1/* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 */
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16#include "libm.h"
17
18static const float
19half[2] = {0.5,-0.5},
20ln2hi   = 6.9314575195e-1f,  /* 0x3f317200 */
21ln2lo   = 1.4286067653e-6f,  /* 0x35bfbe8e */
22invln2  = 1.4426950216e+0f,  /* 0x3fb8aa3b */
23/*
24 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
25 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
26 */
27P1 =  1.6666625440e-1f, /*  0xaaaa8f.0p-26 */
28P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
29
30float expf(float x)
31{
32	float_t hi, lo, c, xx, y;
33	int k, sign;
34	uint32_t hx;
35
36	GET_FLOAT_WORD(hx, x);
37	sign = hx >> 31;   /* sign bit of x */
38	hx &= 0x7fffffff;  /* high word of |x| */
39
40	/* special cases */
41	if (hx >= 0x42aeac50) {  /* if |x| >= -87.33655f or NaN */
42		if (hx > 0x7f800000) /* NaN */
43			return x;
44		if (hx >= 0x42b17218 && !sign) {  /* x >= 88.722839f */
45			/* overflow */
46			x *= 0x1p127f;
47			return x;
48		}
49		if (sign) {
50			/* underflow */
51			FORCE_EVAL(-0x1p-149f/x);
52			if (hx >= 0x42cff1b5)  /* x <= -103.972084f */
53				return 0;
54		}
55	}
56
57	/* argument reduction */
58	if (hx > 0x3eb17218) {  /* if |x| > 0.5 ln2 */
59		if (hx > 0x3f851592)  /* if |x| > 1.5 ln2 */
60			k = invln2*x + half[sign];
61		else
62			k = 1 - sign - sign;
63		hi = x - k*ln2hi;  /* k*ln2hi is exact here */
64		lo = k*ln2lo;
65		x = hi - lo;
66	} else if (hx > 0x39000000) {  /* |x| > 2**-14 */
67		k = 0;
68		hi = x;
69		lo = 0;
70	} else {
71		/* raise inexact */
72		FORCE_EVAL(0x1p127f + x);
73		return 1 + x;
74	}
75
76	/* x is now in primary range */
77	xx = x*x;
78	c = x - xx*(P1+xx*P2);
79	y = 1 + (x*c/(2-c) - lo + hi);
80	if (k == 0)
81		return y;
82	return scalbnf(y, k);
83}
84