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 #include <sys/cdefs.h>
17 __FBSDID("$FreeBSD$");
18 
19 #include <float.h>
20 
21 #include "math.h"
22 #include "math_private.h"
23 
24 static const float
25 ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
26 ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
27 two25 =    3.355443200e+07,	/* 0x4c000000 */
28 Lp1 = 6.6666668653e-01,	/* 3F2AAAAB */
29 Lp2 = 4.0000000596e-01,	/* 3ECCCCCD */
30 Lp3 = 2.8571429849e-01, /* 3E924925 */
31 Lp4 = 2.2222198546e-01, /* 3E638E29 */
32 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
33 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
34 Lp7 = 1.4798198640e-01; /* 3E178897 */
35 
36 static const float zero = 0.0;
37 static volatile float vzero = 0.0;
38 
39 float
log1pf(float x)40 log1pf(float x)
41 {
42 	float hfsq,f,c,s,z,R,u;
43 	int32_t k,hx,hu,ax;
44 
45 	GET_FLOAT_WORD(hx,x);
46 	ax = hx&0x7fffffff;
47 
48 	k = 1;
49 	if (hx < 0x3ed413d0) {			/* 1+x < sqrt(2)+  */
50 	    if(ax>=0x3f800000) {		/* x <= -1.0 */
51 		if(x==(float)-1.0) return -two25/vzero; /* log1p(-1)=+inf */
52 		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
53 	    }
54 	    if(ax<0x38000000) {			/* |x| < 2**-15 */
55 		if(two25+x>zero			/* raise inexact */
56 	            &&ax<0x33800000) 		/* |x| < 2**-24 */
57 		    return x;
58 		else
59 		    return x - x*x*(float)0.5;
60 	    }
61 	    if(hx>0||hx<=((int32_t)0xbe95f619)) {
62 		k=0;f=x;hu=1;}		/* sqrt(2)/2- <= 1+x < sqrt(2)+ */
63 	}
64 	if (hx >= 0x7f800000) return x+x;
65 	if(k!=0) {
66 	    if(hx<0x5a000000) {
67 		STRICT_ASSIGN(float,u,(float)1.0+x);
68 		GET_FLOAT_WORD(hu,u);
69 	        k  = (hu>>23)-127;
70 		/* correction term */
71 	        c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
72 		c /= u;
73 	    } else {
74 		u  = x;
75 		GET_FLOAT_WORD(hu,u);
76 	        k  = (hu>>23)-127;
77 		c  = 0;
78 	    }
79 	    hu &= 0x007fffff;
80 	    /*
81 	     * The approximation to sqrt(2) used in thresholds is not
82 	     * critical.  However, the ones used above must give less
83 	     * strict bounds than the one here so that the k==0 case is
84 	     * never reached from here, since here we have committed to
85 	     * using the correction term but don't use it if k==0.
86 	     */
87 	    if(hu<0x3504f4) {			/* u < sqrt(2) */
88 	        SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
89 	    } else {
90 	        k += 1;
91 		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
92 	        hu = (0x00800000-hu)>>2;
93 	    }
94 	    f = u-(float)1.0;
95 	}
96 	hfsq=(float)0.5*f*f;
97 	if(hu==0) {	/* |f| < 2**-20 */
98 	    if(f==zero) {
99 		if(k==0) {
100 		    return zero;
101 		} else {
102 		    c += k*ln2_lo;
103 		    return k*ln2_hi+c;
104 		}
105 	    }
106 	    R = hfsq*((float)1.0-(float)0.66666666666666666*f);
107 	    if(k==0) return f-R; else
108 	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
109 	}
110  	s = f/((float)2.0+f);
111 	z = s*s;
112 	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
113 	if(k==0) return f-(hfsq-s*(hfsq+R)); else
114 		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
115 }
116