1 /* s_log1pf.c -- float version of s_log1p.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
13 * ====================================================
16 #include <sys/cdefs.h>
17 __FBSDID("$FreeBSD$");
22 #include "math_private.h"
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 */
36 static const float zero = 0.0;
37 static volatile float vzero = 0.0;
42 float hfsq,f,c,s,z,R,u;
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 */
54 if(ax<0x38000000) { /* |x| < 2**-15 */
55 if(two25+x>zero /* raise inexact */
56 &&ax<0x33800000) /* |x| < 2**-24 */
59 return x - x*x*(float)0.5;
61 if(hx>0||hx<=((int32_t)0xbe95f619)) {
62 k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
64 if (hx >= 0x7f800000) return x+x;
67 STRICT_ASSIGN(float,u,(float)1.0+x);
71 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
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.
87 if(hu<0x3504f4) { /* u < sqrt(2) */
88 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
91 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
92 hu = (0x00800000-hu)>>2;
97 if(hu==0) { /* |f| < 2**-20 */
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);
110 s = f/((float)2.0+f);
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);