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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 #if defined(LIBM_SCCS) && !defined(lint)
     18 __RCSID("$NetBSD: s_log1pf.c,v 1.9 2024/07/16 14:52:50 riastradh Exp $");
     19 #endif
     20 
     21 #include "namespace.h"
     22 
     23 #include "math.h"
     24 #include "math_private.h"
     25 
     26 static const float
     27 ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
     28 ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
     29 two25 =    3.355443200e+07,	/* 0x4c000000 */
     30 Lp1 = 6.6666668653e-01,	/* 3F2AAAAB */
     31 Lp2 = 4.0000000596e-01,	/* 3ECCCCCD */
     32 Lp3 = 2.8571429849e-01, /* 3E924925 */
     33 Lp4 = 2.2222198546e-01, /* 3E638E29 */
     34 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
     35 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
     36 Lp7 = 1.4798198640e-01; /* 3E178897 */
     37 
     38 static const float zero = 0.0;
     39 
     40 __weak_alias(log1pf, _log1pf)
     41 float
     42 log1pf(float x)
     43 {
     44 	float hfsq,f,c,s,z,R,u;
     45 	int32_t k,hx,hu,ax;
     46 
     47 	f = c = 0;
     48 	hu = 0;
     49 	GET_FLOAT_WORD(hx,x);
     50 	ax = hx&0x7fffffff;
     51 
     52 	k = 1;
     53 	if (hx < 0x3ed413d7) {			/* x < 0.41422  */
     54 	    if(ax>=0x3f800000) {		/* x <= -1.0 */
     55 		if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
     56 		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
     57 	    }
     58 	    if(ax<0x31000000) {			/* |x| < 2**-29 */
     59 		if(two25+x>zero			/* raise inexact */
     60 	            &&ax<0x24800000) 		/* |x| < 2**-54 */
     61 		    return x;
     62 		else
     63 		    return x - x*x*(float)0.5;
     64 	    }
     65 	    if(hx>0||hx<=((int32_t)0xbe95f61f)) {
     66 		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
     67 	}
     68 	if (hx >= 0x7f800000) return x+x;
     69 	if(k!=0) {
     70 	    if(hx<0x5a000000) {
     71 		u  = (float)1.0+x;
     72 		GET_FLOAT_WORD(hu,u);
     73 	        k  = (hu>>23)-127;
     74 		/* correction term */
     75 	        c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
     76 		c /= u;
     77 	    } else {
     78 		u  = x;
     79 		GET_FLOAT_WORD(hu,u);
     80 	        k  = (hu>>23)-127;
     81 		c  = 0;
     82 	    }
     83 	    hu &= 0x007fffff;
     84 	    if(hu<0x3504f7) {
     85 	        SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
     86 	    } else {
     87 	        k += 1;
     88 		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
     89 	        hu = (0x00800000-hu)>>2;
     90 	    }
     91 	    f = u-(float)1.0;
     92 	}
     93 	hfsq=(float)0.5*f*f;
     94 	if(hu==0) {	/* |f| < 2**-20 */
     95 	    if(f==zero) { if(k==0) return zero;
     96 			  else {c += k*ln2_lo; return k*ln2_hi+c;}
     97 	    }
     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