1 /*
2 * Single-precision e^x function.
3 *
4 * Copyright (c) 2017-2018, Arm Limited.
5 * SPDX-License-Identifier: MIT
6 */
7
8 #include <math.h>
9 #include <stdint.h>
10 #include "libm.h"
11 #include "exp2f_data.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
top12(float x)28 static inline uint32_t top12(float x)
29 {
30 return asuint(x) >> 20;
31 }
32
expf(float x)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;
38
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);
51 }
52
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;
69
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);
80 }
81