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#include <sys/cdefs.h>
17#if defined(LIBM_SCCS) && !defined(lint)
18__RCSID("$NetBSD: e_expf.c,v 1.8 1999/07/02 15:37:39 simonb Exp $");
19#endif
20
21#include "math.h"
22#include "math_private.h"
23
24static const float huge = 1.0e+30;
25
26static const float
27one	= 1.0,
28halF[2]	= {0.5,-0.5,},
29twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
30o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
31u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
32ln2HI[2]   ={ 6.9313812256e-01,		/* 0x3f317180 */
33	     -6.9313812256e-01,},	/* 0xbf317180 */
34ln2LO[2]   ={ 9.0580006145e-06,  	/* 0x3717f7d1 */
35	     -9.0580006145e-06,},	/* 0xb717f7d1 */
36invln2 =  1.4426950216e+00, 		/* 0x3fb8aa3b */
37P1   =  1.6666667163e-01, /* 0x3e2aaaab */
38P2   = -2.7777778450e-03, /* 0xbb360b61 */
39P3   =  6.6137559770e-05, /* 0x388ab355 */
40P4   = -1.6533901999e-06, /* 0xb5ddea0e */
41P5   =  4.1381369442e-08; /* 0x3331bb4c */
42
43float
44__ieee754_expf(float x)	/* default IEEE double exp */
45{
46	float y,hi,lo,c,t;
47	int32_t k,xsb;
48	u_int32_t hx;
49
50	hi = lo = 0;
51	k = 0;
52	GET_FLOAT_WORD(hx,x);
53	xsb = (hx>>31)&1;		/* sign bit of x */
54	hx &= 0x7fffffff;		/* high word of |x| */
55
56    /* filter out non-finite argument */
57	if(hx >= 0x42b17218) {			/* if |x|>=88.721... */
58	    if(hx>0x7f800000)
59		 return x+x;	 		/* NaN */
60            if(hx==0x7f800000)
61		return (xsb==0)? x:0.0;		/* exp(+-inf)={inf,0} */
62	    if(x > o_threshold) return huge*huge; /* overflow */
63	    if(x < u_threshold) return twom100*twom100; /* underflow */
64	}
65
66    /* argument reduction */
67	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
68	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
69		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
70	    } else {
71		k  = invln2*x+halF[xsb];
72		t  = k;
73		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
74		lo = t*ln2LO[0];
75	    }
76	    x  = hi - lo;
77	}
78	else if(hx < 0x31800000)  {	/* when |x|<2**-28 */
79	    if(huge+x>one) return one+x;/* trigger inexact */
80	}
81	else k = 0;
82
83    /* x is now in primary range */
84	t  = x*x;
85	c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
86	if(k==0) 	return one-((x*c)/(c-(float)2.0)-x);
87	else 		y = one-((lo-(x*c)/((float)2.0-c))-hi);
88	if(k >= -125) {
89	    u_int32_t hy;
90	    GET_FLOAT_WORD(hy,y);
91	    SET_FLOAT_WORD(y,hy+(k<<23));	/* add k to y's exponent */
92	    return y;
93	} else {
94	    u_int32_t hy;
95	    GET_FLOAT_WORD(hy,y);
96	    SET_FLOAT_WORD(y,hy+((k+100)<<23));	/* add k to y's exponent */
97	    return y*twom100;
98	}
99}
100