e_expf.c revision 176451 
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__FBSDID("$FreeBSD: head/lib/msun/src/e_expf.c 176451 2008-02-22 02:30:36Z das $");
18
19#include "math.h"
20#include "math_private.h"
21
22static const float
23one	= 1.0,
24halF[2]	= {0.5,-0.5,},
25huge	= 1.0e+30,
26o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
27u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
28ln2HI[2]   ={ 6.9314575195e-01,		/* 0x3f317200 */
29	     -6.9314575195e-01,},	/* 0xbf317200 */
30ln2LO[2]   ={ 1.4286067653e-06,  	/* 0x35bfbe8e */
31	     -1.4286067653e-06,},	/* 0xb5bfbe8e */
32invln2 =  1.4426950216e+00, 		/* 0x3fb8aa3b */
33/*
34 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
35 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
36 */
37P1 =  1.6666625440e-1,		/*  0xaaaa8f.0p-26 */
38P2 = -2.7667332906e-3;		/* -0xb55215.0p-32 */
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,twopk;
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	if(k >= -125)
83	    SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));
84	else
85	    SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23));
86	c  = x - t*(P1+t*P2);
87	if(k==0) 	return one-((x*c)/(c-(float)2.0)-x);
88	else 		y = one-((lo-(x*c)/((float)2.0-c))-hi);
89	if(k >= -125) {
90	    if(k==128) return y*2.0F*0x1p127F;
91	    return y*twopk;
92	} else {
93	    return y*twopk*twom100;
94	}
95}
96