1 /* Single-precision e^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 #ifdef __expf
20 # undef libm_hidden_proto
21 # define libm_hidden_proto(ignored)
22 #endif
23
24 #include <math.h>
25 #include <math-narrow-eval.h>
26 #include <stdint.h>
27 #include <libm-alias-finite.h>
28 #include <libm-alias-float.h>
29 #include "math_config.h"
30
31 /*
32 EXP2F_TABLE_BITS = 5
33 EXP2F_POLY_ORDER = 3
34
35 ULP error: 0.502 (nearest rounding.)
36 Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
37 Wrong count: 170635 (all nearest rounding wrong results with fma.)
38 Non-nearest ULP error: 1 (rounded ULP error)
39 */
40
41 #define N (1 << EXP2F_TABLE_BITS)
42 #define InvLn2N __exp2f_data.invln2_scaled
43 #define T __exp2f_data.tab
44 #define C __exp2f_data.poly_scaled
45
46 static inline uint32_t
top12(float x)47 top12 (float x)
48 {
49 return asuint (x) >> 20;
50 }
51
52 float
__expf(float x)53 __expf (float x)
54 {
55 uint32_t abstop;
56 uint64_t ki, t;
57 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
58 double_t kd, xd, z, r, r2, y, s;
59
60 xd = (double_t) x;
61 abstop = top12 (x) & 0x7ff;
62 if (__glibc_unlikely (abstop >= top12 (88.0f)))
63 {
64 /* |x| >= 88 or x is nan. */
65 if (asuint (x) == asuint (-INFINITY))
66 return 0.0f;
67 if (abstop >= top12 (INFINITY))
68 return x + x;
69 if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
70 return __math_oflowf (0);
71 if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
72 return __math_uflowf (0);
73 #if WANT_ERRNO_UFLOW
74 if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
75 return __math_may_uflowf (0);
76 #endif
77 }
78
79 /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
80 z = InvLn2N * xd;
81
82 /* Round and convert z to int, the result is in [-150*N, 128*N] and
83 ideally ties-to-even rule is used, otherwise the magnitude of r
84 can be bigger which gives larger approximation error. */
85 #if TOINT_INTRINSICS
86 kd = roundtoint (z);
87 ki = converttoint (z);
88 #else
89 # define SHIFT __exp2f_data.shift
90 kd = math_narrow_eval ((double) (z + SHIFT)); /* Needs to be double. */
91 ki = asuint64 (kd);
92 kd -= SHIFT;
93 #endif
94 r = z - kd;
95
96 /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
97 t = T[ki % N];
98 t += ki << (52 - EXP2F_TABLE_BITS);
99 s = asdouble (t);
100 z = C[0] * r + C[1];
101 r2 = r * r;
102 y = C[2] * r + 1;
103 y = z * r2 + y;
104 y = y * s;
105 return (float) y;
106 }
107
108 #ifndef __expf
109 hidden_def (__expf)
110 strong_alias (__expf, __ieee754_expf)
111 libm_alias_finite (__ieee754_expf, __expf)
112 versioned_symbol (libm, __expf, expf, GLIBC_2_27);
113 libm_alias_float_other (__exp, exp)
114 #endif
115