1*412f47f9SXin Li /*
2*412f47f9SXin Li * Single-precision 2^x function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2017-2018, Arm Limited.
5*412f47f9SXin Li * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*412f47f9SXin Li */
7*412f47f9SXin Li
8*412f47f9SXin Li #include <math.h>
9*412f47f9SXin Li #include <stdint.h>
10*412f47f9SXin Li #include "math_config.h"
11*412f47f9SXin Li
12*412f47f9SXin Li /*
13*412f47f9SXin Li EXP2F_TABLE_BITS = 5
14*412f47f9SXin Li EXP2F_POLY_ORDER = 3
15*412f47f9SXin Li
16*412f47f9SXin Li ULP error: 0.502 (nearest rounding.)
17*412f47f9SXin Li Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
18*412f47f9SXin Li Wrong count: 168353 (all nearest rounding wrong results with fma.)
19*412f47f9SXin Li Non-nearest ULP error: 1 (rounded ULP error)
20*412f47f9SXin Li */
21*412f47f9SXin Li
22*412f47f9SXin Li #define N (1 << EXP2F_TABLE_BITS)
23*412f47f9SXin Li #define T __exp2f_data.tab
24*412f47f9SXin Li #define C __exp2f_data.poly
25*412f47f9SXin Li #define SHIFT __exp2f_data.shift_scaled
26*412f47f9SXin Li
27*412f47f9SXin Li static inline uint32_t
top12(float x)28*412f47f9SXin Li top12 (float x)
29*412f47f9SXin Li {
30*412f47f9SXin Li return asuint (x) >> 20;
31*412f47f9SXin Li }
32*412f47f9SXin Li
33*412f47f9SXin Li float
exp2f(float x)34*412f47f9SXin Li exp2f (float x)
35*412f47f9SXin Li {
36*412f47f9SXin Li uint32_t abstop;
37*412f47f9SXin Li uint64_t ki, t;
38*412f47f9SXin Li /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
39*412f47f9SXin Li double_t kd, xd, z, r, r2, y, s;
40*412f47f9SXin Li
41*412f47f9SXin Li xd = (double_t) x;
42*412f47f9SXin Li abstop = top12 (x) & 0x7ff;
43*412f47f9SXin Li if (unlikely (abstop >= top12 (128.0f)))
44*412f47f9SXin Li {
45*412f47f9SXin Li /* |x| >= 128 or x is nan. */
46*412f47f9SXin Li if (asuint (x) == asuint (-INFINITY))
47*412f47f9SXin Li return 0.0f;
48*412f47f9SXin Li if (abstop >= top12 (INFINITY))
49*412f47f9SXin Li return x + x;
50*412f47f9SXin Li if (x > 0.0f)
51*412f47f9SXin Li return __math_oflowf (0);
52*412f47f9SXin Li if (x <= -150.0f)
53*412f47f9SXin Li return __math_uflowf (0);
54*412f47f9SXin Li #if WANT_ERRNO_UFLOW
55*412f47f9SXin Li if (x < -149.0f)
56*412f47f9SXin Li return __math_may_uflowf (0);
57*412f47f9SXin Li #endif
58*412f47f9SXin Li }
59*412f47f9SXin Li
60*412f47f9SXin Li /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */
61*412f47f9SXin Li kd = eval_as_double (xd + SHIFT);
62*412f47f9SXin Li ki = asuint64 (kd);
63*412f47f9SXin Li kd -= SHIFT; /* k/N for int k. */
64*412f47f9SXin Li r = xd - kd;
65*412f47f9SXin Li
66*412f47f9SXin Li /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
67*412f47f9SXin Li t = T[ki % N];
68*412f47f9SXin Li t += ki << (52 - EXP2F_TABLE_BITS);
69*412f47f9SXin Li s = asdouble (t);
70*412f47f9SXin Li z = C[0] * r + C[1];
71*412f47f9SXin Li r2 = r * r;
72*412f47f9SXin Li y = C[2] * r + 1;
73*412f47f9SXin Li y = z * r2 + y;
74*412f47f9SXin Li y = y * s;
75*412f47f9SXin Li return eval_as_float (y);
76*412f47f9SXin Li }
77*412f47f9SXin Li #if USE_GLIBC_ABI
78*412f47f9SXin Li strong_alias (exp2f, __exp2f_finite)
79*412f47f9SXin Li hidden_alias (exp2f, __ieee754_exp2f)
80*412f47f9SXin Li #endif
81