1/*
 2 * Single-precision 2^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/*
14EXP2F_TABLE_BITS = 5
15EXP2F_POLY_ORDER = 3
16
17ULP error: 0.502 (nearest rounding.)
18Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
19Wrong count: 168353 (all nearest rounding wrong results with fma.)
20Non-nearest ULP error: 1 (rounded ULP error)
21*/
22
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
28static inline uint32_t top12(float x)
29{
30	return asuint(x) >> 20;
31}
32
33float exp2f(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(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);
51	}
52
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;
58
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);
69}