xref: /freebsd/lib/msun/src/s_log1pf.c (revision 1e413cf93298b5b97441a21d9a50fdcd0ee9945e)
1 /* s_log1pf.c -- float version of s_log1p.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
17 static char rcsid[] = "$FreeBSD$";
18 #endif
19 
20 #include "math.h"
21 #include "math_private.h"
22 
23 static const float
24 ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
25 ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
26 two25 =    3.355443200e+07,	/* 0x4c000000 */
27 Lp1 = 6.6666668653e-01,	/* 3F2AAAAB */
28 Lp2 = 4.0000000596e-01,	/* 3ECCCCCD */
29 Lp3 = 2.8571429849e-01, /* 3E924925 */
30 Lp4 = 2.2222198546e-01, /* 3E638E29 */
31 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
32 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
33 Lp7 = 1.4798198640e-01; /* 3E178897 */
34 
35 static const float zero = 0.0;
36 
37 float
38 log1pf(float x)
39 {
40 	float hfsq,f,c,s,z,R,u;
41 	int32_t k,hx,hu,ax;
42 
43 	GET_FLOAT_WORD(hx,x);
44 	ax = hx&0x7fffffff;
45 
46 	k = 1;
47 	if (hx < 0x3ed413d0) {			/* 1+x < sqrt(2)+  */
48 	    if(ax>=0x3f800000) {		/* x <= -1.0 */
49 		if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
50 		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
51 	    }
52 	    if(ax<0x31000000) {			/* |x| < 2**-29 */
53 		if(two25+x>zero			/* raise inexact */
54 	            &&ax<0x24800000) 		/* |x| < 2**-54 */
55 		    return x;
56 		else
57 		    return x - x*x*(float)0.5;
58 	    }
59 	    if(hx>0||hx<=((int32_t)0xbe95f619)) {
60 		k=0;f=x;hu=1;}		/* sqrt(2)/2- <= 1+x < sqrt(2)+ */
61 	}
62 	if (hx >= 0x7f800000) return x+x;
63 	if(k!=0) {
64 	    if(hx<0x5a000000) {
65 		*(volatile float *)&u = (float)1.0+x;
66 		GET_FLOAT_WORD(hu,u);
67 	        k  = (hu>>23)-127;
68 		/* correction term */
69 	        c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
70 		c /= u;
71 	    } else {
72 		u  = x;
73 		GET_FLOAT_WORD(hu,u);
74 	        k  = (hu>>23)-127;
75 		c  = 0;
76 	    }
77 	    hu &= 0x007fffff;
78 	    /*
79 	     * The approximation to sqrt(2) used in thresholds is not
80 	     * critical.  However, the ones used above must give less
81 	     * strict bounds than the one here so that the k==0 case is
82 	     * never reached from here, since here we have committed to
83 	     * using the correction term but don't use it if k==0.
84 	     */
85 	    if(hu<0x3504f4) {			/* u < sqrt(2) */
86 	        SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
87 	    } else {
88 	        k += 1;
89 		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
90 	        hu = (0x00800000-hu)>>2;
91 	    }
92 	    f = u-(float)1.0;
93 	}
94 	hfsq=(float)0.5*f*f;
95 	if(hu==0) {	/* |f| < 2**-20 */
96 	    if(f==zero) if(k==0) return zero;
97 			else {c += k*ln2_lo; return k*ln2_hi+c;}
98 	    R = hfsq*((float)1.0-(float)0.66666666666666666*f);
99 	    if(k==0) return f-R; else
100 	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
101 	}
102  	s = f/((float)2.0+f);
103 	z = s*s;
104 	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
105 	if(k==0) return f-(hfsq-s*(hfsq+R)); else
106 		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
107 }
108