/* s_log1pf.c -- float version of s_log1p.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #ifndef lint static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_log1pf.c,v 1.9 2005/12/04 12:30:44 bde Exp $"; #endif #include "math.h" #include "math_private.h" static const float ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ two25 = 3.355443200e+07, /* 0x4c000000 */ Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ Lp3 = 2.8571429849e-01, /* 3E924925 */ Lp4 = 2.2222198546e-01, /* 3E638E29 */ Lp5 = 1.8183572590e-01, /* 3E3A3325 */ Lp6 = 1.5313838422e-01, /* 3E1CD04F */ Lp7 = 1.4798198640e-01; /* 3E178897 */ static const float zero = 0.0; float log1pf(float x) { float hfsq,f,c,s,z,R,u; int32_t k,hx,hu,ax; GET_FLOAT_WORD(hx,x); ax = hx&0x7fffffff; k = 1; if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */ if(ax>=0x3f800000) { /* x <= -1.0 */ if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ } if(ax<0x31000000) { /* |x| < 2**-29 */ if(two25+x>zero /* raise inexact */ &&ax<0x24800000) /* |x| < 2**-54 */ return x; else return x - x*x*(float)0.5; } if(hx>0||hx<=((int32_t)0xbe95f619)) { k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ } if (hx >= 0x7f800000) return x+x; if(k!=0) { if(hx<0x5a000000) { *(volatile float *)&u = (float)1.0+x; GET_FLOAT_WORD(hu,u); k = (hu>>23)-127; /* correction term */ c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); c /= u; } else { u = x; GET_FLOAT_WORD(hu,u); k = (hu>>23)-127; c = 0; } hu &= 0x007fffff; /* * The approximation to sqrt(2) used in thresholds is not * critical. However, the ones used above must give less * strict bounds than the one here so that the k==0 case is * never reached from here, since here we have committed to * using the correction term but don't use it if k==0. */ if(hu<0x3504f4) { /* u < sqrt(2) */ SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ } else { k += 1; SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ hu = (0x00800000-hu)>>2; } f = u-(float)1.0; } hfsq=(float)0.5*f*f; if(hu==0) { /* |f| < 2**-20 */ if(f==zero) if(k==0) return zero; else {c += k*ln2_lo; return k*ln2_hi+c;} R = hfsq*((float)1.0-(float)0.66666666666666666*f); if(k==0) return f-R; else return k*ln2_hi-((R-(k*ln2_lo+c))-f); } s = f/((float)2.0+f); z = s*s; R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); if(k==0) return f-(hfsq-s*(hfsq+R)); else return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); }