1 /*
2 * Single-precision e^x function.
3 *
4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 * See https://llvm.org/LICENSE.txt for license information.
6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 */
8
9 #include <math.h>
10 #include <stdint.h>
11 #include "math_config.h"
12
13 /*
14 EXP2F_TABLE_BITS = 5
15 EXP2F_POLY_ORDER = 3
16
17 ULP error: 0.502 (nearest rounding.)
18 Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
19 Wrong count: 170635 (all nearest rounding wrong results with fma.)
20 Non-nearest ULP error: 1 (rounded ULP error)
21 */
22
23 #define N (1 << EXP2F_TABLE_BITS)
24 #define InvLn2N __exp2f_data.invln2_scaled
25 #define T __exp2f_data.tab
26 #define C __exp2f_data.poly_scaled
27
28 static inline uint32_t
top12(float x)29 top12 (float x)
30 {
31 return asuint (x) >> 20;
32 }
33
34 float
expf(float x)35 expf (float x)
36 {
37 uint32_t abstop;
38 uint64_t ki, t;
39 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
40 double_t kd, xd, z, r, r2, y, s;
41
42 xd = (double_t) x;
43 abstop = top12 (x) & 0x7ff;
44 if (unlikely (abstop >= top12 (88.0f)))
45 {
46 /* |x| >= 88 or x is nan. */
47 if (asuint (x) == asuint (-INFINITY))
48 return 0.0f;
49 if (abstop >= top12 (INFINITY))
50 return x + x;
51 if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
52 return __math_oflowf (0);
53 if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
54 return __math_uflowf (0);
55 #if WANT_ERRNO_UFLOW
56 if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
57 return __math_may_uflowf (0);
58 #endif
59 }
60
61 /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */
62 z = InvLn2N * xd;
63
64 /* Round and convert z to int, the result is in [-150*N, 128*N] and
65 ideally nearest int is used, otherwise the magnitude of r can be
66 bigger which gives larger approximation error. */
67 #if TOINT_INTRINSICS
68 kd = roundtoint (z);
69 ki = converttoint (z);
70 #else
71 # define SHIFT __exp2f_data.shift
72 kd = eval_as_double (z + SHIFT);
73 ki = asuint64 (kd);
74 kd -= SHIFT;
75 #endif
76 r = z - kd;
77
78 /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
79 t = T[ki % N];
80 t += ki << (52 - EXP2F_TABLE_BITS);
81 s = asdouble (t);
82 z = C[0] * r + C[1];
83 r2 = r * r;
84 y = C[2] * r + 1;
85 y = z * r2 + y;
86 y = y * s;
87 return eval_as_float (y);
88 }
89 #if USE_GLIBC_ABI
90 strong_alias (expf, __expf_finite)
91 hidden_alias (expf, __ieee754_expf)
92 #endif
93