e_expf.c revision 175468 
1/* e_expf.c -- float version of e_exp.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
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#ifndef lint
17static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_expf.c 175468 2008-01-18 22:19:04Z das $";
18#endif
19
20#include "math.h"
21#include "math_private.h"
22
23static const float
24one	= 1.0,
25halF[2]	= {0.5,-0.5,},
26huge	= 1.0e+30,
27o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
28u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
29ln2HI[2]   ={ 6.9314575195e-01,		/* 0x3f317200 */
30	     -6.9314575195e-01,},	/* 0xbf317200 */
31ln2LO[2]   ={ 1.4286067653e-06,  	/* 0x35bfbe8e */
32	     -1.4286067653e-06,},	/* 0xb5bfbe8e */
33invln2 =  1.4426950216e+00, 		/* 0x3fb8aa3b */
34P1   =  1.6666667163e-01, /* 0x3e2aaaab */
35P2   = -2.7777778450e-03, /* 0xbb360b61 */
36P3   =  6.6137559770e-05, /* 0x388ab355 */
37P4   = -1.6533901999e-06, /* 0xb5ddea0e */
38P5   =  4.1381369442e-08; /* 0x3331bb4c */
39
40static volatile float twom100 = 7.8886090522e-31;      /* 2**-100=0x0d800000 */
41
42float
43__ieee754_expf(float x)	/* default IEEE double exp */
44{
45	float y,hi=0.0,lo=0.0,c,t;
46	int32_t k=0,xsb;
47	u_int32_t hx;
48
49	GET_FLOAT_WORD(hx,x);
50	xsb = (hx>>31)&1;		/* sign bit of x */
51	hx &= 0x7fffffff;		/* high word of |x| */
52
53    /* filter out non-finite argument */
54	if(hx >= 0x42b17218) {			/* if |x|>=88.721... */
55	    if(hx>0x7f800000)
56		 return x+x;	 		/* NaN */
57            if(hx==0x7f800000)
58		return (xsb==0)? x:0.0;		/* exp(+-inf)={inf,0} */
59	    if(x > o_threshold) return huge*huge; /* overflow */
60	    if(x < u_threshold) return twom100*twom100; /* underflow */
61	}
62
63    /* argument reduction */
64	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
65	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
66		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
67	    } else {
68		k  = invln2*x+halF[xsb];
69		t  = k;
70		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
71		lo = t*ln2LO[0];
72	    }
73	    x  = hi - lo;
74	}
75	else if(hx < 0x31800000)  {	/* when |x|<2**-28 */
76	    if(huge+x>one) return one+x;/* trigger inexact */
77	}
78	else k = 0;
79
80    /* x is now in primary range */
81	t  = x*x;
82	c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
83	if(k==0) 	return one-((x*c)/(c-(float)2.0)-x);
84	else 		y = one-((lo-(x*c)/((float)2.0-c))-hi);
85	if(k >= -125) {
86	    u_int32_t hy;
87	    GET_FLOAT_WORD(hy,y);
88	    SET_FLOAT_WORD(y,hy+(k<<23));	/* add k to y's exponent */
89	    return y;
90	} else {
91	    u_int32_t hy;
92	    GET_FLOAT_WORD(hy,y);
93	    SET_FLOAT_WORD(y,hy+((k+100)<<23));	/* add k to y's exponent */
94	    return y*twom100;
95	}
96}
97