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d4db3fa2 DG |
1 | /* |
2 | * Single-precision 2^x function. | |
320054e8 | 3 | * |
d4db3fa2 DG |
4 | * Copyright (c) 2017-2018, Arm Limited. |
5 | * SPDX-License-Identifier: MIT | |
320054e8 DG |
6 | */ |
7 | ||
d4db3fa2 DG |
8 | #include <math.h> |
9 | #include <stdint.h> | |
320054e8 | 10 | #include "libm.h" |
d4db3fa2 | 11 | #include "exp2f_data.h" |
320054e8 | 12 | |
d4db3fa2 DG |
13 | /* |
14 | EXP2F_TABLE_BITS = 5 | |
15 | EXP2F_POLY_ORDER = 3 | |
320054e8 | 16 | |
d4db3fa2 DG |
17 | ULP error: 0.502 (nearest rounding.) |
18 | Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.) | |
19 | Wrong count: 168353 (all nearest rounding wrong results with fma.) | |
20 | Non-nearest ULP error: 1 (rounded ULP error) | |
21 | */ | |
320054e8 | 22 | |
d4db3fa2 DG |
23 | #define N (1 << EXP2F_TABLE_BITS) |
24 | #define T __exp2f_data.tab | |
25 | #define C __exp2f_data.poly | |
26 | #define SHIFT __exp2f_data.shift_scaled | |
27 | ||
28 | static inline uint32_t top12(float x) | |
29 | { | |
30 | return asuint(x) >> 20; | |
31 | } | |
320054e8 | 32 | |
320054e8 DG |
33 | float exp2f(float x) |
34 | { | |
d4db3fa2 DG |
35 | uint32_t abstop; |
36 | uint64_t ki, t; | |
37 | double_t kd, xd, z, r, r2, y, s; | |
320054e8 | 38 | |
d4db3fa2 DG |
39 | xd = (double_t)x; |
40 | abstop = top12(x) & 0x7ff; | |
41 | if (predict_false(abstop >= top12(128.0f))) { | |
42 | /* |x| >= 128 or x is nan. */ | |
43 | if (asuint(x) == asuint(-INFINITY)) | |
44 | return 0.0f; | |
45 | if (abstop >= top12(INFINITY)) | |
46 | return x + x; | |
47 | if (x > 0.0f) | |
48 | return __math_oflowf(0); | |
49 | if (x <= -150.0f) | |
50 | return __math_uflowf(0); | |
320054e8 DG |
51 | } |
52 | ||
d4db3fa2 DG |
53 | /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */ |
54 | kd = eval_as_double(xd + SHIFT); | |
55 | ki = asuint64(kd); | |
56 | kd -= SHIFT; /* k/N for int k. */ | |
57 | r = xd - kd; | |
320054e8 | 58 | |
d4db3fa2 DG |
59 | /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ |
60 | t = T[ki % N]; | |
61 | t += ki << (52 - EXP2F_TABLE_BITS); | |
62 | s = asdouble(t); | |
63 | z = C[0] * r + C[1]; | |
64 | r2 = r * r; | |
65 | y = C[2] * r + 1; | |
66 | y = z * r2 + y; | |
67 | y = y * s; | |
68 | return eval_as_float(y); | |
320054e8 | 69 | } |