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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
17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_expf.c,v 1.10 2005/11/30 04:56:49 bde Exp $";
18 #endif
19 
20 #include "math.h"
21 #include "math_private.h"
22 
23 static const float
24 one	= 1.0,
25 halF[2]	= {0.5,-0.5,},
26 huge	= 1.0e+30,
27 twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
28 o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
29 u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
30 ln2HI[2]   ={ 6.9314575195e-01,		/* 0x3f317200 */
31 	     -6.9314575195e-01,},	/* 0xbf317200 */
32 ln2LO[2]   ={ 1.4286067653e-06,  	/* 0x35bfbe8e */
33 	     -1.4286067653e-06,},	/* 0xb5bfbe8e */
34 invln2 =  1.4426950216e+00, 		/* 0x3fb8aa3b */
35 P1   =  1.6666667163e-01, /* 0x3e2aaaab */
36 P2   = -2.7777778450e-03, /* 0xbb360b61 */
37 P3   =  6.6137559770e-05, /* 0x388ab355 */
38 P4   = -1.6533901999e-06, /* 0xb5ddea0e */
39 P5   =  4.1381369442e-08; /* 0x3331bb4c */
40 
41 float
__ieee754_expf(float x)42 __ieee754_expf(float x)	/* default IEEE double exp */
43 {
44 	float y,hi=0.0,lo=0.0,c,t;
45 	int32_t k=0,xsb;
46 	u_int32_t hx;
47 
48 	GET_FLOAT_WORD(hx,x);
49 	xsb = (hx>>31)&1;		/* sign bit of x */
50 	hx &= 0x7fffffff;		/* high word of |x| */
51 
52     /* filter out non-finite argument */
53 	if(hx >= 0x42b17218) {			/* if |x|>=88.721... */
54 	    if(hx>0x7f800000)
55 		 return x+x;	 		/* NaN */
56             if(hx==0x7f800000)
57 		return (xsb==0)? x:0.0;		/* exp(+-inf)={inf,0} */
58 	    if(x > o_threshold) return huge*huge; /* overflow */
59 	    if(x < u_threshold) return twom100*twom100; /* underflow */
60 	}
61 
62     /* argument reduction */
63 	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
64 	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
65 		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
66 	    } else {
67 		k  = invln2*x+halF[xsb];
68 		t  = k;
69 		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
70 		lo = t*ln2LO[0];
71 	    }
72 	    x  = hi - lo;
73 	}
74 	else if(hx < 0x31800000)  {	/* when |x|<2**-28 */
75 	    if(huge+x>one) return one+x;/* trigger inexact */
76 	}
77 	else k = 0;
78 
79     /* x is now in primary range */
80 	t  = x*x;
81 	c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
82 	if(k==0) 	return one-((x*c)/(c-(float)2.0)-x);
83 	else 		y = one-((lo-(x*c)/((float)2.0-c))-hi);
84 	if(k >= -125) {
85 	    u_int32_t hy;
86 	    GET_FLOAT_WORD(hy,y);
87 	    SET_FLOAT_WORD(y,hy+(k<<23));	/* add k to y's exponent */
88 	    return y;
89 	} else {
90 	    u_int32_t hy;
91 	    GET_FLOAT_WORD(hy,y);
92 	    SET_FLOAT_WORD(y,hy+((k+100)<<23));	/* add k to y's exponent */
93 	    return y*twom100;
94 	}
95 }
96