s_expm1f.c revision 97409 
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#ifndef lint
17static char rcsid[] = "$FreeBSD: head/lib/msun/src/s_expm1f.c 97409 2002-05-28 17:51:46Z alfred $";
18#endif
19
20#include "math.h"
21#include "math_private.h"
22
23static const float
24one		= 1.0,
25huge		= 1.0e+30,
26tiny		= 1.0e-30,
27o_threshold	= 8.8721679688e+01,/* 0x42b17180 */
28ln2_hi		= 6.9313812256e-01,/* 0x3f317180 */
29ln2_lo		= 9.0580006145e-06,/* 0x3717f7d1 */
30invln2		= 1.4426950216e+00,/* 0x3fb8aa3b */
31	/* scaled coefficients related to expm1 */
32Q1  =  -3.3333335072e-02, /* 0xbd088889 */
33Q2  =   1.5873016091e-03, /* 0x3ad00d01 */
34Q3  =  -7.9365076090e-05, /* 0xb8a670cd */
35Q4  =   4.0082177293e-06, /* 0x36867e54 */
36Q5  =  -2.0109921195e-07; /* 0xb457edbb */
37
38	float expm1f(float x)
39{
40	float y,hi,lo,c,t,e,hxs,hfx,r1;
41	int32_t k,xsb;
42	u_int32_t hx;
43
44	GET_FLOAT_WORD(hx,x);
45	xsb = hx&0x80000000;		/* sign bit of x */
46	if(xsb==0) y=x; else y= -x;	/* y = |x| */
47	hx &= 0x7fffffff;		/* high word of |x| */
48
49    /* filter out huge and non-finite argument */
50	if(hx >= 0x4195b844) {			/* if |x|>=27*ln2 */
51	    if(hx >= 0x42b17218) {		/* if |x|>=88.721... */
52                if(hx>0x7f800000)
53		    return x+x; 	 /* NaN */
54		if(hx==0x7f800000)
55		    return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
56	        if(x > o_threshold) return huge*huge; /* overflow */
57	    }
58	    if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
59		if(x+tiny<(float)0.0)	/* raise inexact */
60		return tiny-one;	/* return -1 */
61	    }
62	}
63
64    /* argument reduction */
65	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
66	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
67		if(xsb==0)
68		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
69		else
70		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
71	    } else {
72		k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
73		t  = k;
74		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */
75		lo = t*ln2_lo;
76	    }
77	    x  = hi - lo;
78	    c  = (hi-x)-lo;
79	}
80	else if(hx < 0x33000000) {  	/* when |x|<2**-25, return x */
81	    t = huge+x;	/* return x with inexact flags when x!=0 */
82	    return x - (t-(huge+x));
83	}
84	else k = 0;
85
86    /* x is now in primary range */
87	hfx = (float)0.5*x;
88	hxs = x*hfx;
89	r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
90	t  = (float)3.0-r1*hfx;
91	e  = hxs*((r1-t)/((float)6.0 - x*t));
92	if(k==0) return x - (x*e-hxs);		/* c is 0 */
93	else {
94	    e  = (x*(e-c)-c);
95	    e -= hxs;
96	    if(k== -1) return (float)0.5*(x-e)-(float)0.5;
97	    if(k==1)
98	       	if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
99	       	else 	      return  one+(float)2.0*(x-e);
100	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
101	        int32_t i;
102	        y = one-(e-x);
103		GET_FLOAT_WORD(i,y);
104		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
105	        return y-one;
106	    }
107	    t = one;
108	    if(k<23) {
109	        int32_t i;
110	        SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
111	       	y = t-(e-x);
112		GET_FLOAT_WORD(i,y);
113		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
114	   } else {
115	        int32_t i;
116		SET_FLOAT_WORD(t,((0x7f-k)<<23));	/* 2^-k */
117	       	y = x-(e+t);
118	       	y += one;
119		GET_FLOAT_WORD(i,y);
120		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
121	    }
122	}
123	return y;
124}
125