| /* 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); |
| } |