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Commit | Line | Data |
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320054e8 | 1 | /* |
d4db3fa2 | 2 | * Single-precision e^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 | |
320054e8 | 13 | /* |
d4db3fa2 DG |
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 [-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) | |
320054e8 | 29 | { |
d4db3fa2 DG |
30 | return asuint(x) >> 20; |
31 | } | |
320054e8 | 32 | |
d4db3fa2 DG |
33 | float expf(float x) |
34 | { | |
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(88.0f))) { | |
42 | /* |x| >= 88 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 > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */ | |
48 | return __math_oflowf(0); | |
49 | if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */ | |
50 | return __math_uflowf(0); | |
320054e8 DG |
51 | } |
52 | ||
d4db3fa2 DG |
53 | /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */ |
54 | z = InvLn2N * xd; | |
55 | ||
56 | /* Round and convert z to int, the result is in [-150*N, 128*N] and | |
57 | ideally ties-to-even rule is used, otherwise the magnitude of r | |
58 | can be bigger which gives larger approximation error. */ | |
59 | #if TOINT_INTRINSICS | |
60 | kd = roundtoint(z); | |
61 | ki = converttoint(z); | |
62 | #else | |
63 | # define SHIFT __exp2f_data.shift | |
64 | kd = eval_as_double(z + SHIFT); | |
65 | ki = asuint64(kd); | |
66 | kd -= SHIFT; | |
67 | #endif | |
68 | r = z - kd; | |
320054e8 | 69 | |
d4db3fa2 DG |
70 | /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ |
71 | t = T[ki % N]; | |
72 | t += ki << (52 - EXP2F_TABLE_BITS); | |
73 | s = asdouble(t); | |
74 | z = C[0] * r + C[1]; | |
75 | r2 = r * r; | |
76 | y = C[2] * r + 1; | |
77 | y = z * r2 + y; | |
78 | y = y * s; | |
79 | return eval_as_float(y); | |
320054e8 | 80 | } |