| /* e_logf.c -- float version of e_log.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. |
| * ==================================================== |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| #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 */ |
| /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ |
| Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ |
| Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ |
| Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ |
| Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ |
| |
| static const float zero = 0.0; |
| |
| float |
| __ieee754_logf(float x) |
| { |
| float hfsq,f,s,z,R,w,t1,t2,dk; |
| int32_t k,ix,i,j; |
| |
| GET_FLOAT_WORD(ix,x); |
| |
| k=0; |
| if (ix < 0x00800000) { /* x < 2**-126 */ |
| if ((ix&0x7fffffff)==0) |
| return -two25/zero; /* log(+-0)=-inf */ |
| if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ |
| k -= 25; x *= two25; /* subnormal number, scale up x */ |
| GET_FLOAT_WORD(ix,x); |
| } |
| if (ix >= 0x7f800000) return x+x; |
| k += (ix>>23)-127; |
| ix &= 0x007fffff; |
| i = (ix+(0x95f64<<3))&0x800000; |
| SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ |
| k += (i>>23); |
| f = x-(float)1.0; |
| if((0x007fffff&(0x8000+ix))<0xc000) { /* -2**-9 <= f < 2**-9 */ |
| if(f==zero) { |
| if(k==0) { |
| return zero; |
| } else { |
| dk=(float)k; |
| return dk*ln2_hi+dk*ln2_lo; |
| } |
| } |
| R = f*f*((float)0.5-(float)0.33333333333333333*f); |
| if(k==0) return f-R; else {dk=(float)k; |
| return dk*ln2_hi-((R-dk*ln2_lo)-f);} |
| } |
| s = f/((float)2.0+f); |
| dk = (float)k; |
| z = s*s; |
| i = ix-(0x6147a<<3); |
| w = z*z; |
| j = (0x6b851<<3)-ix; |
| t1= w*(Lg2+w*Lg4); |
| t2= z*(Lg1+w*Lg3); |
| i |= j; |
| R = t2+t1; |
| if(i>0) { |
| hfsq=(float)0.5*f*f; |
| if(k==0) return f-(hfsq-s*(hfsq+R)); else |
| return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); |
| } else { |
| if(k==0) return f-s*(f-R); else |
| return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); |
| } |
| } |
