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 * ====================================================
14 * $FreeBSD: head/lib/msun/src/s_log1pf.c 251024 2013-05-27 08:50:10Z das $
20 #include "math_private.h"
23 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
24 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
25 two25 = 3.355443200e+07, /* 0x4c000000 */
26 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
27 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
28 Lp3 = 2.8571429849e-01, /* 3E924925 */
29 Lp4 = 2.2222198546e-01, /* 3E638E29 */
30 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
31 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
32 Lp7 = 1.4798198640e-01; /* 3E178897 */
34 static const float zero = 0.0;
35 static volatile float vzero = 0.0;
40 float hfsq,f,c,s,z,R,u;
47 if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */
48 if(ax>=0x3f800000) { /* x <= -1.0 */
49 if(x==(float)-1.0) return -two25/vzero; /* log1p(-1)=+inf */
50 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
52 if(ax<0x38000000) { /* |x| < 2**-15 */
53 if(two25+x>zero /* raise inexact */
54 &&ax<0x33800000) /* |x| < 2**-24 */
57 return x - x*x*(float)0.5;
59 if(hx>0||hx<=((int32_t)0xbe95f619)) {
60 k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
62 if (hx >= 0x7f800000) return x+x;
65 STRICT_ASSIGN(float,u,(float)1.0+x);
69 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
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.
85 if(hu<0x3504f4) { /* u < sqrt(2) */
86 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
89 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
90 hu = (0x00800000-hu)>>2;
95 if(hu==0) { /* |f| < 2**-20 */
104 R = hfsq*((float)1.0-(float)0.66666666666666666*f);
105 if(k==0) return f-R; else
106 return k*ln2_hi-((R-(k*ln2_lo+c))-f);
108 s = f/((float)2.0+f);
110 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
111 if(k==0) return f-(hfsq-s*(hfsq+R)); else
112 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);