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/*
14EXP2F_TABLE_BITS = 5
15EXP2F_POLY_ORDER = 3
16
17ULP error: 0.502 (nearest rounding.)
18Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
19Wrong count: 170635 (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 InvLn2N __exp2f_data.invln2_scaled
25#define T __exp2f_data.tab
26#define C __exp2f_data.poly_scaled
27
28static inline uint32_t top12(float x)
29{
30	return asuint(x) >> 20;
31}
32
33float 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