1 /*
2 * Single-precision 2^x function.
3 *
4 * Copyright (c) 2017-2018, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include <math.h>
9 #include <stdint.h>
10 #include "math_config.h"
11
12 /*
13 EXP2F_TABLE_BITS = 5
14 EXP2F_POLY_ORDER = 3
15
16 ULP error: 0.502 (nearest rounding.)
17 Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
18 Wrong count: 168353 (all nearest rounding wrong results with fma.)
19 Non-nearest ULP error: 1 (rounded ULP error)
20 */
21
22 #define N (1 << EXP2F_TABLE_BITS)
23 #define T __exp2f_data.tab
24 #define C __exp2f_data.poly
25 #define SHIFT __exp2f_data.shift_scaled
26
27 static inline uint32_t
top12(float x)28 top12 (float x)
29 {
30 return asuint (x) >> 20;
31 }
32
33 float
exp2f(float x)34 exp2f (float x)
35 {
36 uint32_t abstop;
37 uint64_t ki, t;
38 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
39 double_t kd, xd, z, r, r2, y, s;
40
41 xd = (double_t) x;
42 abstop = top12 (x) & 0x7ff;
43 if (unlikely (abstop >= top12 (128.0f)))
44 {
45 /* |x| >= 128 or x is nan. */
46 if (asuint (x) == asuint (-INFINITY))
47 return 0.0f;
48 if (abstop >= top12 (INFINITY))
49 return x + x;
50 if (x > 0.0f)
51 return __math_oflowf (0);
52 if (x <= -150.0f)
53 return __math_uflowf (0);
54 #if WANT_ERRNO_UFLOW
55 if (x < -149.0f)
56 return __math_may_uflowf (0);
57 #endif
58 }
59
60 /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */
61 kd = eval_as_double (xd + SHIFT);
62 ki = asuint64 (kd);
63 kd -= SHIFT; /* k/N for int k. */
64 r = xd - kd;
65
66 /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
67 t = T[ki % N];
68 t += ki << (52 - EXP2F_TABLE_BITS);
69 s = asdouble (t);
70 z = C[0] * r + C[1];
71 r2 = r * r;
72 y = C[2] * r + 1;
73 y = z * r2 + y;
74 y = y * s;
75 return eval_as_float (y);
76 }
77 #if USE_GLIBC_ABI
78 strong_alias (exp2f, __exp2f_finite)
79 hidden_alias (exp2f, __ieee754_exp2f)
80 #endif
81