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      1 /* s_log1pf.c -- float version of s_log1p.c.
      2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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
     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