s_expm1f.c revision 226596 
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 226596 2011-10-21 06:26:38Z das $");
18
19#include <float.h>
20
21#include "math.h"
22#include "math_private.h"
23
24static const float
25one		= 1.0,
26huge		= 1.0e+30,
27tiny		= 1.0e-30,
28o_threshold	= 8.8721679688e+01,/* 0x42b17180 */
29ln2_hi		= 6.9313812256e-01,/* 0x3f317180 */
30ln2_lo		= 9.0580006145e-06,/* 0x3717f7d1 */
31invln2		= 1.4426950216e+00,/* 0x3fb8aa3b */
32/*
33 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
34 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
35 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
36 */
37Q1 = -3.3333212137e-2,		/* -0x888868.0p-28 */
38Q2 =  1.5807170421e-3;		/*  0xcf3010.0p-33 */
39
40float
41expm1f(float x)
42{
43	float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
44	int32_t k,xsb;
45	u_int32_t hx;
46
47	GET_FLOAT_WORD(hx,x);
48	xsb = hx&0x80000000;		/* sign bit of x */
49	hx &= 0x7fffffff;		/* high word of |x| */
50
51    /* filter out huge and non-finite argument */
52	if(hx >= 0x4195b844) {			/* if |x|>=27*ln2 */
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:-1.0;/* exp(+-inf)={inf,-1} */
58	        if(x > o_threshold) return huge*huge; /* overflow */
59	    }
60	    if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
61		if(x+tiny<(float)0.0)	/* raise inexact */
62		return tiny-one;	/* return -1 */
63	    }
64	}
65
66    /* argument reduction */
67	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
68	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
69		if(xsb==0)
70		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
71		else
72		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
73	    } else {
74		k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
75		t  = k;
76		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */
77		lo = t*ln2_lo;
78	    }
79	    STRICT_ASSIGN(float, x, hi - lo);
80	    c  = (hi-x)-lo;
81	}
82	else if(hx < 0x33000000) {  	/* when |x|<2**-25, return x */
83	    t = huge+x;	/* return x with inexact flags when x!=0 */
84	    return x - (t-(huge+x));
85	}
86	else k = 0;
87
88    /* x is now in primary range */
89	hfx = (float)0.5*x;
90	hxs = x*hfx;
91	r1 = one+hxs*(Q1+hxs*Q2);
92	t  = (float)3.0-r1*hfx;
93	e  = hxs*((r1-t)/((float)6.0 - x*t));
94	if(k==0) return x - (x*e-hxs);		/* c is 0 */
95	else {
96	    SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));	/* 2^k */
97	    e  = (x*(e-c)-c);
98	    e -= hxs;
99	    if(k== -1) return (float)0.5*(x-e)-(float)0.5;
100	    if(k==1) {
101	       	if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
102	       	else 	      return  one+(float)2.0*(x-e);
103	    }
104	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
105	        y = one-(e-x);
106		if (k == 128) y = y*2.0F*0x1p127F;
107		else y = y*twopk;
108	        return y-one;
109	    }
110	    t = one;
111	    if(k<23) {
112	        SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
113	       	y = t-(e-x);
114		y = y*twopk;
115	   } else {
116		SET_FLOAT_WORD(t,((0x7f-k)<<23));	/* 2^-k */
117	       	y = x-(e+t);
118	       	y += one;
119		y = y*twopk;
120	    }
121	}
122	return y;
123}
124