {
44 return asuint (x) >> 20;
45 }
46
47 float
__exp2f(float x)48 __exp2f (float x)
49 {
50 uint32_t abstop;
51 uint64_t ki, t;
52 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
53 double_t kd, xd, z, r, r2, y, s;
54
55 xd = (double_t) x;
56 abstop = top12 (x) & 0x7ff;
57 if (__glibc_unlikely (abstop >= top12 (128.0f)))
58 {
59 /* |x| >= 128 or x is nan. */
60 if (asuint (x) == asuint (-INFINITY))
61 return 0.0f;
62 if (abstop >= top12 (INFINITY))
63 return x + x;
64 if (x > 0.0f)
65 return __math_oflowf (0);
66 if (x <= -150.0f)
67 return __math_uflowf (0);
68 #if WANT_ERRNO_UFLOW
69 if (x < -149.0f)
70 return __math_may_uflowf (0);
71 #endif
72 }
73
74 /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */
75 kd = math_narrow_eval ((double) (xd + SHIFT)); /* Needs to be double. */
76 ki = asuint64 (kd);
77 kd -= SHIFT; /* k/N for int k. */
78 r = xd - kd;
79
80 /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
81 t = T[ki % N];
82 t += ki << (52 - EXP2F_TABLE_BITS);
83 s = asdouble (t);
84 z = C[0] * r + C[1];
85 r2 = r * r;
86 y = C[2] * r + 1;
87 y = z * r2 + y;
88 y = y * s;
89 return (float) y;
90 }
91 #ifndef __exp2f
92 strong_alias (__exp2f, __ieee754_exp2f)
93 libm_alias_finite (__ieee754_exp2f, __exp2f)
94 versioned_symbol (libm, __exp2f, exp2f, GLIBC_2_27);
95 libm_alias_float_other (__exp2, exp2)
96 #endif
97