s_expm1f.c revision 177711 
1/* s_expm1f.c -- float version of s_expm1.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/s_expm1f.c 177711 2008-03-29 16:37:59Z das $");
18
19#include "math.h"
20#include "math_private.h"
21
22static const float
23one		= 1.0,
24huge		= 1.0e+30,
25tiny		= 1.0e-30,
26o_threshold	= 8.8721679688e+01,/* 0x42b17180 */
27ln2_hi		= 6.9313812256e-01,/* 0x3f317180 */
28ln2_lo		= 9.0580006145e-06,/* 0x3717f7d1 */
29invln2		= 1.4426950216e+00,/* 0x3fb8aa3b */
30/*
31 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
32 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
33 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
34 */
35Q1 = -3.3333212137e-2,		/* -0x888868.0p-28 */
36Q2 =  1.5807170421e-3;		/*  0xcf3010.0p-33 */
37
38float
39expm1f(float x)
40{
41	float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
42	int32_t k,xsb;
43	u_int32_t hx;
44
45	GET_FLOAT_WORD(hx,x);
46	xsb = hx&0x80000000;		/* sign bit of x */
47	if(xsb==0) y=x; else y= -x;	/* y = |x| */
48	hx &= 0x7fffffff;		/* high word of |x| */
49
50    /* filter out huge and non-finite argument */
51	if(hx >= 0x4195b844) {			/* if |x|>=27*ln2 */
52	    if(hx >= 0x42b17218) {		/* if |x|>=88.721... */
53                if(hx>0x7f800000)
54		    return x+x; 	 /* NaN */
55		if(hx==0x7f800000)
56		    return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
57	        if(x > o_threshold) return huge*huge; /* overflow */
58	    }
59	    if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
60		if(x+tiny<(float)0.0)	/* raise inexact */
61		return tiny-one;	/* return -1 */
62	    }
63	}
64
65    /* argument reduction */
66	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
67	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
68		if(xsb==0)
69		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
70		else
71		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
72	    } else {
73		k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
74		t  = k;
75		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */
76		lo = t*ln2_lo;
77	    }
78	    x  = hi - lo;
79	    c  = (hi-x)-lo;
80	}
81	else if(hx < 0x33000000) {  	/* when |x|<2**-25, return x */
82	    t = huge+x;	/* return x with inexact flags when x!=0 */
83	    return x - (t-(huge+x));
84	}
85	else k = 0;
86
87    /* x is now in primary range */
88	hfx = (float)0.5*x;
89	hxs = x*hfx;
90	r1 = one+hxs*(Q1+hxs*Q2);
91	t  = (float)3.0-r1*hfx;
92	e  = hxs*((r1-t)/((float)6.0 - x*t));
93	if(k==0) return x - (x*e-hxs);		/* c is 0 */
94	else {
95	    SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));	/* 2^k */
96	    e  = (x*(e-c)-c);
97	    e -= hxs;
98	    if(k== -1) return (float)0.5*(x-e)-(float)0.5;
99	    if(k==1) {
100	       	if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
101	       	else 	      return  one+(float)2.0*(x-e);
102	    }
103	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
104	        y = one-(e-x);
105		if (k == 128) y = y*2.0F*0x1p127F;
106		else y = y*twopk;
107	        return y-one;
108	    }
109	    t = one;
110	    if(k<23) {
111	        SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
112	       	y = t-(e-x);
113		y = y*twopk;
114	   } else {
115		SET_FLOAT_WORD(t,((0x7f-k)<<23));	/* 2^-k */
116	       	y = x-(e+t);
117	       	y += one;
118		y = y*twopk;
119	    }
120	}
121	return y;
122}
123